An econometric property of the g-index     

L. Egghe 《Information processing & management》2009

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The thermal conductivity of the Earth's core and implications for its thermal and compositional evolution     

Kenji Ohta  Kei Hirose 《国家科学评论(英文版)》2021,8(4)

Determining the thermal conductivity of iron alloys at high pressures and temperatures are essential for understanding the thermal history and dynamics of the Earth''s metallic cores. The authors summarize relevant high-pressure experiments using a diamond-anvil cell and discuss implications of high core conductivity for its thermal and compositional evolution.

The thermal conductivity of iron alloys is a key to understanding the mechanism of convection in the Earth''s liquid core and its thermal history. The Earth''s magnetic field is formed by a dynamo action that requires convection in the liquid core. Present-day outer core convection can be driven by the buoyancy of light-element-enriched liquid that is released upon inner core solidification in addition to thermal buoyancy associated with secular cooling. In contrast, before the birth of the inner core, the core heat loss must be more than the heat conducted down the isentropic gradient in order to drive convection by thermal buoyancy alone, which can be a tight constraint upon the core thermal evolution.Recent mineral physics studies throw the traditional value of the Earth''s core thermal conductivity into doubt (Fig. ​(Fig.1).1). Conventionally the thermal conductivity of the outer core had been considered to be ∼30 W m⁻¹ K⁻¹, an estimate based on shock experiments and simple physical models including the Wiedemann-Franz law: κ_el = LTρ⁻¹, where κ_el, L, T and ρ are electronic thermal conductivity, Lorenz number, temperature and electrical resistivity, respectively [1]. Such relatively low core conductivity indicates that liquid core convection could have been driven thermally even with relatively slow cooling rate. However, in 2012–2013, our conventional view was challenged by both computational and experimental studies showing much higher core conductivity [2–4].Open in a separate windowFigure 1.(a) Electrical resistivity and (b) thermal conductivity values at the top of the Earth''s core in the literature [1,2,4–7,9,16]. Filled symbols were calculated on the basis of the Wiedemann-Franz law with ideal Lorenz number (L₀ = 2.44 × 10⁻⁸ W Ω K⁻²). Gray bands indicate (a) the range of saturation resistivity [9] and (b) thermal conductivity computed from the saturation resistivity and the Wiedemann-Franz law.Since then, experimental determinations of the thermal conductivity of iron and alloys have been controversial (Fig. ​(Fig.1).1). Ohta et al. [5] measured the electrical resistivity of iron under core conditions in a laser-heated diamond-anvil cell (DAC). The results demonstrate relatively high thermal conductivity of ∼90 W m⁻¹ K⁻¹ for liquid Fe-Ni-Si alloy based on their measured resistivity for pure iron, Matthissen''s rule and Wiedemann-Franz law, which is compatible with ab initio simulations [2,4]. On the other hand, flash laser-heating and fast thermal radiation detection experiments demonstrated the low core conductivity of 20–35 W m⁻¹ K⁻¹ based on finite element method simulations [6,7], in accordance with the traditional estimate [1]. Since transport properties that describe non-equilibrium phenomena are difficult to measure, the fact that determinations of the iron conductivity under core conditions have become viable these days is a remarkable success in mineral physics. Nevertheless, the discrepancy in core conductivity makes a big difference in the expected age of the inner core, mechanism of liquid core convection and thermal history [3].Despite a number of subsequent studies based on a variety of different techniques, we still see a dichotomy of proposed core conductivity values (Fig. ​(Fig.1).1). The ‘saturation’ resistivity, which is derived from the fact that the mean free path of electron–phonon interaction cannot be longer than the interatomic distance, gives the lower bound for conductivity. Such saturation resistivity lies between two clusters of reported high and low resistivity values. While the resistivity saturation is important in highly resistive transition metals and their alloys [3,8] (Fig. ​(Fig.2),2), the conventional estimate [1] did not include the effect of saturation in their models, which resulted in much higher resistivity than the saturation value and hence low core conductivity. The core electrical resistivity measured by recent DAC experiments [3,5,9] shows resistivity saturation (Fig. ​(Fig.2),2), demonstrating the high core conductivity as far as the Wiedemann-Franz law holds with ideal Lorenz number (Fig. ​(Fig.1).1). Additionally, since temperature has a large effect on resistivity, temperature gradient in a laser-heated sample is an issue. An internally-resistance-heated DAC provides homogenous and stable sample heating and is thus a promising technique for conductivity measurements at high pressure and temperature (P–T) [9]. The validity of the Wiedemann-Franz law under extreme conditions has also been an issue. Simultaneous measurements of the electrical resistivity and the thermal conductivity of iron alloy under core high P–T conditions will provide decisive evidence for it.Open in a separate windowFigure 2.Temperature response of the electrical resistivity of (a) fcc iron estimated at 1 bar [8] (blue curve) and (b) hcp iron at 115 GPa [5]. Red curve and black line with gray uncertainty band indicate the predicted resistivity based on the Bloch-Grüneisen model with and without the resistivity saturation, respectively.As introduced above, the most recent high P–T measurements for Fe containing 2, 4, 6.5 wt.% Si using an internally-resistance-heated DAC have demonstrated that the thermal conductivity of Fe-12.7 wt.% (22.5 at.%) Si is ∼88 W m⁻¹ K⁻¹ at core-mantle boundary (CMB) conditions when the effects of resistivity saturation, melting and crystallographic anisotropy at measurements are taken into account [9] (Fig. ​(Fig.1).1). Thermal conductivity of Fe-10 at.% Ni-22.5 at.% Si alloy, a possible outer core composition, could be ∼79 W m⁻¹ K⁻¹ considering the impurity effect of Ni [10]. Si exhibits the largest ‘impurity resistivity’, indicating that the 79 W m⁻¹ K⁻¹ is the lower bound for the thermal conductivity of the Earth''s liquid core. The core thermal evolution models by Labrosse [11] demonstrated that if liquid core convection has been driven by thermal buoyancy with the core thermal conductivity of 79 W m⁻¹ K⁻¹ at the CMB and no radiogenic heating in the core, the CMB temperature is calculated to be ∼5500 K at 3.2 Ga and ∼4800 K at 2.0 Ga. Such high CMB temperature suggests that the whole mantle was fully molten until 2.0–3.2 Ga. It is not consistent with geological records, calling for a different mechanism of core convection.Chemical buoyancy may be an alternate means of driving convection in the core from the early history of the Earth. It has been proposed that the compositional buoyancy in the core could arise from the exsolution of MgO, SiO₂ or both [12–14]. Recent core formation models based on the core-mantle distributions of siderophile elements suggest that core metals segregated from silicate at high temperatures, typically at 3000–4000 K and possibly higher [13,15], which enhances the incorporation of lithophile elements including Si and O, and possibly Mg into metals. It is suggested that the (Si, O)-rich liquid core may have become saturated with SiO₂ upon secular cooling [14]. Indeed, the original core compositions proposed in recent core formation models include Si and O beyond the saturation limit at CMB conditions [15], i.e. 136 GPa and 4000 K, leading to SiO₂ crystallization [13]. The rate of SiO₂ crystallization required to sustain geodynamo is as low as 1 wt.% per 10⁹ years, which corresponds to a cooling rate of 100–200 K Gyr⁻¹ [14]. The most recent model of the core compositional evolution by Helffrich et al. [13] showed that MgO saturation follows SiO₂ saturation only when >1.7 wt.% Mg in the core. If this is the case, in addition to solid SiO₂, (Mg, Fe)-silicate melts exsolve from the core and transfer core-hosted elements such as Mo, W and Pt to the mantle. The core-derived silicate melts may have evolved toward FeO-rich compositions and now represent the ultra-low velocity zones above the CMB.  相似文献   

