bounded imaginary powers of cone differential operators on higher order mellin sobolev spaces and applications to the cahn hilliard equation abstract extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted l p spaces h p 0 b over a manifold with conical singularities we show how the same assumptions also yield the existence of bounded imaginary powers on higher order mellin sobolev spaces h p s b s 0 as an application we consider the cahn hilliard equation on a manifold with possibly warped conical singularities relying on our work for the case of straight cones we first establish r sectoriality and thus maximal regularity for the linearized equation and then deduce the existence of a short time solution with the help of a theorem by clement and li we also obtain the short time asymptotics of the solution near the conical point

an energetic variational approach for the cahn hilliard equation with dynamic boundary condition model derivation and mathematical analysis the cahn hilliard equation is a fundamental model that describes phase separation processes of binary mixtures in recent years several types of dynamic boundary conditions have been proposed in order to account for possible short range interactions of the material with the solid wall our first aim in this paper is to propose a new class of dynamic boundary conditions for the cahn hilliard equation in a rather general setting the derivation is based on an energetic variational approach that combines the least action principle and onsager s principle of maximum energy dissipation one feature of our model is that it naturally fulfills three important physical constraints conservation of mass dissipation of energy and force balance relations next we provide a comprehensive analysis of the resulting system of partial differential equations under suitable assumptions we prove the existence and uniqueness of global weak strong solutions to the initial boundary value problem with or without surface diffusion furthermore we establish the uniqueness of the asymptotic limit as t to infty and characterize the stability of local energy minimizers for the system

error control for the approximation of allen cahn and cahn hilliard equations with a logarithmic potential a fully computable upper bound for the finite element approximation error of allen cahn and cahn hilliard equations with logarithmic potentials is derived numerical experiments show that for the sharp interface limit this bound is robust past topological changes modifications of the abstract results to derive quasi optimal error estimates in different norms for lowest order finite element methods are discussed and lead to weaker conditions on the residuals under which the conditional error estimates hold

asymptotic stability of solutions for 1 d compressible navier stokes cahn hilliard system abstract this paper is concerned with the evolution of the periodic boundary value problem and the mixed boundary value problem for a compressible mixture of binary fluids modeled by the navier stokes cahn hilliard system in one dimensional space the global existence and the large time behavior of the strong solutions for these two systems are studied the solutions are proved to be asymptotically stable even for the large initial disturbance of the density and the large velocity data we show that the average concentration difference for the two components of the initial state determines the long time behavior of the diffusive interface for the two phase flow

an l bound for solutions of the cahn hilliard equation in this paper we consider the equation partial t u varepsilon delta u varepsilon sum limits i j 1 n partial ij f ij u varepsilon x varepsilon 2 delta 2 u varepsilon with fij constant when u e is large and we obtain l bounds independent of 0

global existence for systems of parabolic conservation laws in several space variables abstract we prove the global existence of solutions of the cauchy problem for certain systems of conservation laws with artificial viscosity terms added the system is assumed to admit a quadratic entropy which is consistent with the viscosity matrix and the initial data is assumed to be close to a constant in l2 l in particular our result applies to the equations of compressible fluid flow in two and three space variables

stochastic chemical reaction networks for robustly approximating arbitrary probability distributions abstract we show that discrete distributions on the d dimensional non negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks we begin by providing a class of detailed balanced networks and prove that they can approximate any discrete distribution to any desired accuracy however these detailed balanced constructions rely on the ability to initialize a system precisely and are therefore susceptible to perturbations in the initial conditions we therefore provide another construction based on the ability to approximate point mass distributions and prove that this construction is capable of approximating arbitrary discrete distributions for any choice of initial condition in particular the developed models are ergodic so their limit distributions are robust to a finite number of perturbations over time in the counts of molecules

optimal decay rate of solutions for cahn hilliard equation with inertial term in multi dimensions abstract the cauchy problem of the cahn hilliard equation with inertial term is considered based on green s function method together with energy estimates we get the global in time existence and optimal decay rate of solutions furthermore the viscous case is investigated in the last section

numerical approximations to a new phase field model for two phase flows of complex fluids abstract we derive a new phase field theory for immiscible mixtures of nematic liquid crystals and viscous fluids using the variational principle coupled with the generalized onsager principle a novel phase transition mechanism is implemented to couple the nematic liquid crystal phase with the viscous fluid phase to arrive at the dissipative hydrodynamic model for incompressible fluid mixtures through a delicate explicit implicit numerical discretization we develop a decoupled linear scheme for a simplified version of the phase field model as well as a coupled nonlinear scheme for the full model both schemes are shown as unconditionally energy stable with consistent discrete dissipative energy laws several numerical examples are presented to show the effectiveness of the new model and the new numerical schemes developed for it

