Volume of Geodesic Balls in Finsler Manifolds of Hyperbolic Type

Let ?be a compact Finsler manifold of hyperbolic type, and ?be its universal Finslerian covering. In this paper we show that the growth function of the volume of geodesic balls of ?is of purely exponential type.

Numerical simulation of vortex-induced drag of elastic swimmer models

We present numerical simulations of simplified models for swimming organisms or robots, using chordwise flexible elastic plates. We focus on the tip vortices originating from three-dimensional effects due to the finite span of the plate. These effects play an important role when predicting the swimmer＇s cruising velocity, since they contribute significantly to the drag force. First we simulate swimmers with rectangular plates of different aspect ratios and compare the results with a recent experimental study. Then we consider plates with expanding and contracting shapes. We find the cruising velocity of the contracting swimmer to be higher than the rectangular one, which in turn is higher than the expanding one. We provide some evidence that this result is due to the tip vortices interacting differently with the swimmer.

Two upper bounds for the Erdos-Hooley Delta-function

For integer n≥1 and real u,let Δ(n,u):=|{d:d] n,e^(u)<d≤e^(u+1)}|.The Erdos-Hooley Deltafunction is then defined by Δ(n):=Max_(u∈R)Δ(n,u).We improve the current upper bounds for the average and normal orders of this arithmetic function.

On Bifurcation from Infinity and Multipoint Boundary Value Problems

We generalize a result on bifurcation from infinity of high order ordinary differential equations with multi-point boundary conditions. Our abstract setting represents a variant of Nonlinear Krein-Ruthman theorems. Furthermore, an analysis of this abstract setting raises an open question motivated by some misunderstanding and inconclusive proofs about the simplicity of principal eigenvalues in some articles in the literature.

A Remark on the Uniform Convergence of Some Sequences of Functions

We stress a basic criterion that shows in a simple way how a sequence of real-valued functions can converge uniformly when it is more or less evident that the sequence converges uniformly away from a finite number of points of the closure of its domain. For functions of a real variable, unlike in most classical textbooks our criterion avoids the search of extrema (by differential calculus) of their general term.

Bounded critical Fatou components are Jordan domains for polynomials

We prove that any bounded Fatou component of a polynomial of degree at least two, which is not(eventually) a Siegel disk, is a Jordan domain.

Bounded type Siegel disks of finite type maps with few singular values Dedicated to the Memory of Professor Lei Tan

Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.

High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms

In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms.This scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)paradigm.In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff.The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study.Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D.The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.

Development of Residual Distribution Schemes for the Discontinuous Galerkin Method:The Scalar Case with Linear Elements

In this paper,we reformulate the piecewise linear discontinuous Galerkin(DG)method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution(RD)schemes.This allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the schemes.Numerical results are shown to demonstrate the behavior of this approach.

A Stein deficit for the logarithmic Sobolev inequality

We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution.The techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.

On a fractional stochastic Hodgkin-Huxley model

The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for R× [0, 1]3. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided.

Degenerate Anisotropic Elliptic Problems and Magnetized Plasma Simulations

This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially adapted coordinate system.It is also designed to be equally accurate in the strongly and the mildly anisotropic cases.The method is applied to the Euler-Lorentz system,in the drift-fluid limit.This system provides a model for magnetized plasmas.

A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws

In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and computationally efficient Finite Volume(FV)scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions,respectively.The Multi-dimensional Optimal Order Detection(MOOD)method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes.It is an arbitrary high-order accurate Finite Volume scheme in space,using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other discontinuities.In the following work,the time discretization is performed with an elegant and efficient one-step ADER procedure.Doing so,we retain the good properties of the MOOD scheme,that is to say the optimal high-order of accuracy is reached on smooth solutions,while spurious oscillations near singularities are prevented.The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D,but it also increases the stability of the overall scheme.A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost,robustness,accuracy and efficiency.The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive(memory and/or CPU time),or because it is more accurate for a given grid resolution.A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws:the Euler equations of compressible gas dynamics,the classical equations of ideal magneto-Hydrodynamics(MHD)and finally the relativistic MHD equations(RMHD),which constitutes a particularly challenging nonlinear system of hyperbolic partial differential equation.All tests are run on genuinely unstructured grids composed of simplex elements.