Separation of DNA by length in rotational flow: Lattice-Boltzmann-based simulations     

Faihan Alfahani  Michael Antonelli  Jennifer Kreft Pearce 《Biomicrofluidics》2015,9(4)

We use a lattice-Boltzmann based Brownian dynamics simulation to investigate the separation of different lengths of DNA through the combination of a trapping force and the microflow created by counter-rotating vortices. We can separate most long DNA molecules from shorter chains that have lengths differing by as little as 30%. The sensitivity of this technique is determined by the flow rate, size of the trapping region, and the trapping strength. We expect that this technique can be used in microfluidic devices to separate long DNA fragments that result from techniques such as restriction enzyme digests of genomic DNA.The development of novel methods for manipulating biopolymers such as DNA is required for the continued advancement of microfluidic devices. Techniques such as restriction enzyme digests for genomic sequencing rely on the detection of DNA that differ in length by sometimes thousands of base pairs.¹ Methods that separate DNA strands with resolutions on the order of kilobase pairs are required to analyze the products of this technique. To gain an insight into possible techniques to separate polymers, it can be helpful to review the methods to separate particles in microfluidic devices. Experimental work has shown how hydrodynamic mechanisms can lead to separation of particles based on size and deformability.² Eddies, microvortices, and hydrodynamic tweezers have been used to trap and sort particles. The mechanism of the trapping and sorting arises from the differences between interactions of the particles with the fluid.^2–8 In particular, counter-rotating vortices have been used to sort particles and manipulate biopolymers. They have been used to deposit DNA precisely across electrodes⁹ and trap DNA.^10,11 Vortex flow may therefore be a good basis for a technique for sorting DNA by length.Streaming flow has been used in experiments to separate colloids of different size.^3,4 Particles are passed through a channel with a flow field driven by oscillating bubbles and pressure. The flow field becomes a combination of closed and open streamlines. The vortex flow is controlled by the accoustic driving of the bubbles while pressure controls the net flow of the fluid. Larger particles are trapped in the closed vortex flow created by the bubbles, while smaller particles can escape the neighborhood of a bubble in the open streamlines. This leads to efficient separation of particles with size differences as small as 1 μm.Previous work on DNA has shown that counter-rotating vortices can be used to trap DNA dynamically. Long strands of DNA have been observed to stretch between the centers of two counter-rotating vortices. The polymer stays trapped in this state for significant amounts of time.¹² In a different experiment, the vortices were used to thermally cycle the polymer and allow replication via the polymerase chain reaction (PCR). The DNA is also trapped against one wall by a thermophoretic force in these experiments.¹⁰ The strength of the trap is controlled by the gradient in temperature created by a focused infrared laser beam.Trapping DNA at one wall by counter-rotating vortices has also been explored in simulation and found to depend on the Peclet number, Pe = u_maxL/D_m, where u_max is the maximum speed of the vortex, L is the box size, and D_m is the diffusion coefficient of one bead in the polymer chain.¹¹ The trapping rate of the DNA was shown to depend on the competition between the flow compressing the DNA into the trap region and the diffusion of the DNA out of the trap. For the work presented here, Pe ≅ 2000, similar to the previous work done with the same simulation.We extend the previous work to investigate if counter-rotating vortices can be used to separate DNA of different lengths. We use the same type of simulation outlined in Refs. ¹¹ and ^13–17, based on the lattice-Boltzmann method. The simulation method has successfully modeled systems as diverse as thermophoresis of DNA,¹⁴ migration of DNA in a microchannel,¹⁶ and translocation of DNA through a micropore.^17,18 Using this method, the fluid is broken into a lattice with size, ΔL, chosen to be 0.5 μm, and is coupled to a worm-like chain model with Brownian dynamics for the polymer.^19,20 The fluid velocity distribution function, n_i(r, t), describes the fraction of fluid particles with a discretized velocity, c_i, at each lattice site.^21–24 A discrete velocity scheme with nineteen different velocities in three dimensions is used. The velocity distributions will evolve according to ni(r+ciΔτ,t+Δτ)=ni(r,t)+Lij[nj(r,t)−njeq(r,t)],(1)where L is a collision operator such that the fluid relaxes to the equilibrium distribution, nieq given by a second-order expansion of the Maxwell-Boltzmann distribution nieq=ρaci[1+(ci·u)/cs2+uu:(cici−cs2I)/(2cs4)],(2)where cs=1/3ΔLΔτ is the speed of sound. Δτ is the time step for the fluid in the simulation, Δτ = 8.8 × 10⁻⁵. The coefficients a^c_i are determined by satisfying a local isotropy condition ∑iaciciαciβciγciδ=cs4(δαβδγδ+δαγδbetaγ+δαδδβγ).(3)To simplify computation, the velocity distributions are transformed into moment space. The density ρ, momentum density j, and momentum flux density Π are some of the hydrodynamic moments of n_i(r, t). The equilibrium conditions for these three moments are given by ρ=∑nieq,(4) j=∑ci·nieq,(5) Π=∑nieq·cici.(6)L has eigenvalues τ0−1,τ1−1,…,τ18−1, which are the characteristic relaxation times of the moments. The Bhatanagar-Gross-Krook model is used to determine L:²⁵ the non-conserved moments have a single relaxation time, τ_s = 1.0. The conserved moments are density and momentum; for these, τ⁻¹= 0. Fluctuations are added to the fluid stress as in the method of Ladd.²⁴ We have also compared simulations with lattice sizes of 1 μm and 0.25 μm and found no significant differences in the results.The DNA used in the simulation is represented by a worm-like chain model parameterized to capture the dynamics of YOYO-stained λ DNA in bulk solution at room temperature.^15,16,26 Long, flexible DNA is modeled since techniques to separate long DNA molecules with kilobase pair resolution are necessary to complete techniques such as genomic level sequencing using restriction enzyme digests.¹ In addition, such DNA is often used in experiment. Its properties are similar to unstained DNA or DNA stained by other methods.²⁷ Each molecule is represented by N_b beads and N_b − 1 springs. A chain composed of N_b − 1 springs will have a contour length of (N_b − 1) × 2.1 μm. The forces acting on each monomer include: an excluded volume force, a non-linear spring force, the viscous drag force, a random force that produces Brownian motion, a repulsive force from the container walls, and an attractive trapping force only at one wall as shown in Fig. ​Fig.11.¹³ The excluded volume interaction between beads i and j located at r_i and r_j is modeled using the following potential: Uijev=12kBTνNks2(34πSs2)exp(−3|ri−rj|24Ss2),(7)where ν=σk3 is the excluded volume parameter with σ_k = 0.105 μm, the length of one Kuhn segment, N_ks = 19.8 is the number of Kuhn segments per spring, and Ss2=Nks/6)σk2 is the characteristic size of the bead. This excluded volume potential reproduces self avoiding walk statistics. The non-linear spring force is based on force-extension curves from experiments and is given by fijS=kBT2σk[(1−|rj−ri|Nksσk)−2+4|rj−ri|nKσk−1]rj−ri|rj−ri|,(8)which applies when N_ks ≫ 1.Open in a separate windowFIG. 1.Simulation set-up. Arrows indicate direction of fluid flow. The region where the trapping force is active is shaded, and its width (X_stick) is shown. The region used to determine the trapping rate is indicated by the area labeled trap region. Figure is not to scale, the trap region and X_stick are smaller than shown.The beads are modeled as freely draining but subject to a drag force given by F_f = ?6πηa(u_p ? u_f).(9)The beads are also subjected to a random forcing term that is drawn from a Gaussian distribution with zero mean and a variance σ_v = 2k_BTζΔt.(10)The random force reproduces Brownian motion. To conserve total momentum, the momentum change imparted to the beads through their interactions with the fluid is balanced by a momentum change in the fluid. The momentum change is distributed to the three closest fluid lattice sites using a linear interpolation scheme based on the proximity of the lattice site to the polymer beads. Through this momentum transfer, hydrodynamic interactions between the beads occur.The beads are repelled from the walls with a force of magnitude Fwall=250kBTσk3(xbead−xwall)2, xbead>(xwall−1),(11)where the repulsion range is 1ΔL. Each monomer will also be attracted to the top wall by a force with magnitude Fstick=KstickkBTσk3(xbead−xwall+10)2, xbead>(xwall−Xstick)(12)and range X_stick (see Fig. ​Fig.1).1). The sticking force is turned off every one out of one hundred time steps of the polymer (1% of the simulation time steps). We vary both X_stick and K_stick to achieve separation of the polymers.In previous experiments, DNA has been trapped against one wall by using thermophoresis,¹⁰ dielectrophoresis,²⁸ and nanoplasmonic tweezers.