finite volume modeling of poroelastic fluid wave propagation with mapped grids in this work we develop a high resolution mapped grid finite volume method code to model wave propagation in two dimensions in systems of multiple orthotropic poroelastic media and or fluids with curved interfaces between different media we use a unified formulation to simplify modeling of the various interface conditions open pores imperfect hydraulic contact or sealed pores that may exist between such media our numerical code is based on the clawpack framework but in order to obtain correct results at a material interface we use a modified transverse riemann solution scheme and at such interfaces are forced to drop the second order correction term typical of high resolution finite volume methods we verify our code against analytical solutions for reflection and transmission of waves at a material interface and for scattering of an acoustic wave train around an isotropic poroelastic cylinder for reflection and transmission at a flat interface we achieve second order convergence in the 1 no

on the extendability of projective surfaces and a genus bound for enriques fano threefolds we introduce a technique based on gaussian maps to study whether a surface can lie on a threefold as a very ample divisor with given normal bundle we give applications among which one to surfaces of general type and another to enriques surfaces in particular we prove the genus bound g 17 for enriquesfano threefolds moreover we find a new enriques fano threefold of genus 9 whose normalization has canonical but not terminal singularities and does not admit q smoothings

dispersive and dissipative behaviour of high order discontinuous galerkin finite element methods the dispersive and dissipative properties of hp version discontinuous galerkin finite element approximation are studied in three different limits for the small wave number limit hk 0 we show the discontinuous galerkin gives a higher order of accuracy than the standard galerkin procedure thereby confirming the conjectures of hu and atkins j comput phys 182 2 2002 516 if the mesh is fixed and the order p is increased it is shown that the dissipation and dispersion errors decay at a super exponential rate when the order p is much larger than hk finally if the order is chosen so that 2p 1 hk for some fixed constant 1 then it is shown that an exponential rate of decay is obtained

brill noether theory of curves on enriques surfaces i the positive cone and gonality we study the existence of linear series on curves lying on an enriques surface and general in their complete linear system using a method that works also below the bogomolov reider range we compute in all cases the gonality of such curves we also give a new result about the positive cone of line bundles on an enriques surface and we show how this relates to the gonality

a separation principle for the h2 control of continuous time infinite markov jump linear systems with partial observations abstract in this paper we devise a separation principle for the h 2 optimal control problem of continuous time markov jump linear systems with partial observations and the markov process taking values in an infinite countable set s we consider that only an output and the jump parameters are available to the controller it is desired to design a dynamic markov jump controller such that the closed loop system is stochastically stable and minimizes the h 2 norm of the system as in the case with no jumps we show that an optimal controller can be obtained from two sets of infinite coupled algebraic riccati equations one associated with the optimal control problem when the state variable is available and the other one associated with the optimal filtering problem an important feature of our approach not previously found in the literature is to introduce an adjoint operator of the continuous time markov jump linear system to derive our results

stability radii of systems with stochastic uncertainty and their optimization by output feedback we consider linear plants controlled by dynamic output feedback which are subjected to blockdiagonal stochastic parameter perturbations the stability radii of these systems are characterized and it is shown that for real data the real and the complex stability radii coincide a corresponding result does not hold in the deterministic case even for perturbations of single output feedback type in a second part of the paper we study the problem of optimizing the stability radius by dynamic linear output feedback necessary and sufficient conditions are derived for the existence of a compensator which achieves a suboptimal stability radius these conditions consist of a parametrized riccati equation a parametrized liapunov inequality a coupling inequality and a number of linear matrix inequalities one for each disturbance term the corresponding problem in the deterministic case the optimal mu synthesis problem is still unsolved

stability radii of linear systems with respect to stochastic perturbations abstract real and complex stability radii for stable linear systems with respect to structured stochastic multiperturbations are introduced and completely characterized

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

on stabilization of uncertain linear systems with jump parameters in this paper we study the problem of robust stabilizability of the class of uncertain linear systems with markovian jumping parameters under the assumption of complete access to the continuous state the stochastic stabilizability of the nominal system and the boundedness of the system s uncertainties sufficient conditions which guarantee the robust stability of the uncertain systems are presented which are in terms of a set of coupled algebraic riccati equations a numerical example is given to illustrate the potential of the proposed technique

