Effective transport properties for flashing ratchets using homogenization theory

We study effective transport properties of Brownian motor models of molecular motors. The effective drift and diffusivity can be calculated by solving cell problems, given explicitly by homogenization theory. We briefly describe how this approach is equivalent to theWang-Peskin-Elston (WPE) [3] numerical algorithm for calculating effective transport properties of flashing ratchets. For an on-off flashing ratchet we examine the optimization of the Peclet number as a function of the free parameters of the system. We also present a numerical method for solving the cell equations for a flashing ratchet with Gaussian multiplicative noise. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Momentum and heat transfer of the Falkner–Skan flow with algebraic decay: An analytical solution

In this paper, an analytical solution of the Falkner–Skan equation with mass transfer and wall movement is obtained for a special case, namely a velocity power index of ?1/3, with an algebraically decaying velocity profile. The solution is given in a closed form. Under different values of the mass transfer parameter, the wall can be fixed, moving in the same direction as the free stream, or opposite to the free stream (reversal flow near the wall). The thermal boundary layer solution is also presented with a closed form for a prescribed power-law wall temperature, which is expressed by the confluent hypergeometric function of the second kind. The temperature profiles and the wall temperature gradients are plotted. Interesting but complicated variation trends for certain combinations of controlling parameters are observed. Under certain parameter combinations, there exist singular points or poles for the wall temperature gradients, namely wall heat flux. With poles, the temperature profiles can cross the zero temperature line and become negative. From the results, it is also found empirically that under certain given values of the Prandtl number (Pr) and flow controlling parameter (b), the number of times for the temperature profiles crossing the zero line is the same as the number of poles when the wall temperature power index varies between zero and a given value n. The current result provides a new analytical solution for the Falkner–Skan equation with algebraic decay and greatly enriches the understanding of this important equation as well as the heat transfer characteristics for this flow.     

Intermittency and deterministic diffusion in chaotic ratchets

We consider the problem of deterministic transport of particles in an asymmetric periodic ratchet potential of the rocking type. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. We calculate the bifurcation diagram as a function of the amplitude of forcing and analyze in detail the crisis bifurcation that leads to current reversals. Near this bifurcation we obtain intermittency and anomalous deterministic diffusion.     

Une série génératrice des formes paraboliques de Maass

A certain periodic function F_μ,ν(z), an eigenfunction of the Laplacian on the upper half-plane with respect to z depending on some parameters μ, ν, is not automorphic, but the function μ → F_μ,ν(z)−F_μ,ν(−1/0 extends to a larger domain than the function F_μ,ν(z) itself. Consequently, at the poles of this latter function of μ, the coefficients of the polar parts provide non-analytic modular forms: all Maass cusp forms are finite linear combinations of forms obtained in this way, allowing the second parameter ν to vary     

The projected GSURE for automatic parameter tuning in iterative shrinkage methods

Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage methods for image deblurring and image zooming. Our work uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for determining the threshold value λ and the iterations number K in these algorithms. The proposed parameter selection is shown to handle any degradation operator, including ill-posed and even rectangular ones. This is achieved by using GSURE on the projected expected error. We further propose an efficient greedy parameter setting scheme, that tunes the parameter while iterating without impairing the resulting deblurring performance. Finally, we provide extensive comparisons to conventional methods for parameter selection, showing the superiority of the use of the projected GSURE.     

Cooperative concurrent asynchronous computation of the solution of symmetric linear systems

This paper extends the idea of Brezinski’s hybrid acceleration procedure, for the solution of a system of linear equations with a symmetric coefficient matrix of dimension n, to a new context called cooperative computation, involving m agents (m ? n), each one concurrently computing the solution of the whole system, using an iterative method. Cooperation occurs between the agents through the communication, periodic or probabilistic, of the estimate of each agent to one randomly chosen agent, thus characterizing the computation as concurrent and asynchronous. Every time one agent receives solution estimates from the others, it carries out a least squares computation, involving a small linear system of dimension m, in order to replace its current solution estimate by an affine combination of the received estimates, and the algorithm continues until a stopping criterion is met. In addition, an autocooperative algorithm, in which estimates are updated using affine combinations of current and past estimates, is also proposed. The proposed algorithms are shown to be efficient for certain matrices, specifically in relation to the popular Barzilai–Borwein algorithm, through numerical experiments.     