²⁹ In the case of thermophoresis, the trap strength (K_stick) can be controlled by tuning the intensity of the temperature gradient and the trap extension (X_stick) can be controlled through the area over which the gradient extends. Both of these are set through focusing of the laser used to produce local heating. Similarly, the trap parameters can be controlled when using plasmonic tweezers by controlling the laser beam exciting the nanoplasmonic structures. In dielectrophoresis, the DNA is trapped by an AC electric field and can be controlled by tuning the frequency and amplitude of the field.In this work, the number of polymers, N_p, is 10 unless otherwise noted, and the container size is 25 ΔL × 50 ΔL × 2 ΔL. The time step for the fluid is Δτ = 8.8 × 10⁻⁵ s, and for the polymer is Δt = 3.7 × 10⁻⁶ s. The total simulation time is over 100 chain relaxation times, allowing sufficient independent samples to perform statistical analysis.Two counter-rotating vortices, shown in 1, are produced by introducing external forces to the fluid bound by walls in the x-direction and periodic in the y and z. Two forces of equal magnitude push on the fluid in the upper x region (12ΔL < x < 25ΔL): one in the +y-direction along y = 10ΔL, and one in the –y-direction along y = 40ΔL. Such counter-rotating vortices can be produced in microfluidic channels using acoustically driven bubbles,^3,4,30 local heating,¹⁰ or plasmonic nanostructures.⁵ The flow speed is controlled by very different external mechanisms in each case. We therefore choose a simple model to produce fluid flow that is not specific to one mechanism.The simulations are started using random initial conditions, and therefore, both lengths of polymer are dispersed throughout the channel. Within a few minutes, the steady state configurations pictured in Figs. ​Figs.22 and ​and33 are reached. We define the steady state as when the number of polymer chains in the trap changes by less than one chain (10 beads) per 1000 polymer time steps. Intermittently, some polymers may still escape and re-enter the trap even in the steady state. Three final configurations are possible: Both the lengths of DNA have become trapped, both lengths continue to rotate freely, or the shorter strand has become trapped while the longer rotates freely. Two of these states leave the polymers mixed; in the third, the strands have separated by size.Open in a separate windowFIG. 2.Snapshots at t = 0Δt (left) and t = 2500Δt (right) showing the separation of 15-bead strands (grey) from 10-bead strands (black) of DNA. For these simulations, K_stick = 55 and Y_stick = 0.7ΔL.Open in a separate windowFIG. 3.Snapshots at t = 0Δt and t = 2500Δt showing the separation of 13-bead strands (grey) from 10-bead strands (black) of DNA. For these simulations, K_stick = 55 and Y_stick = 0.7ΔL as in Fig. ​Fig.2.2. Note that one long polymer is trapped, as well as all of the shorter polymers.By tuning the attractive wall force parameters and fluid flow, the separated steady state can be realized. We first set the flow parameters that allow the larger chains to rotate freely at the center of the vortices while the shorter chains rotate closer to the wall. The trap strength, K_stick, and extension, X_stick, are changed until the shorter polymers do not leave the trap. The same parameters were used to separate 10-bead chains from 15-bead and 13-bead chains.As shown in Fig. ​Fig.2,2, we have been able to separate shorter 10-bead chains from longer 15-bead chains. In the steady state, 97% of the rotating polymers were long polymers averaged over twenty simulations initialized with different random starting conditions. For three simulations, one small polymer would intermittently leave the trap region. In two of these simulations, one long polymer became stably trapped in the steady state. In another simulation, one 15-bead chain was intermittently trapped. On average, the trapped polymers were 5% 15-bead chains and 95% 10-bead chains. Again, 97% of the rotating polymers were 15-bead chains.Simulations conducted with 10-bead and 13-bead chains also showed significant separation of the two sizes as can be seen in Fig. ​Fig.3.3. In the steady state, 30% of the trapped polymers are 13-bead chains and 70% are 10-bead chains, averaged over twenty different random initial starting conditions and 1000 polymer time steps. Only 14.8% of the shorter polymers were not trapped, leading to 85.2% of the freely rotating chains being 13-bead chains. This is therefore a viable test to detect the presence of these longer chains.We have also separated 20-bead chains from 10-bead chains with all of the shorter chains trapped and all of the longer chains freely rotating in the steady-state. These results do not change for twenty different random initial starting conditions and 1000 polymer time steps. None of the longer polymers intermittently enter the trap region nor do any of the shorter polymers intermittently escape.The separation is achieved by tuning the trapping force and flow rate. Strong flows will push all the DNA molecules into the trap. The final state is mixed, with both short and long strands trapped. For flows that are too weak, the short molecules are not sufficiently compressed by the flow and therefore do not enter the trap region. The end state is mixed, with all polymers freely rotating. Separation is achieved when the flow rate is tuned so that the short strands are compressed against the channel wall while the long polymers rotate near the center of the vortices. The trap strength must then be set sufficiently high enough to prevent the short strands from being pulled by the hydrodynamic drag force out of the trap.The mechanism of the separation depends on the differences in the steady state configurations of the polymers and chances of a polymer escaping the trap. As shown in Fig. ​Fig.4,4, both longer and shorter chains are pulled into the trap region by the flow. However, the longer chains have a larger chance of a bead escaping into a region of the flow where the fluid velocity is sufficient to pull the entire strand out of the trap. As shown in Ref. ¹¹, the trapping rate depends on diffusion in a polymer depleted region near the trap, in agreement with classical theory which neglects bead-wall interactions. In addition, the theory depends on the single bead diffusion rate and does not take into account the elastic force holding the beads together. Diffusion becomes as significant as convection in the polymer depleted region leading to dependence on the Peclet number. Since longer polymers have more beads; they have more chances of a single bead diffusing through this layer into the region where convection is again more important. Thus, they are pulled out of the trap at a faster rate than the shorter chains.Open in a separate windowFIG. 4.N, number of beads in the trap region, versus time for 15-bead DNA strands (solid line) and 10-bead DNA strands (dashed line). Here, ΔT = 10000Δt. The simulation parameters are the same as in Fig. ​Fig.22.In addition, longer chains have a second trap resulting from the microflow. As shown in Ref. ¹², DNA in counter-rotating vortices can tumble at the center of one vortex or be stretched between the centers of the two vortices. We have observed both these conformations for the longer polymer strand. They are a stable trajectory for the longer polymer that remains outside of the trapping region. As seen in Fig. ​Fig.4,4, few monomers of the longer chains enter the trap region once the steady state has been reached. However, the shorter polymer rotates at a larger radius than the longer polymer as seen in Fig. ​Fig.5.5. The shorter polymers therefore are pushed back into the trap while the longer strands rotate stably outside the trapping region.Open in a separate windowFIG. 5.Trajectories of 15-bead DNA (grey) and 10-bead DNA (black). The position of each monomer is plotted for 100 consecutive time steps. Note that the longer polymers rotate in the center of the channel while the shorter polymers rotate at the edges. Simulation parameters are the same as in Fig. ​Fig.22.This mechanism is similar to the one proposed for the separation of colloids by size in Refs. ³ and ⁴. In that experimental work, the smaller colloidal particles rotated at larger radii. This allowed the smaller beads to be pushed out of the vicinity of the vortices by the streaming flow, while the larger beads continued to circle. However, in our simulations, we have the additional mechanism of separation based on the increased chance of a longer polymer escaping the trap region. This mechanism is important for maintaining the separation. Long polymers initially in the trap region or which diffuse into the trap would not be able to escape without it.We expect that this technique could be used to detect the sizes of DNA fragments on the order of thousands of base pairs. It relies on the flexibility of the molecule and its interaction with the flow. Common lab procedures such as restriction enzyme digests for DNA fingerprinting can produce these long fragments. Current techniques such as gel electrophoresis require significant time to separate the long strands that move more slowly through the matrix. This effect could therefore be a good candidate for developing a microfluidic analysis that is significantly faster than traditional procedures. Our separation occurs in minutes rather than in hours as for gel electrophoresis.As pointed out in Ref. ², hydrodynamic effects have been shown to be important for microfluidic devices for separation. We have demonstrated, in simulation, a novel hydrodynamic mechanism for separating polymers by length. We hope that these promising calculations will inspire experiments to verify these results.  相似文献   