a discontinuous galerkin method for wave propagation in orthotropic poroelastic media with memory terms abstract poroelastic materials play an important role in biomechanical and geophysical research in this paper we investigate wave propagation in orthotropic poroelastic media by studying the time domain poroelastic wave equations both the low frequency biot s lf biot equations and the biot johnson koplik dashen biot jkd model are considered in lf biot equations the dissipation terms are proportional to the relative velocity between the fluid and the solid by a constant contrast to this the dissipation terms in the biot jkd model are in the form of time convolution memory as a result of the frequency dependence of fluid solid interaction at the underlying microscopic scale in the frequency domain the dynamic tortuosity and permeability described by darcy s law are two crucial factors in this problem and highly linked to the viscous force in the biot model the key difficulty is to handle the viscous term when the pore fluid is viscous in the biot jkd model the convolution operator involves order 1 2 shifted fractional derivatives in the time domain which is challenging to discretize in this work a new method of the multipoint pade or rational approximation for stieltjes function is applied to approximate the jkd dynamic tortuosity and then an augmented system of biot jkd model is obtained where the kernel of the memory term is replaced by the finite auxiliary variables satisfying a local system of ordinary differential equations the runge kutta discontinuous galerkin rkdg method with the un splitting method is used to compute the numerical solution and numerical examples are presented to demonstrate the high order accuracy and stability of the method compared with the existing approaches for solving the biot jkd equations the augmented system presented here require neither the storage of solution history nor the computation of the flux of the auxiliary variables

lyapunov coupled equations for continuous time infinite markov jump linear systems this paper deals with lyapunov equations for continuous time markov jump linear systems mjls out of the bent which wends most of the literature on mjls we focus here on the case in which the markov chain has a countably infinite state space it is shown that the infinite mjls is stochastically stabilizable ss if and only if the associated countably infinite coupled lyapunov equations have a unique norm bounded strictly positive solution it is worth mentioning here that this result do not hold for mean square stabilizability mss since ss and mss are no longer equivalent in our set up see e g j baczynski optimal control for continuous time lq problems with infinite markov jump parameters ph d thesis federal university of rio de janeiro ufrj coppe 2000 to some extent a decomplexification technique and tools from operator theory in banach space and in particular from semigroup theory are the very technical underpinning of the paper

cell centered finite volume method for elastic deformation of heterogeneous media with full tensor properties abstract we propose a cell centered finite volume method for the heterogeneous anisotropic linear elasticity problem the internal traction vector is represented as a discrete flux on the interface this elastic flux is decomposed into a discrete two point flux approximation and a semi discrete transversal part we introduce an interpolation method in the presence of discontinuity in the full tensor material properties the scheme yields an accurate reconstruction of the gradient of the displacement in each cell the formulation is based on the assumption of linearity of the displacement and we enforce continuity of the internal traction vector and the displacement at the interface the treatment of the boundary conditions can be complicated in finite volume methods here we describe a general treatment of boundary conditions that does not entail the introduction of additional degrees of freedom the finite volume method is tested for a series of challenging elasticity problems

a new perspective on the robustness of markov jump linear systems this paper is concerned with the robust analysis and control of continuous time markov jump linear systems the centerpiece of the paper is an alternative to the small gain theorem which hinges on the robustification of a certain adjoint lyapunov operator by means of this technique it is proven that the small gain theorem of markov jump linear systems may sometimes be arbitrarily conservative even when nonlinear lipschitz disturbances are taken into account the adjoint approach on the other hand provides the maximal degree of robustness for this particular setup in addition we prove that the adjoint design of controllers is solved more efficiently than the design based on small gain analysis bearing these new facts in mind we derive an iterative algorithm for the design of robust controllers based on linear matrix inequalities by means of numerical examples regarding the robust control of an underactuated manipulator arm and of a simplified power systems model it is shown that the adjoint design methodology can be much more advantageous than its small gain counterpart

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

a new look at the robust control of discrete time markov jump linear systems abstractin this paper we make a foray in the role played by a set of four operators on the study of robust h2 and mixed h2 h control problems for discrete time markov jump linear systems these operators appear in the study of mean square stability for this class of systems by means of new linear matrix inequality lmi characterisations of controllers which include slack variables that to some extent separate the robustness and performance objectives we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of h2 performance since each operator provides a different degree of conservatism the results are unified in the form of an iterative lmi technique for designing robust h2 controllers whose convergence is attained in a finite number of steps the method yields a new way of computing mixed h2 h controllers whose conservatism decreases with iteration two numerical examples illustrate the applicability