Multi-parameter Tikhonov regularization and model function approach to the damped Morozov principle for choosing regularization parameters

In this paper, we study the multi-parameter Tikhonov regularization method which adds multiple different penalties to exhibit multi-scale features of the solution. An optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters. Some theoretical results of the regularization solution about the dependence on regularization parameters are presented. Then, an a posteriori parameter choice, i.e., the damped Morozov discrepancy principle, is introduced to determine multiple regularization parameters. Five model functions, i.e., two hyperbolic model functions, a linear model function, an exponential model function and a logarithmic model function, are proposed to solve the damped Morozov discrepancy principle. Furthermore, four efficient model function algorithms are developed for finding reasonable multiple regularization parameters, and their convergence properties are also studied. Numerical results of several examples show that the damped discrepancy principle is competitive with the standard one, and the model function algorithms are efficient for choosing regularization parameters.     

Une méthode combinée d'éléments finis à deux grilles/bases réduites pour l'approximation des solutions d'une E.D.P. paramétrique

In the frame of mathematical optimization procedures or parameter fitting the same problem, modeled with partial differential equations depending on a parameter has to be solved many times for different sets of parameters. The reduced basis method may be successful in this frame and recent progress have permitted to make the computations reliable thanks to a posteriori estimators and to extend the method to non linear problems thanks to the “magic points” interpolation. However, in an industrial context, it may not be possible to use the code (for example of finite element type that allows for evaluating the elements of the reduced basis) to perform all the “off-line” computations necessary for an efficient performance of the reduced basis method. We propose here an alternating approach based on a coarse grid finite element the convergence of which is accelerated through the reduced basis. To cite this article: R. Chakir, Y. Maday, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Prevalence of locally parameter identifiable systems

The problem of local parameter identifiability of an input–output system is considered. A set lf of systems is studied for which the property of local parameter identifiability holds for almost all values of input signals and parameters in both topological and metric senses. Sufficient conditions are pointed out under which the set LI contains a prevalent subset. The proof is based on the prevalent transversality theorem proved by Kaloshin. Systems are considered that are characterized by a family of (structural) parameters a and a control block. It is shown that if the dimension of the set of parameters a is large enough (the structure of the system is rich enough), then, generically, a system f _a belongs to the class lf for a set of parameters a having full measure.     

Estimation of Parameters for the Multi-peaked AEF Current Functions

An examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is presented in the paper. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks is presented. This framework is used to find parameters for some common waveforms with a single peak, such as Standard IEC 62305 lightning currents. Illustration of fitting a p-peak AEF to recorded lightning current data is also presented.     

Struktur der Grenzschicht zwischen einem feldfreien Plasma und einem Magnetfeld im Vakuum

Self-consistent solutions of Vlasov's equations describing a plane boundary layer without shear are given. The currents within the layer are due to free and trapped electrons. The ion current is neglected sincem _e ?m _i . The free electrons and the ions are assumed Maxwellian at infinity. For the trapped electrons a one parameter family of distribution functions is assumed. Profiles are computed for potentials, fields, densities and currents for different numbers of trapped electrons. Numerical solutions are obtained by applying the method of finite elements to a variational formulation of the problem.     

Gradual degradation in the supercurrent state of a chaotic superconducting tunnel junction under time-varying perturbation

We report on the degradation of the zero-voltage supercurrent generated in a Josephson tunnel junction residing in an asymmetric potential of the ratchet type, and driven by a quasiperiodic external signal having incommensurable frequencies with irrational ratio ω₂/ω₁ equals to the Golden Mean. In the underdamped regime and via computing the current–voltage (I–V) characteristic curves, we demonstrate that the disappearance of the superconducting state can be correlated to chaotic behaviour, where dynamical phase fluctuations and symmetry breakings associated with the potential and modulating signal are substantially taking place.     

A multicriteria approach to the location of public facilities

We argue that practical problems involving the location of public facilities are really multicriteria problems, and ought to be modeled as much. The general criteria are those of cost and service, but there exist several distinct criteria in each of those two categories. For the first category, fixed investment cost, fixed operating cost, variable operating cost, total operating cost, and total discounted cost are all reasonable criteria to consider. In terms of service, both demand served and response time (or distance traveled) are appropriate criteria, either agglomerated or considered on the basis of the individual clients. In this paper we treat such multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points. We show that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution. In most other cases the efficient solutions can be found through parametric solution of a GAP with additional constraints of a type which can be incorporated into an existing algorithm for the GAP. Rather than attempting to find all efficient solutions, however, we advocate an interactive approach to the resolution of multicriteria location problems and elaborate on a specific interactive algorithm for multicriteria optimization which for the present model solves a finite sequence of GAP's or GAP-type problems. Finally, some similar aspects of private sector location problems are discussed.     