Uniform exponential stability of periodic discrete switched linear system     

Akbar Zada  Bakht Zada  Jinde Cao  Tongxing Li 《Journal of The Franklin Institute》2017,354(14):6247-6257

Let {Π_τ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λ_τ(n), where $\tau :[0,1,2,?)\to \Omega$ is an arbitrary switching signal. We prove that the family {Π_τ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence $n?{\sum }_{k=0}^n{e}^{i\alpha k}{\Pi }_{\tau }(n,k)w\left(k\right):{\mathbb{Z}}_{+}\to \mathbb{R}$ is bounded.  相似文献   

Artificial helical microswimmers with mastigoneme-inspired appendages     

Soichiro Tottori  Bradley J. Nelson 《Biomicrofluidics》2013,7(6)

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Null controllability of some nonlinear degenerate 1D parabolic equations     

M.M. Cavalcanti  E. Fernández-Cara  A.L. Ferreira 《Journal of The Franklin Institute》2017,354(14):6405-6421

The main goal of the present paper is twofold: (i) to establish the well-posedness of a class of nonlinear degenerate parabolic equations and (ii) to investigate the related null controllability and decay rate properties. In a previous step, we consider an appropriate regularized system, where a small parameter α is involved. More precisely, the usual nonlinear term b(x)uu_x is replaced by b(x)zu_x, where $z={(\text{Id}.?{\alpha }^{2}A)}^{?1}u$ and A is a Poisson–Dirichlet operator. We investigate the behavior of the null controls and their associated states as α → 0.  相似文献   

Fixed point properties of the binomial function     

Douglas N. Green 《Journal of The Franklin Institute》1983,316(1):51-62

Fixed point properties of the binomial function

are developed. It is shown that for any 1 < L < N, T^L_Nhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability p_FAand an initial detection probability p_D, then T^L_N(p_FA) < p_FAand T^L_N(p_D) > p_Dif, and only if, p_FA < p? < p_D. When this condition is satisfied, as N → ∞, T^L_N(p_FA) → 0 and T^L_N(p_D → 1.  相似文献   

Fractional multiple birth-death processes with birth probabilities λ_i(Δt)+o((Δt))     

Guy Jumarie 《Journal of The Franklin Institute》2010,347(10):1797-1813

The usual model for (Poissonian) linear birth-death processes is extended to multiple birth-death processes with fractional birth probabilities in the form λ_i(Δt)^α+o((Δt)^α, 0<α<1. The probability generating function for the time dependent population size is provided by a fractional partial differential equation. The solution of the latter is obtained and comparison with the usual model is made. The probability of ultimate extinction is obtained. One considers the special case of fractional Poissonian processes with individual arrivals only, and then one outlines basic results for continuous processes defined by fractional Poissonian noises. The key is the Taylor’s series of fractional order f(x+h)=E_α(h^αD_x^α)f(x), where E_α(·) is the Mittag-Leffler function, and D_x^α is the modified Riemann-Liouville fractional derivative, as previously introduced by the author.  相似文献   

Editorial     

Patrick Cohendet  Frieder Meyer-Krahmer   《Research Policy》2001,30(9):1353

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Label-free density difference amplification-based cell sorting     

Jihwan Song  Minsun Song  Taewook Kang  Dongchoul Kim  Luke P. Lee 《Biomicrofluidics》2014,8(6)