asymptotics of solutions of nonlinear parabolic equations abstract this paper is concerned with the large time behaviour of solutions to the cauchy problem of the following nonlinear parabolic equations u t u f u d x u d x 2 u u r n u t x t 0 u 0 x x r n n 1 under the optimal growth conditions on the smooth nonlinear function f u dxu dx2u we obtain the global existence results to the above cauchy problem the influence of the nonlinear function f u dxu dx2u on the large time behaviour of the global smooth solution u t x is also studied

analysis of the cahn hilliard equation with a relaxation boundary condition modeling the contact angle dynamics we analyze the cahn hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary an l estimate is established which enables us to prove the global existence of the solution we also study the sharp interface limit of the system the dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations

stability of cahn hilliard fronts we prove stability of the kink solution of the cahn hilliard equation partial derivative t u partial derivative x 2 partial derivative x 2 u u 2 u 3 2 x is an element of r the proof is based on an inductive renormalization group method and we obtain detailed asymptotics of the solution as t infinity we prove stability of the kink solution of the cahn hilliard equation partial derivative t u partial derivative x 2 partial derivative x 2 u u 2 u 3 2 x is an element of r the proof is based on an inductive renormalization group method and we obtain detailed asymptotics of the solution as t infinity c 1999 john wiley sons inc

convergence of solutions for the fractional cahn hilliard system abstract this paper deals with the cauchy dirichlet problem for the fractional cahn hilliard equation the main results consist of global in time existence of weak solutions characterization of parabolic smoothing effects implying under proper condition eventual boundedness of trajectories and convergence of each solution to a single equilibrium in particular to prove the convergence result a variant of the so called ojasiewicz simon inequality is provided for the fractional dirichlet laplacian and possibly non analytic but c 1 nonlinearities

global existence and asymptotics of solutions of the cahn hilliard equation abstract this paper is concerned with the cauchy problem of the cahn hilliard equation u t u 2 u 0 x r n t 0 u t 0 u 0 x x r n first we construct a local smooth solution u t x to the above cauchy problem then by combining some a priori estimates sobolev s embedding theorem and the continuity argument the local smooth solution u t x is extended step by step to all t 0 provided that the smooth nonlinear function u satisfies a certain local growth condition at some fixed point u r and that u 0 x u l 1 r n is suitably small secondly we show that the global smooth solution u t x satisfies the following temporal decay estimates d k u t x u l p r n c 1 t k 4 n 4 1 1 p t 0 k 0 1 here p 1 c 0 is a constant depending on and 0 is any positive constant which can be chosen sufficiently small at last we show that under a strong assumption on the growth of the nonlinear function u at u u the asymptotics of solutions of the above cauchy problem is described by u 0 t n 4 g x t 4 here 0 r n u 0 x u d x g x r n exp 4 i x d

decoupled energy stable schemes for phase field models of two phase incompressible flows in this paper we construct two classes based on stabilization and convex splitting of decoupled unconditionally energy stable schemes for cahn hilliard phase field models of two phase incompressible flows at each time step these schemes require solving only a sequence of elliptic equations including a pressure poisson equation furthermore all of these elliptic equations are linear for the schemes based on stabilization making them the first to the best of the authors knowledge totally decoupled linear unconditionally energy stable schemes for phase field models of two phase incompressible flows thus the schemes constructed in this paper are very efficient and easy to implement

computing the aspect graph for line drawings of polyhedral objects an algorithm for computing the aspect graph for polyhedral objects is described the aspects graph is a representation of three dimensional objects by a set of two dimensional views the set of viewpoints on the gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same at the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes it is shown that for polyhedral objects there are two fundamental visual events 1 the projections of an edge and a vertex coincide and 2 the projections of three nonadjacent edges intersect at a point the geometry of the object is reflected in the locus of the accidental viewpoints the algorithm computes the partition together with a representative view for each region of the partition

convergence of the cahn hilliard equation to the hele shaw model we prove that level surfaces of solutions to the cahn hilliard equation tend to solutions of the hele shaw problem under the assumption that classical solutions of the latter exist the method is based on a new matched asymptotic expansion for solutions a spectral analysis for linearizd operators and an estimate for the difference between the true solutions and certain approximate ones