Reconstructing f(T) modified gravity from ECHDE and ECNADE models

We investigate alternative candidates to dark energy(DE) that can explain the current state of the Universe in the framework of the generalized teleparallel theory of gravity f(T), where T denotes the torsion scalar. To achieve this, we carry out a series of reconstructions taking into account the ordinary and entropy-corrected versions of the holographic and new agegraphic DE models.These models are used as alternatives to DE in the literature in order to describe the current state of our Universe. It is remarked that the proposed models indicate behavior akin to phantom or quintessence models. Furthermore, we also generate the parameters of the equation of state associated with entropy-corrected models and we observe a phase transition between the quintessence state and phantom state as it is shown by the recent observational data. We also investigate the stability of these models and we create the {r-s} trajectories and compare with the ΛCDM limit. The behavior of certain physical parameters such as the speed of sound and the Statefinder diagnostic pair {r-s} is compatible with the current observational data.

High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows

Within the projection schemes for the incompressible Navier-Stokes equations(namely"pressure-correction"method),we consider the simplest method(of order one in time)which takes into account the pressure in both steps of the splitting scheme.For this scheme,we construct,analyze and implement a new high order compact spatial approximation on nonstaggered grids.This approach yields a fourth order accuracy in space with an optimal treatment of the boundary conditions(without error on the velocity)which could be extended to more general splitting.We prove the unconditional stability of the associated Cauchy problem via von Neumann analysis.Then we carry out a normal mode analysis so as to obtain more precise results about the behavior of the numerical solutions.Finally we present detailed numerical tests for the Stokes and the Navier-Stokes equations(including the driven cavity benchmark)to illustrate the theoretical results.

A Model of a Quantum Particle in a Quantum Environment: A Numerical Study

We define and investigate,via numerical analysis,a one dimensional toymodel of a cloud chamber.An energetic quantum particle,whose initial state is a superposition of two identical wave packets with opposite average momentum,interacts during its evolution and exchanges(small amounts of)energy with an array of localized spins.Triggered by the interaction with the environment,the initial superposition state turns into an incoherent sum of two states describing the following situation:or the particle is going to the left and a large number of spins on the left side changed their states,or the same is happening on the right side.This evolution is reminiscent of what happens in a cloud chamber where a quantum particle,emitted as a spherical wave by a radioactive source,marks its passage inside a supersaturated vapour-chamber in the form of a sequence of small liquid bubbles arranging themselves around a pssible classical trajectory of the particle.

Thin Layer Models for Electromagnetism

We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer,that makes possible to replace the thin layer by approximate conditions.We present the advantages and the drawbacks of several approximations together with numerical validations and simulations.The main motivation of this work concerns the computation of electromagnetic field in biological cells.The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane,which provides a specific behavior of the electromagnetic field at low frequencies.

Relaxation Schemes for the M1 Model with Space-Dependent Flux:Application to Radiotherapy Dose Calculation

Because of stability constraints,most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar.This problem emerges with the M_(1)system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities.Additionally,the flux term of the M_(1)system is non-linear,and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability.In this paper,we propose a numerical method that overcomes the stability constraint and preserves the realizability property.For this purpose,we relax the M_(1)system to obtain a linear flux term.Then we extend the stencil of the difference quotient to obtain stability.The scheme is applied to a radiotherapy dose calculation example.

Implied fractional hazard rates and default risk distributions

Default probability distributions are often defined in terms of their conditional default probability distribution,or their hazard rate.By their definition,they imply a unique probability density function.The applications of default probability distributions are varied,including the risk premium model used to price default bonds,reliability measurement models,insurance,etc.Fractional probability density functions(FPD),however,are not in general conventional probability density functions(Tapiero and Vallois,Physica A,.Stat.Mech.Appl.462:1161–1177,2016).As a result,a fractional FPD does not define a fractional hazard rate.However,a fractional hazard rate implies a unique and conventional FPD.For example,an exponential distribution fractional hazard rate implies a Weibull probability density function while,a fractional exponential probability distribution is not a conventional distribution and therefore does not define a fractional hazard rate.The purpose of this paper consists of defining fractional hazard rates implied fractional distributions and to highlight their usefulness to granular default risk distributions.Applications of such an approach are varied.For example,pricing default bonds,pricing complex insurance contracts,as well as complex network risks of various granularity,that have well defined and quantitative definitions of their hazard rates.

数学家讨论Snowden的惊人揭秘

Edward Snowden，前美国国家安全局（NSA）的签约雇员，在2013年上半年亲手把国家安全局的一批秘密文件交给了媒体记者．2013年6月媒体首次发表这些文件，披露了美国国家安全局和其他政府组织——如英国的政府通讯总部（GCHQ）——的大量秘密监视项目．这些文件的披露引起全世界的反响．它触及到一些大企业的损益底线，牵动着国际社会上层人物的关系，也影响到普通民众与日俱增的使用网络和手机的日常活动．