The selective cell separation is a critical step in fundamental life sciences, translational medicine, biotechnology, and energy harvesting. Conventional cell separation methods are fluorescent activated cell sorting and magnetic-activated cell sorting based on fluorescent probes and magnetic particles on cell surfaces. Label-free cell separation methods such as Raman-activated cell sorting, electro-physiologically activated cell sorting, dielectric-activated cell sorting, or inertial microfluidic cell sorting are, however, limited when separating cells of the same kind or cells with similar sizes and dielectric properties, as well as similar electrophysiological phenotypes. Here we report a label-free density difference amplification-based cell sorting (dDACS) without using any external optical, magnetic, electrical forces, or fluidic activations. The conceptual microfluidic design consists of an inlet, hydraulic jump cavity, and multiple outlets. Incoming particles experience gravity, buoyancy, and drag forces in the separation chamber. The height and distance that each particle can reach in the chamber are different and depend on its density, thus allowing for the separation of particles into multiple outlets. The separation behavior of the particles, based on the ratio of the channel heights of the inlet and chamber and Reynolds number has been systematically studied. Numerical simulation reveals that the difference between the heights of only lighter particles with densities close to that of water increases with increasing the ratio of the channel heights, while decreasing Reynolds number can amplify the difference in the heights between the particles considered irrespective of their densities.Separating specific cells from heterogeneous or homogeneous mixtures has been considered as a key step in a wide variety of applications ranging from biomedicine to energy harvesting. For example, the separation and sorting of rare circulating tumor cells (CTCs) from whole blood has gained significant importance in the potential diagnosis and treatment of metastatic cancers.^1,2 Similarly, malaria detection relies on the collection of infected red blood cells (RBCs) from whole blood.^3,4 In addition, the selective separation of lipid-rich microalgae from homogeneous mixtures of microalgae is a promising technique in biomass conversion.⁵To date, conventional cell separation can be done by labelling cells with biomolecules to induce differences in physical properties. For instance, in a fluorescence-activated cell sorter (FACS), cells to be separated are labelled with antibodies or aptamers with fluorescent molecules, and then sorted by applying an electrical potential.^6,7 Similarly, magnetic-activated cell sorter (MACS) uses magnetic.^8,9 Alternatively, label-free cell separation methods have exploited inherent differences in the physical properties (e.g., size and dielectric properties) of different kinds of cells. For example, acoustophoresis forces particles larger than a desired size to move into the center of a fluidic channel by using ultrasonic standing waves.^10–12 Inertial microfluidics takes advantage of curved fluidic channels in order to amplify the size differences between particles.^13,14 Mass-dependent separation of particles based on gravity and hydrodynamic flow was also reported.¹⁵ Particles with different dielectric properties can also be sorted by dielectrophoresis which induces the movement of polarizable particles.^16–18The disadvantage of these methods, however, is that they require external forces and labels that may cause unexpected damage to biological cells.^19–21 More importantly, most methods are limited in separating cells of the same kind or cells with similar sizes and dielectric properties.Here we designed a novel, label-free density difference amplification-based cell sorting (dDACS) that allows the separation of particles with the same size and charge by exploiting subtle differences in density without the use of external forces. Figure 1(a) illustrates the proposed microfluidic model and its underlying mechanism. The conceptual microfluidic system consists of an inlet, a separation chamber (hydraulic jump cavity), and multiple outlets. Particles entering through the inlet experience gravity (F_G), buoyancy (F_B), and drag (F_D) forces in the separation chamber. The net force acting on the particles can be described as F = F_G + F_B + F_D.(1)As particles enter the separation chamber (i.e., hydraulic jump cavity), F_D acting on the particles changes its direction along the streamline. The particles experience additional forces in the y direction due to large tangential angle (Fig. 1(b)). For lighter particles, whose densities are close to that of the surrounding water, F_D becomes comparable to F_G (i.e., in the y direction), while the net force for heavier particles is less affected by this additional contribution of F_D due to a large F_G. As a result, the height (H) and distance (D) that each particle can travel are different depending on its density. The difference in the maximum height (ΔH_max) between two particles with different density (ρ_p1 and ρ_p2) can be further approximated as ΔHmax∝(vyp0)2(vyf−vyp0), (ρp1−ρp2) ,(2)where v_yp0 and v_yf represent the velocity of particle and fluid along the y direction at the entrance of hydraulic jump cavity, respectively.Open in a separate windowFIG. 1.Schematic illustration of label-free density difference amplification-based cell sorting (dDACS), which exploits differences in the densities (ρ₁ > ρ₂) of particles with similar diameters (d) and charge. (a) The conceptual microfluidic design consists of an inlet, a separation chamber (hydraulic jump cavity), and multiple outlets. Incoming particles experience gravity (F_G), buoyancy (F_B), and drag (F_D) forces in the separation chamber, and depending on their densities, the height (H) and distance (D) that each particle is able to reach will be different, allowing the particles to be separated into multiple outlets. (b) Possible microfluidic channel configurations for density-based separation: Uniform channel height (left), gradual channel expansion (middle), and hydraulic jump cavity with sudden channel expansion (right). The height difference between particles with different densities can be amplified by the sudden channel expansion compared to the other two cases due to the relatively large tangential angle, θ of F_D. (|θ₁|≪ |θ₂|) (see Fig. S1 in the supplementary material²²).In comparison with the other two cases (Fig. 1(b) uniform channel height and gradual channel expansion), the height difference between the particles with different densities can be amplified by the sudden channel expansion in the hydraulic jump cavity due to relatively large tangential angle (see supplementary material²²). Therefore, the particles can be separated through the multiple outlets, depending on their height and distance.In order to analyze the separation behavior of particles in the chamber according to differences in their densities, H and D are systematically investigated. The numerical simulations are performed using a commercial CFD software (CFX 14.0; ANSYS 14.0; ANSYS, Inc.). Particles with the same density may have different trajectories in the separation chamber depending on their inlet positions (Fig. 2(a)). Prior to this investigation, the maximum height (H_max) and distance (D_max) for each particle are compared by examining H and D of 100 identical particles at different inlet positions since the inlet position of particles could be controlled.²⁰ Fig. 2(b) shows H_max and D_max of particles with respect to density at a fixed Reynolds number (Re = 0.1). Note that Reynolds number is defined as Re = ρ_fv_fD_h/μ, where ρ_f, v_f, D_h, μ are density of fluid, velocity of the fluid, hydraulic diameter of a channel, and dynamic viscosity of the fluid, respectively. The hydraulic diameter in the Reynolds number is determined with the inlet channel. Particle densities in the range of 1.1 to 2.0 g/cm³ are chosen with the increase of 0.1 g/cm³. These values are quite reasonable in that the densities of many microorganisms such as microalgae are typically within this range and their densities can be varied by 0.2 g/m³ depending on their cellular context.