analysis and approximation of a fractional cahn hilliard equation we derive a fractional cahn hilliard equation fche by considering a gradient flow in the negative order sobolev space h alpha alpha in 0 1 where the choice alpha 1 corresponds to the classical cahn hilliard equation while the choice alpha 0 recovers the allen cahn equation the existence of a unique solution is established and it is shown that the equation preserves mass for all positive values of fractional order alpha and that it indeed reduces the free energy we then turn to the delicate question of the l infty boundedness of the solution and establish an l infty bound for the fche in the case where the nonlinearity is a quartic polynomial as a consequence of the estimates we are able to show that the fourier galerkin method delivers a spectral rate of convergence for the fche in the case of a semidiscrete approximation scheme finally we present results obtained using computational simulation of the fche for a variety of choices of fractional order alpha it is

on lossless approximations the fluctuation dissipation theorem and limitations of measurements in this paper we take a control theoretic approach to answering some standard questions in statistical mechanics and use the results to derive limitations of classical measurements a central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless we show that a linear system is dissipative if and only if it can be approximated by a linear lossless system over arbitrarily long time intervals hence lossless systems are in this sense dense in dissipative systems a linear active system can be approximated by a nonlinear lossless system that is charged with initial energy as a by product we obtain mechanisms explaining the onsager relations from time reversible lossless approximations and the fluctuation dissipation theorem from uncertainty in the initial state of the lossless system the results are applied to measurement devices and are used to quantify limits on the so called observer effect also called back action which is the impact the measurement device has on the observed system in particular it is shown that deterministic back action can be compensated by using active elements whereas stochastic back action is unavoidable and depends on the temperature of the measurement device

a class of convergent finite difference schemes for certain nonlinear parabolic systems on considere le systeme des equations v t u x ev xx u t p v x u xx x t rxr avec les donnees initiales v u x 0 v 0 x u 0 x x r

a simple proof of stability of fronts for the cahn hilliard equation we apply a method developed in our earlier work on a non local phase kinetics equation to give a simple proof of the non linear stability of fronts for the cahn hilliard equation

multiple mode diffusion waves for viscous nonstrictly hyperbolic conservation laws we study the large time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system the initial data considered here is a perturbation of a constant state it is shown that the solutions converge to single mode diffusion waves in directions of strictly hyperbolic fields and to multiple mode diffusion waves in directions of nonstrictly hyperbolic fields the multiple mode diffusion waves which are the new elements here are the self similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields with the nonlinear fluxes replaced by their quadratic parts the convergence rate to these diffusion waves iso t 3 4 1 2p inl p 1 p with 0 being arbitrarily small

convergence of the cahn hilliard equation to the mullins sekerka problem in spherical symmetry abstract we show that as e 0 the solution of the cahn hilliard equation formula converges to a solution of the mullins sekerka problem formula where denotes a normal v the normal velocity and k the sum of principal curvatures of the interface provided the solutions are radially symmetric we use energy type estimates to show that the solution of the cahn hilliard equation can be approximated by the well known stationary wave solution that corresponds to the potential w

approximate solutions of the cahn hilliard equation via corrections to the mullins sekerka motion we develop an alternative method to matched asymptotic expansions for the construction of approximate solutions of the cahn hilliard equation suitable for the study of its sharp interface limit the method is based on the hilbert expansion used in kinetic theory besides its relative simplicity it leads to calculable higher order corrections to the interface motion

a phase field model for the mixture of two incompressible fluids and its approximation by a fourier spectral method abstract a phase field model for the mixture of two incompressible fluids is presented in this paper the model is based on an energetic variational formulation it consists of a navier stokes system linear momentum equation coupled with a cahn hilliard equation phase field equation through an extra stress term and the transport term the extra stress represents the phase induced capillary effect for the mixture due to the surface tension a fourier spectral method for the numerical approximation of this system is proposed and analyzed numerical results illustrating the robustness and versatility of the model are presented

an l bound for solutions of a fractional cahn hilliard equation abstract recently some fractional cahn hilliard equations are proposed for phase transition and image process etc which have attracted a lot of attention in this paper we concern the l bound of the solutions to a class of fractional cahn hilliard equations which extends the results of integer order by an invariant derivative technique the crucial uniform estimates related to the kernel function of fractional cahn hilliard are established the technique presented here can be also applied to the other related fractional models