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

low storage implicit explicit runge kutta schemes for the simulation of stiff high dimensional ode systems implicit explicit imex runge kutta rk schemes are effective for time marching ode systems with both stiff and nonstiff terms on the rhs such schemes implement an often a stable or better implicit rk scheme for the stiff part of the ode which is often linear and simultaneously a more convenient explicit rk scheme for the nonstiff part of the ode which is often nonlinear low storage rk schemes are especially effective for time marching high dimensional ode discretizations of pde systems on modern cache based computational hardware in which memory management is often the most significant computational bottleneck in this paper we develop and characterize eight new low storage implicit explicit rk schemes which have higher accuracy and better stability properties than the only low storage implicit explicit rk scheme available previously the venerable second order crank nicolson runge kutta wray cn rkw3 algorithm that has dominated the dns les literature for the last 25 years while requiring similar storage two three or four registers of length n and comparable floating point operations per timestep

on the robust stability stabilization and stability radii of continuous time infinite markov jump linear systems this paper addresses the robust stochastic stability and stabilization of continuous time markov jump linear systems mjls with the markov jump parameters taking values in a countably infinite set it is assumed that the state and input matrices are subjected to norm bounded uncertainty with a prespecified structure which encompasses the block diagonal setting we introduce new robust analysis and synthesis characterizations such that unlike previous approaches in the mjls literature the scaling parameters are treated as decision variables in linear matrix inequalities as a by product new contributions to the theory of stability radii of mjls are provided when restricted to the finite case we further introduce new adjoint linear matrix inequality lmi characterizations for each of the robust analysis and synthesis problems as well as for stability radii besides the interest in its own right the adjoint approach allows us to verify that in the general mjls case there is a gap between the complex stability radius and what can be assessed with scaled versions of the small gain theorem this suggests a fundamental limitation of the robustness against linear perturbations that the h infty control of mjls may provide some numerical examples which include the robust control of two interconnected oscillators illustrate the main results

projective degenerations of k3 surfaces gaussian maps and fano threefolds in this article we exhibit certain projective degenerations of smoothk3 surfaces of degree 2g 2 in g whose picard group is generated by the hyperplane class to a union of two rational normal scrolls and also to a union of planes as a consequence we prove that the general hyperplane section of suchk3 surfaces has a corank one gaussian map ifg 11 org 13 we also prove that the general such hyperplane section lies on a uniquek3 surface up to projectivities finally we present a new approach to the classification of prime fano threefolds of index one which does not rely on the existence of a line

robust finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

a discontinuous galerkin method for poroelastic wave propagation the two dimensional case abstract in this paper we consider a high order discontinuous galerkin dg method for modelling wave propagation in coupled poroelastic elastic media the upwind numerical flux is derived as an exact solution for the riemann problem including the poroelastic elastic interface attenuation mechanisms in both biot s low and high frequency regimes are considered the current implementation supports non uniform basis orders which can be used to control the numerical accuracy element by element in the numerical examples we study the convergence properties of the proposed dg scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions

on the picard group of enriques surfaces an enriques surface over an algebraically closed field k of characteristic 4 2 is a non singular projective surface s with h s d s h2 s cs 0 and 2ks 0 the unramitied double cover defined by ks is a k3 surface r a non singular projective surface with hi r d r 0 kr 0 illusie has shown i that the group of divisors modulo numerical equivalence is isomorphic to the enriques lattice u e 8 1 where u and e s 1 denote respectively the unique even unimodular lattices of index of inertia 1 1 and 0 8 the purpose of this note is to use this isomorphism to study the picard group of s we prove the existence of certain configurations of irreducible curves of arithmetic genus 0 or 1 and deduce from them the existence of certain projective models for s and r for example we prove the following results

discontinuous galerkin methods for wave propagation in poroelastic media we have developed a new numerical method to solve the heterogeneous poroelastic wave equations in bounded three dimensional domains this method is a discontinuous galerkin method that achieves arbitrary high order accuracy on unstructured tetrahedral meshes for the low frequency range and the inviscid case by using biot s equations and darcy s dynamic laws we have built a scheme that can successfully model wave propagation in fluid saturated porous media when anisotropy of the pore structure is allowed zero inflow fluxes are used as absorbing boundary conditions a continuous arbitrary high order derivatives time integration is used for the high frequency inviscid case whereas a space time discontinuous scheme is applied for the low frequency case we conducted a numerical convergence test of the proposed methods we used a series of examples to quantify the quality of our numerical results comparing them to analytic solutions as well as numerical solutions obtained by other methodologies in partic

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

moduli of curves on enriques surfaces abstract we compute the number of moduli of all irreducible components of the moduli space of smooth curves on enriques surfaces in most cases the moduli maps to the moduli space of prym curves are generically injective or dominant exceptional behavior is related to existence of enriques fano threefolds and to curves with nodal prym canonical model