²³ The lighter particles travel with a higher H_max, and longer D_max. With the separation chamber, the height difference between particles with densities of 1.1 and 1.2 g/cm³ can be amplified by about 10 times as compared to that in a channel without the chamber, judging from the position where the 1.1 g/cm³ particle reaches its H_max.Open in a separate windowFIG. 2.Microfluidic particle separation with respect to Reynolds number (Re). (a) Trajectories in the separation chamber of a hundred particles with the same density starting from inlet positions chosen arbitrarily in order to investigate the effect of the inlet positions on the maxima of the height (H_max) and distance (D_max) prior to further simulation. (b) Representative trajectories of particles having different densities from 1.1 to 2.0 g/cm³. (c) The maximum height (H_max) of each particle with respect to Re. (d) Representative maximum distance (D_max) of each particle at Re = 0.1. (Left) Streamline of fluid and representative trajectories of particles with densities of 1.1 and 2.0 g/cm³ in the separation chamber at Re = 0.1 (right).In Fig. 2(c), the values for H_max of particles with respect to Reynolds number (Re) are presented. Since in our study, the maximum height (H_max) and distance (D_max) for each particle were compared by examining H and D of 100 identical particles that are randomly distributed in the channel (throughout all figures), there is little variation in H_max and D_max between each simulation. However, the standard deviation between each simulation is quite small and can be negligible. The H_max values particles at Re = 0.5 with densities of 1.1 g/cm³ and 1.2 g/cm³ are 2.21 × 10³μm and 2.17 × 10³μm, respectively. The difference between H_max of different particles, ΔH_max, increases with decreasing Re. For example, ΔH_max between particles with densities of 1.1 and 2.0 g/cm³ becomes 0.26 × 10³μm at Re = 1.0, but increases to 1.38 × 10³μm as Re decreases to 0.1. As Re increases (velocity of fluid increases), the relative velocity in the y direction between the fluid and the particle increases resulting in increasing of F_D in the y direction since the velocity of particle in the y direction is very small at the entrance of the separation chamber. Thus, contribution of F_D becomes comparable to the net force in the y direction. As a result, most of the particles even in the case of heavier ones travel quite similarly with the streamline, and ΔH_max subsequently decreases. On the other hand, as Re decreases, the contribution of F_G becomes dominant due to the decrease of F_D in the y direction. Consequently, the particles start to cross downwards streamlines as the density of the particles increases and H_max gradually decreases. In addition, irrespective of their densities, ΔH_max of the particles increases with decreasing Re.Fig. 2(d) shows D_max with respect to the density of the particles (left). Different densities of particles show different trajectories due to the relative contribution of F_D to the net force in the y direction depending on the particle density (right). At Re = 0.1, D_max of particles with densities of 1.1 cm³ and 1.2 g/cm³ are 2.91 × 10⁴μm and 1.43 × 10⁴μm, respectively. As the density of a particle increases, its D_max dramatically decreases. The difference in D_max between particles with densities of 1.1 and 1.2 g/cm³ is 1.48 × 10⁴μm, and 0.0037 × 10⁴μm for particles with densities of 1.9 and 2.0 g/cm³. The effect of F_D is stronger compared to that of F_G on lighter particles. Thus, lighter particles travel quite similarly with the streamline and finally have a large D_max. On the other hand, heavier particles where effect of F_G is stronger compared to that of F_D cross downwards streamlines and finally have a small D_max.Next, in order to investigate the separation behavior of particles with respect to the geometry of the microfluidic device, the effect of the ratio of the height of the separation chamber (h_c) to the inlet (h_i) on H_max is investigated as shown in Fig. ​Fig.3.3. Interestingly, H_max of particles with density of 1.1 g/cm³ increases from 1.93 × 10³μm to 6.48 × 10³μm while that of particles with density of 1.9 g/cm³ slightly changes from 0.70 × 10³μm to 0.73 × 10³μm as h_c/h_i increases from 5 to 20.Open in a separate windowFIG. 3.Microfluidic particle separation with respect to the ratio of the height of the inlet (h_i) to the separation chamber (h_c).This result can be attributed to two effects: (1) the change in the streamline and (2) the relative contribution of drag force to the net force depending on the density. With increasing h_c/h_i, dramatic increase in H_max for lighter particles is because the streamline for the lighter ones experiences more vertical displacement in the separation chamber and the contribution of F_D to the net force acting on the lighter one is more significant (see Fig. S2 in the supplementary material²²).Based on this approach, we propose a microfluidic device for the selective separation of the lightest particle. Fig. 4(a) shows one unit (with three outlets) of the proposed microfluidic device that can be connected in series. The ratio of channel heights (h_c/h_i) is set to 20, and the particle densities are in the range of 1.1 ∼ 1.5 g/m³. Fig. 4(b) shows the representative separation behavior of the particles. A portion of the lightest particles (1.1 g/cm³) is selectively separated into the upper and middle outlets, while remaining light particles together with four other heavier particles with densities in the range of 1.2 to 1.5 g/cm³ leave through the lowest outlet. With a single operation of this unit, 40% of the lightest particles are recovered. In addition, the yield increases with increasing number of cycles (Fig. 4(c)).Open in a separate windowFIG. 4.(a) One unit of the proposed microfluidic device for the selective separation of the lightest particle based on the simulation results. Particles are separated into two outlets based on differences in both the height and distance travelled stemming from differences in density. (b) Representative separation behavior of particles observed in the device. (c) The yield of the lightest particle (1.1 g/cm³) with the proposed microfluidic device according to the number of cycles (i.e., this unit is assumed to be connected in series).In summary, we have demonstrated a label-free microfluidic system for the separation of particles according to subtle differences in their densities without external forces. Our microfluidic design consists simply of an inlet, a separation chamber, and multiple outlets. When entering the separation chamber, the particles experience an additional drag force in the y direction, amplifying the difference in both the height and the distance that the particles with different densities can travel within the chamber. At a fixed Reynolds number, with increasing particle density, H_max decreases monotonously, and D_max decreases dramatically. On the other hand, as Reynolds number increases, the difference between the heights of particles with different densities is attenuated. In addition, the simulation reveals that increasing the ratio of the channel heights increases the difference between the heights of particles only when their densities are close to that of the surrounding water. Based on this approach, a microfluidic device for the separation of the lightest particles has been proposed. We expect that our density-based separation design can be beneficial to the selective separation of specific microorganisms such as lipid-rich microalgae for energy harvesting application.  相似文献   