an efficient time adaptivity based on chemical potential for surface cahn hilliard equation using finite element approximation abstract we present numerical simulations for the surface cahn hilliard equation which describes phase separation phenomenon occurred on general surfaces the spatial discretization is based on surface finite element method while the temporal discretization methods are first and second order stabilized semi implicit schemes which guarantee the free energy decay an efficient and parameter free adaptive time stepping strategy is proposed based on the numerical energy stability generated by stabilized semi implicit scheme the main idea is to use discrete chemical potential the byproduct of stabilized semi implicit scheme to estimate the variation of numerical energy that is used as a indicator to update the time step the operation avoid calculating numerical energy with gauss integral in each time step and reduce the calculated cost in addition optimal error estimate of first order stabilized semi implicit scheme in the case of curved surface are provided finally numerical experiments are presented to demonstrate the stability accuracy and efficiency of the proposed algorithms

an output sensitive algorithm for computing visibility the visibility graph of a set of nonintersecting polygonal obstacles in the plane is an undirected graph whose vertex set consists of the vertices of the obstacles and whose edges are pairs of vertices u v such that the open line segment between u and v does not intersect any of the obstacles the visibility graph is an important combinatorial structure in computational geometry and is used in applications such as solving visibility problems and computing shortest paths this paper presents an algorithm that computes the visibility graph of a set of obstacles in time o e n log n where e is the number of edges in the visibility graph and n is the total number of vertices in all the obstacles

uniform decay rated for parabolic conservations laws on etablit des taux de decroissance uniformes optimaux pour des solutions du probleme de cauchy avec donnees grandes pour des lois de conservation paraboliques scalaires a plusieurs dimensions d espace

visibility occlusion and the aspect graph this chapter studies the ways in which the topology of the image of a polyhedron changes with changing viewpoint we catalog the ways that the topological appearance or aspect can change this enables us to find maximal regions of viewpoints of the same aspect we use these techniques to construct the viewpoint space partition vsp a partition of viewpoint space into maximal regions of constant aspect and its dual the aspect graph here we present tight bounds on the maximum size of the vsp and the aspect graph and give algorithms for their construction first in the convex case and then in the general case in particular we give bounds on the maximum size of n 2 and n 6 under an orthographic projection viewing model and of n 3 and n 9 under a perspective viewing model the algorithms make use of a new representation of the appearance of polyhedra from all viewpoints called the aspect representation or asp we believe that this representation is one of the significant contributions of this paper

convergence to diffusion waves of solutions for viscous conservation laws we study the large time behavior of solutions of viscous conservation laws it is shown that solutions tend to diffusion waves which are constructed based on the heat equation and burgers equation the convergence is in thelp 1 p sense and is obtained as a consequence of thel2 decay of the difference between the solution and its asymptotic state of diffusion waves

nonlinear stability and optimal decay rate for a multidimensional generalized kuramoto sivashinsky system we study the cauchy problem for a generalized kuramoto sivashinsky system in multidimension the zero equilibrium is linearly stable for coefficients within a certain range we further establish the global existence nonlinear stability and optimal decay rate of the solution for coefficients within the same range though with suitable restriction to the initial data c 2000 academic press

a note on the optimal temporal decay estimates of solutions to the cahn hilliard equation abstract this paper is concerned with the optimal temporal decay estimates on the solutions of the cauchy problem of the cahn hilliard equation it is shown in liu wang and zhao 2007 11 that such a cauchy problem admits a unique global smooth solution u t x provided that the smooth nonlinear function u satisfies a local growth condition furthermore if u satisfies a somewhat stronger local growth condition the optimal temporal decay estimates on u t x are also obtained in liu wang and zhao 2007 11 thus a natural question is how to deduce the optimal temporal decay estimates on u t x only under the local growth condition which is sufficient to guarantee the global solvability of the corresponding cauchy problem and the main purpose of this paper is devoted to this problem our analysis is motivated by the technique developed recently in ukai yang and zhao 2006 15 with a slight modification

an energy stable linear diffusive crank nicolson scheme for the cahn hilliard gradient flow abstract we propose and analyze a linearly stabilized semi implicit diffusive crank nicolson scheme for the cahn hilliard gradient flow in this scheme the nonlinear bulk force is treated explicitly with two second order stabilization terms this treatment leads to linear elliptic system with constant coefficients and provable discrete energy dissipation rigorous error analysis is carried out for the fully discrete scheme when the time step size and the space step size are small enough second order accuracy in time is obtained with a prefactor controlled by some lower degree polynomial of 1 e here e is the thickness of the interface numerical results together with an adaptive time stepping are presented to verify the accuracy and efficiency of the proposed scheme