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

high resolution finite volume modeling of wave propagation in orthotropic poroelastic media poroelasticity theory models the dynamics of porous fluid saturated media it was pioneered by maurice biot in the 1930s through the 1960s and has applications in several fields including geophysics and modeling of in vivo bone a wide variety of methods have been used to model poroelasticity including finite difference finite element pseudospectral and discontinuous galerkin methods in this work we use a cartesian grid high resolution finite volume method to numerically solve biot s equations in the time domain for orthotropic materials with the stiff relaxation source term in the equations incorporated using operator splitting this class of finite volume method has several useful properties including the ability to use wave limiters to reduce numerical artifacts in the solution ease of incorporating material inhomogeneities low memory overhead and an explicit time stepping approach to the authors knowledge this is the first use of high resolution finite volume methods to model poroelastic

wave simulation in 2d heterogeneous transversely isotropic porous media with fractional attenuation a cartesian grid approach a time domain numerical modeling of transversely isotropic biot poroelastic waves is proposed in two dimensions the viscous dissipation occurring in the pores is described using the dynamic permeability model developed by johnson koplik dashen jkd some of the coefficients in the biot jkd model are proportional to the square root of the frequency in the time domain these coefficients introduce shifted fractional derivatives of order 1 2 involving a convolution product based on a diffusive representation the convolution kernel is replaced by a finite number of memory variables that satisfy local in time ordinary differential equations resulting in the biot da diffusive approximation model the properties of both the biot jkd and the biot da models are analyzed hyperbolicity decrease of energy dispersion to determine the coefficients of the diffusive approximation two approaches are analyzed gaussian quadratures and optimization methods in the frequency range of interest the nonlinear optimization is shown to be the better way of determination a splitting strategy is then applied to approximate numerically the biot da equations the propagative part is discretized using a fourth order ader scheme on a cartesian grid whereas the diffusive part is solved exactly an immersed interface method is implemented to take into account heterogeneous media on a cartesian grid and to discretize the jump conditions at interfaces numerical experiments are presented comparisons with analytical solutions show the efficiency and the accuracy of the approach and some numerical experiments are performed to investigate wave phenomena in complex media such as multiple scattering across a set of random scatterers

classification of varieties with canonical curve section via gaussian maps on canonical curves the purpose of this article is to develop further a method to classify varieties x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i having canonical curve section using gaussian map computations in a previous article we applied these techniques to classify prime fano threefolds that is fano threefolds whose picard group is generated by the hyperplane bundle in this article we extend this method and classify fano threefolds of higher index and mukai varieties i e varieties of dimension four or more with canonical curve sections first we determine when the hilbert scheme inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i of such varieties x is nonempty moreover in the case of picard number one we prove that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i is irreducible and that the examples of fano iskovskih and mukai form a dense open subset of smooth points of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i

brief stability radii of discrete time stochastic systems with respect to blockdiagonal perturbations we consider stochastic discrete time systems with multiplicative noise which are controlled by dynamic output feedback and subjected to blockdiagonal stochastic parameter perturbations stability radii for these systems are characterized via scaling techniques and it is shown that for real data the real and the complex stability radii coincide in a second part of the paper we investigate the problem of maximizing the stability radii by dynamic output feedback necessary and sufficient conditions are derived for the existence of a stabilizing compensator which ensures that the stability radius is above a prespecified level these conditions consist of parametrized matrix inequalities and a coupling condition

brief continuous time state feedback h2 control of markovian jump linear systems via convex analysis continuous time h 2 control problem for the class of linear systems with markovian jumps mjls using convex analysis is considered in this paper the definition of the h 2 norm for continuous time mjls is presented and related to the appropriate observability and controllability gramians a convex programming formulation for the h 2 control problem of mjls is developed that enables us to tackle the optimization problem of mjls under the assumption that the transition rate matrix p p i j for the markov chain may not be exactly known but belongs to an appropriate convex set an equivalence between the convex formulation when p is exactly known and the usual dynamic programming approach of quadratic optimal control of mjls is established it is shown that there exists a solution for the convex programming problem if and only if there exists the mean square stabilizing solution for a set of coupled algebraic riccati equations these results are compared with other related works in the current literature

a space time discontinuous galerkin trefftz method for time dependent maxwell s equations we consider the discretization of electromagnetic wave propagation problems by a discontinuous galerkin method based on trefftz polynomials this method fits into an abstract framework for space time discontinuous galerkin methods for which we can prove consistency stability and energy dissipation without the need to completely specify the approximation spaces in detail any method of such a general form results in an implicit time stepping scheme with some basic stability properties for the local approximation on every space time element we then consider trefftz polynomials i e the subspace of polynomials that satisfy maxwell s equations exactly on the respective element we present an explicit construction of a basis for the local trefftz spaces in two and three dimensions and summarize some of their basic properties using local properties of the trefftz polynomials we can establish the well posedness of the resulting discontinuous galerkin trefftz method consistency stability and energy dis