Polyphosphonium‐based bipolar membranes for rectification of ionic currents     

Erik O. Gabrielsson  Magnus Berggren 《Biomicrofluidics》2013,7(6)

Bipolar membranes (BMs) have interesting applications within the field of bioelectronics, as they may be used to create non-linear ionic components (e.g., ion diodes and transistors), thereby extending the functionality of, otherwise linear, electrophoretic drug delivery devices. However, BM based diodes suffer from a number of limitations, such as narrow voltage operation range and/or high hysteresis. In this work, we circumvent these problems by using a novel polyphosphonium-based BM, which is shown to exhibit improved diode characteristics. We believe that this new type of BM diode will be useful for creating complex addressable ionic circuits for delivery of charged biomolecules.Combined electronic and ionic conduction makes organic electronic materials well suited for bioelectronics applications as a technological mean of translating electronic addressing signals into delivery of chemicals and ions.¹ For complex regulation of functions in cells and tissues, a chemical circuit technology is necessary in order to generate complex and dynamic signal gradients with high spatiotemporal resolution. One approach to achieve a chemical circuit technology is to use bipolar membranes (BMs), which can be used to create the ionic equivalents of diodes^{2, 3, 4, 5} and transistors.^{6, 7, 8} A BM consists of a stack of a cation- and an anion-selective membrane, and functions similar to the semiconductor PN-junction, i.e., it offers ionic current rectification^{9, 10} (Figure ​(Figure1a).1a). The high fixed charge concentration in a BM configuration make them more suited in bioelectronic applications as compared to other non-linear ionic devices, such as diodes constructed from surface charged nanopores¹¹ or nanochannels,¹² as the latter devices typically suffers from reduced performance at elevated electrolyte concentration (i.e., at physiological conditions) due to reduced Debye screening length.¹³ However, a unique property of most BMs, as compared to the electronic PN-junction and other ionic diodes, is the electric field enhanced (EFE) water dissociation effect.^{10, 14} This occurs above a threshold reverse bias voltage, typically around −1 V, as the high electric field across the ion-depleted BM interface accelerates the forward reaction rate of the dissociation of water into H⁺ and OH⁻ ions. As these ions migrate out from the BM, there will be an increase in the reverse bias current. The EFE water dissociation is a very interesting effect and is commonly used in industrial electrodialysis applications,¹⁵ where highly efficient water dissociating BMs are being researched.¹⁶ Also, BMs have also been utilized to generate H⁺ and OH⁻ ions in lab-on-a-chip applications.^{2, 17} However, the EFE water dissociation effect diminishes the diode property of BMs when operated outside the ±1 V window, which is unwanted in, for instance, chemical circuits and addressing matrices for delivery of complex gradients of chemical species. The effect can be suppressed by incorporating a neutral electrolyte inside the BM,^{10, 18} for instance, poly(ethylene glycol) (PEG).^{2, 6, 7} However, as previously reported,² the PEG volume will introduce hysteresis when switching from forward to reverse bias, due to its ability to store large amounts of charges. This was circumvented by ensuring that only H⁺ and OH⁻ are present in the diode, which recombines into water within the PEG volume. Such diodes are well suited as integrated components in chemical circuits for pH-regulation, due to the in situ formed H⁺ and OH⁻, but are less attractive if, for instance, other ions, e.g., biomolecules, are to be processed or delivered in and from the circuit. Furthermore, a PEG electrolyte introduces additional patterning layers, making device downscaling more challenging. This is undesired when designing complex, miniaturized, and large-scale ionic circuits. Thus, there is an interest in BM diodes that intrinsically do not exhibit any EFE water dissociation, are easy to miniaturize, and that turn off at relatively high speeds. It has been suggested that tertiary amines in the BM interface are important for efficient EFE water dissociation,^{19, 20, 21} as they function as a weak base and can therefore catalyze dissociation of water by accepting a proton. For example, anion-selective membranes that have undergone complete methylation, converting all tertiary amines to quaternary amines, shows no EFE water dissociation,¹⁹ although this effect was not permanent, as the quaternization was reversed upon application of a current. Similar results were found for anion-selective membranes containing alkali-metal complexing crown ethers as fixed charges.²¹ Also, EFE water dissociation was not observed or reduced in BMs with poor ion selectivity, for example, in BMs with low fixed-charge concentration⁵ or with predominantly secondary and tertiary amines in the anion-selective membrane,²² as the increased co-ion transport reduces the electric field at the BM interface. However, due to decreased ion selectivity, these membranes show reduced rectification. In this work, we present a non-amine based BM diode that avoids EFE water dissociation, enables easy miniaturization, and provides fast turn-off speeds and high rectification.Open in a separate windowFigure 1(a) Ionic current rectification in a BM. In forward bias, mobile ions migrate towards the interface of the BM. The changing ion selectivity causes ion accumulation, resulting in high ion concentration and high conductivity. At high ion concentration, the selectivity of the membranes fails (Donnan exclusion failure), and ions start to pass the BM. In reverse bias, the mobile ions migrate away from the BM, eventually giving a zone with low ion concentration and low conductivity. Reverse bias can cause EFE water dissociation, producing H⁺ and OH^- ions. (b) Chemical structures of PSS, qPVBC, and PVBPPh₃. (c) The device used to characterize the BMs and the BM1A, BM2A, and BM1P designs. The BM interfaces are 50 × 50 μm.An anion-selective phosphonium-based polycation (poly(vinylbenzyl chloride) (PVBC) quaternized by triphenylphospine, PVBPPh₃) was synthesized and compared to the ammonium-based polycation (PVBC quaternized by dimethylbenzylamine, qPVBC) previously used in BM diodes² and transistors,^{7, 8} when included in BM diode structures together with polystyrenesulfonate (PSS) as the cation-selective material (Figure ​(Figure1b).1b). Three types of BM diodes were fabricated using standard photolithography patterning (Figure ​(Figure1c),1c), either with qPVBC (BM1A and BM2A) or PVBPPh₃ (BM1P) as polycation and either with (BM2A) or without PEG (BM1A and BM1P). Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) electrodes covered with aqueous electrolytes were used to convert electronic input signals into ionic currents through the BMs, according to the redox reaction PEDOT⁺:PSS⁻ + M⁺ + e⁻ ↔ PEDOT⁰ + M⁺:PSS⁻.The rectifying behavior of the diodes was evaluated using linear sweep voltammetry (Figure ​(Figure2).2). The BM1A diode exhibited an increase in the reverse bias current for voltages lower than −1 V, a typical signature of EFE water dissociation,^{10, 14} which decreased the current rectification at ±4 V to 6.14. No such deviation in the reverse bias current was observed for BM2A and BM1P, which showed rectification ratios of 751 and 196, respectively. In fact, for BM1P, no evident EFE water dissociation was observed even at −40 V (see inset of Figure ​Figure2).2). Thus, the PVBPPh₃ polycation allows BM diodes to operate at voltages beyond the ±1 V window with maintained high ion current rectification.Open in a separate windowFigure 2Linear sweep voltammetry from −4 to +4 V (25 mV/s) for the BM diodes. The inset shows BM1P scanning from −40 V to +4 V (250 mV/s).The dynamic performance of the diodes was tested by applying a square wave pulse from reverse bias to a forward bias voltage of 4 V with 5–90 s pulse duration (Figure ​(Figure3).3). To access the amount of charge injected and extracted during the forward bias and subsequent turn off, the current through the device was integrated. For BM2A, we observed that the fall time increased with the duration of the forward bias pulse. This hysteresis is due to the efficient storage of ions in the large PEG volume, with no ions crossing the BM due to Donnan exclusion failure.² As a result, during the initial period of the return to reverse bias, a large amount of charge needs to be extracted in order to deplete the BM. After a 90 s pulse, 90.6% of the injected charge during the forward bias was extracted before turn-off. This may be contrasted with BM1P, where the fall time is hardly affected by the pulse duration, and the extracted/injected ratio is only 15.4% for a 90 s pulse. For this type of BM, the interface quickly becomes saturated with ions during forward bias, leading to Donnan exclusion failure and transport of ions across the BM.⁴ Thus, less charge needs to be extracted to deplete the BM, allowing for faster fall times and significantly reduced hysteresis.Open in a separate windowFigure 3Switching characteristics (5, 10, 20, 30, 60, or 90 s pulse) and ion accumulation (at 90 s pulse) of the BM2A and BM1P diodes. BM1A showed similar characteristics as BM1P when switched at ±1V (see supplementary material).²⁴Since the neutral electrolyte is no longer required to obtain high ion current rectification over a wide potential range, the size of the BM can be miniaturized. This translates into higher component density when integrating the BM diode into ionic/chemical circuits. A miniaturized BM1P diode was constructed, where the interface of the BM was shrunk from 50 μm to 10 μm. The 10 μm device showed similar IV and switching characteristics as before (Figure ​(Figure4),4), but with higher ion current rectification ratio (over 800) and decreased rise/fall times (corresponding to 90%/–10% of forward bias steady state) from 10 s/12.5 s to 4 s/4 s. Since the overlap area is smaller, a probable reason for the faster switching times is the reduced amount of ions needed to saturate and deplete the BM interface. In comparison to our previous reported low hysteresis BM diode,² this miniaturized polyphosphonium-based devices shows the same rise and fall times but increased rectification ratio.Open in a separate windowFigure 4(a) Linear sweep voltammetry and (b) switching performance of a BM1P diode with narrow junction.In summary, by using polyphosphonium instead of polyammonium as the polycation in BM ion diodes the EFE water dissociation can be entirely suppressed over a large operational voltage window, supporting the theory that a weak base, such as a tertiary amine, is needed for efficient EFE water dissociation.^{17, 18} As no additional neutral layer at the BM interface is needed, ion diodes that operate outside the usual EFE water dissociation window of ±1 V can be constructed using less active layers, fewer processing steps and with relaxed alignment requirement as compared to polyammonium-based devices. This enables the fabrication of ion rectification devices with an active interface as low as 10 μm. Furthermore, the exclusion of a neutral layer improves the overall dynamic performance of the BM ion diode significantly, as there is less hysteresis due to ion accumulation. Previously, the hysteresis of BM ion diodes has been mitigated by designing the diode so that only H⁺ and OH⁻ enters the BM, which then recombines into water.² Such diodes also show high ion current rectification ratio and switching speed but are more complex to manufacture, and their application in organic bioelectronic systems is limited due to the H⁺/OH⁻ production. By instead using the polyphosphonium-based BM diode, reported here, we foresee ionic, complex, and miniaturized circuits that can include charged biomolecules as the signal carrier to regulate functions and the physiology in cell systems, such as in biomolecule and drug delivery applications, and also in lab-on-a-chip applications.  相似文献   