Parameter identification and optimization algorithm in microbial continuous culture

In this study, a novelty mathematical model is established to formulate the continuous culture of glycerol to 1,3-Propanediol (1,3-PD) by Klebsiella pneumoniae, in which the inhibition of 3-hydroxypropionaldehyde (3-HPA) to cells growth and activity of some enzymes (such as glycerol dehydratase (GDHt) and 1,3-PD oxidoreductase (PDOR)), and the passive diffusion and active transport of glycerol and 1,3-PD across cell membrane are all taken into consideration. Taking the mean relative error between the experimental data and calculated values as the performance index, a parameter identification model involving multiple nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results not only show that the established model can be used to describe the continuous fermentation reasonably, but also the improved PSO algorithm is valid.     

Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime

A mathematical model is presented for multiphysical transport of an optically-dense, electrically-conducting fluid along a permeable isothermal sphere embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The surface of the sphere is maintained at a constant temperature and concentration and is permeable, i.e. transpiration into and from the boundary layer regime is possible. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. Increasing porosity (ε) is found to elevate velocities, i.e. accelerate the flow but decrease temperatures, i.e. cool the boundary layer regime. Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.     

Relaxation analysis in linear vectorvalued maximization

As an analogy to the postoptimal sensitivity analysis in linear programming a theory of postefficient sensitivity analysis in linear vectorvalued maximization problems (LVMP), called relaxation analysis, is developed. Introducing parameters in the most coefficients of the given objective functions, the goal is to define an admissible region of the parameters such that the set E of all the efficient solutions of the initial LVMP does not change. Doing the same with the right hand side, the set of all admissible parameters is defined via an undirected graph which is generated by the initial LVMP.     

Complexity in Complex Analysis

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces.     

Chaotic transport of a matter-wave soliton in a biperiodically driven optical superlattice

Under the effective particle approximation, we study the temporal ratchet effect for chaotic transport of a matter-wave soliton consisting of an attractive Bose–Einstein condensate held in a quasi-one-dimensional symmetric optical superlattice with biperiodic driving. It is known that chaos can substitute for disorder in Anderson’s scenario [Wimberger S, Krug A, Buchleitner A. Phys Rev Lett 2002;89:263601] and only a higher level of disorder can induce Anderson localization for some special systems [Schwartz T, Bartal G, Fishman S, Segev M. Nature 2007;46:52], and a matter-wave soliton can transit to chaos with high or low probability in a high- or low-chaoticity region [Zhu Q, Hai W, Rong S. Phys Rev E 2009;80:016203]. Here we demonstrate that varying the driving phase to break the time reversal symmetry of the system can increase the size of the high-chaoticity region for low- and moderate-frequency regions. Consequently, the parameter region of the exponential spatial localization increases to the same size, and the low-chaoticity and delocalization region, which includes subregions of the ratchet effect and its inverse effect, correspondingly decreases. The positive dependence of the localization on the driving frequency is also revealed. The results indicate that a high-chaoticity region could replace higher disorder and assists in Anderson localization. From the results we suggest a method for controlling directed motion of a matter-wave soliton by adjusting the driving frequency and amplitude to strengthen or suppress, or even reverse, the temporal ratchet effect.     

Solution of the equivalence problem for the Painlevé IV equation

We solve the equivalence problem for the Painlevé IV equation, formulating the necessary and sufficient conditions in terms of the invariants of point transformations for an arbitrary second-order differential equation to be equivalent to the Painlevé IV equation. We separately consider three pairwise nonequivalent cases: both equation parameters are zero, a = b = 0; only one parameter is zero, b = 0; and the parameter b ?? 0. In all cases, we give an explicit point substitution transforming an equation satisfying the described test into the Painlevé IV equation and also give expressions for the equation parameters in terms of invariants.     

Potential transients for an electrochemical corrosion reaction under constant current conditions

Due to the electrochemical nature of almost all corrosion reactions, electrochemical methods are commonly used to measure the corrosion rate of a metal in the laboratory or in the field. In particular, steady state methods are the most widely used for corrosion rate measurements. Transient methods, which can be much more efficient, traditionally rely on an equivalent linear circuit representing the surface kinetics, with negligible mass transport effects. This has been reported to predict transients which are not observed experimentally in many practical situations. In this paper, we consider the galvanostatic method, wherein a constant current is applied across a corroding metal surface and the transient potential response is recorded. The resulting boundary value problems incorporating mixed kinetic and diffusion control involve highly nonlinear, coupled boundary conditions. We present numerical and approximate analytical solutions which can be incorporated into corrosion analysis routines in order to calculate corrosion parameters. The analytical expressions open the possibility of measuring corrosion parameters by merely fitting a class of elementary functions to experimental potential transients. This leads to a significant reduction in the number of computations required for the curve fitting, and hence increasing the overall efficiency of the measurement process compared to the conventional steady state methods.