Mathematical models of information system use     

Robert M. Hayes  Harold Borko 《Information processing & management》1983,19(3):173-186

This report presents the results from a study of mathematical models relating to the usage of information systems. For each of four models, the papers developed during the study provide three types of analyses: reviews of the literature relevant to the model, analytical studies, and tests of the models with data drawn from specific operational situations. (1) The Cobb-Douglas model: x₀ = ax₁^bx₂^(1?b).This classic production model, normally interpreted as applying to the relationship between production, labor, and capital, is applied to a number of information related contexts. These include specifically the performance of libraries, both public and academic, and the use of information resources by the nation's industry. The results confirm not only the utility of the Cobb-Douglas model in evaluation of the use of information resources, but demonstrate the extent to which those resources currently are being used at significantly less than optimum levels. (2) Mixture of Poissons: where x₀ is the usage and (n_j,m_j),j = 0 to p, are the p + 1 components of the distribution. This model of heterogeneity is applied to the usage of library materials and of thesaurus terms. In each case, both the applicability and the analytical value of the model are demonstrated. (3) Inverse effects of distance: x = a e^?md if c(d) = rdx = ad^?m if c(d) = r log(d).These two models reflect different inverse effects of distance, the choice depending upon the cost of transportation. If the cost,c(d), is linear, the usage is inverse exponential; if logarithmic, the usage is inverse power. The literature that discusses the relationship between usage of facilities and the distance from them is reviewed. The models are tested with data from the usage of the Los Angeles Public Library, both Central Library and branches, based on a survey of 3662 users. (4) Weighted entropy: This generalization of the “entropy measure of information” is designed to accommodate the effects of “relevancy”, as measured by r(x), upon the performance of information retrieval systems. The relevant literature is reviewed and the application to retrieval systems is considered.  相似文献   

Chaotic behavior of discrete-time linear inclusion dynamical systems     

Xiongping Dai  Tingwen Huang  Yu Huang  Yi Luo  Gang Wang  Mingqing Xiao 《Journal of The Franklin Institute》2017,354(10):4126-4155

Given any finite family of real d-by-d nonsingular matrices $\{S_1,\dots ,S_l\},$ by extending the well-known Li–Yorke chaos of a deterministic nonlinear dynamical system to a discrete-time linear inclusion or hybrid or switched system: we study the chaotic dynamics of the state trajectory (x_n(x₀, σ))_{n ≥ 1} with initial state $x_0\in {\mathbb{R}}^d,$ governed by a switching law $\sigma :\mathbb{N}\to \{1,\dots ,l\}$. Two sufficient conditions are given so that for a “large” set of switching laws σ, there exhibits the scrambled dynamics as follows: for all $x_0,y_0\in {\mathbb{R}}^d,x_0\ne y_0,$This implies that there coexist positive, zero and negative Lyapunov exponents and that the trajectories (x_n(x₀, σ))_{n ≥ 1} are extremely sensitive to the initial states $x_0\in {\mathbb{R}}^d$. We also show that a periodically stable linear inclusion system, which may be product unbounded, does not exhibit any such chaotic behavior. An explicit simple example shows the discontinuity of Lyapunov exponents with respect to the switching laws.  相似文献   

Existence theorem of the quadruple (P, R, F, M): Precision,recall, fallout and miss     

L. Egghe 《Information processing & management》2007

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Accurate approximate solutions to oscillatory problems with perturbing singular damping     

C.C.H. Tang 《Journal of The Franklin Institute》1973,296(2):137-149

In this paper we attempt to obtain approximate solutions of improved accuracy for a class of differential equations of the form , where ε is a real parameter less than unity, ω_c is a positive real constant of order unity and μ(x) is a singular function of x in the region of interest. It does not appear to be possible to find a general analytic expression for the error estimate of the approximate solution. For the case μ(x) = x^?2, however, it is shown that the approximate solution is accurate to 0(ε²), as x → 0^? from negative values, by comparing it with the numerically integrated solution. For the same case, the approximate solution is orders of magnitude more accurate than Poincaré's first-order perturbation solution, which is accurate to $\text{0(}\text{ε}{}^2\text{ln}\text{|x|}\text{|x|}\text{)}$ as x → 0^?. This work arose in search of analytic solutions to a linearized form of the restricted three-body problem.  相似文献