a gradient flow approach to relaxation rates for the multi dimensional cahn hilliard equation the aim of this paper is to study relaxation rates for the cahn hilliard equation in dimension larger than one we follow the approach of otto and westdickenberg based on the gradient flow structure of the equation and establish differential and algebraic relationships between the energy the dissipation and the squared dot h 1 distance to a kink this leads to a scale separation of the dynamics into two different stages a first fast phase of the order t frac 1 2 where one sees convergence to some kink followed by a slow relaxation phase with rate t frac 1 4 where convergence to the centered kink is observed

pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions abstract in this paper we study the pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions by the green function method furthermore we obtain the l p convergence rate of the solution

on the cahn hilliard equation in h 1 r n in this paper we exhibit the dissipative mechanism of the cahn hilliard equation in h 1 r n we show a weak form of dissipativity by showing that each individual solution is attracted in some sense by the set of equilibria we also indicate that strong dissipativity that is asymptotic compactness in h 1 r n cannot be in general expected then we consider two types of perturbations a nonlinear perturbation and a small linear perturbation in both cases we show that for the resulting equations the dissipative mechanism becomes strong enough to obtain the existence of a compact global attractor

multiphase allen cahn and cahn hilliard models and their discretizations with the effect of pairwise surface tensions in this paper the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an n component mixture are studied for the general choice of phase variables the unisolvent property of the coefficient matrix involved in the n phase models based on the pairwise surface tensions is established moreover the symmetric positive definite property of the coefficient matrix on an n 1 n 1 dimensional hyperplane which is of fundamental importance to the well posedness of the models can be proved equivalent to some physical condition for pairwise surface tensions the n phase allen cahn and n phase cahn hilliard equations can then be derived from the free energy functional a natural property is that the resulting dynamics of concentrations are independent of phase variables chosen finite element discretizations for n phase models can be obtained as a natural extension of the existing discretizations for the two phase model the discrete energy law of the numerical schemes can be proved and numerically observed under some restrictions pertaining to time step size numerical experiments including the spinodal decomposition and the evolution of triple junctions are described in order to investigate the effect of pairwise surface tensions

front migration in the nonlinear cahn hilliard equation the method of matched asymptotic expansions is used to describe solutions of the nonlinear cahn hilliard equation for phase separation in n 1 space dimensions the expansion is formally valid when the thickness of internal transition layers is small compared with the distance separating layers and with their radii of curvature on the dominant slowest timescale the interface velocity is determined by the mean curvature of the interface by a non local relation which is identical to that in a well known quasi static model of solidification which exhibits a shape instability discovered by mullins sekerka j appl phys 34 323 329 1963 on a faster timescale the cahn hilliard equation regularizes a classic two phase stefan problem similarity solutions of the two phase stefan problem should describe boundary layers existence and uniqueness of such similarity solutions which admit metastable states is proved rigorously in an appendix

three dimensional weak visibility complexity and applications abstract in this paper we study the complexity of 3d weak visibility we obtain an o n 8 time and n 6 space algorithm to compute the weakly visible region of a triangle f from another triangle g among general scenes which are a set of n disjoint triangles we also consider the cases when the scenes are rectilinear objects and polyhedral terrains we show that in these special situations the weakly visible regions can be computed much faster in o n 6 time and o n 4 space with these results we obtain the first known polynomial time algorithm to decide whether or not a simple polyhedron is weakly internally or externally visible

efficient energy stable numerical schemes for a phase field moving contact line model in this paper we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line the model is a coupled system that consists of incompressible navier stokes equations with a generalized navier boundary condition and cahn hilliard equation in conserved form in both schemes the projection method is used to deal with the navier stokes equations and stabilization approach is used for the non convex ginzburg landau bulk potential by some subtle explicit implicit treatments we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions an efficient spectral galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes numerical results show that the proposed schemes are very efficient and accurate we proposed two linear energy stable numerical schemes for a phase field moving contact line model discrete energy laws that are consistent to the continuous ones are proved the efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified

the cahn hilliard type equations with periodic potentials and sources we discuss the existence uniqueness and asymptotic estimates of solutions to the cahn hilliard type equations with time periodic potentials and sources

qualitative analysis of a nonlinear viscous diffusion equation abstract we study the cauchy problem of multidimensional viscous diffusion equations by using an equivalent integral equation we first give the existence of local solutions then under some assumptions we obtain the global existence of solutions

asymptotic behavior of solutions to conservation laws with diffusion type terms of regularity gain and regularity loss abstract in this paper we study asymptotic behaviors of solutions to the cauchy problem of nonlinear conservation laws with a diffusion type source term related to an index s r for s 1 and s 1 the diffusion type term takes on a characteristic of regularity gain and regularity loss on the high frequency domain respectively by combining the green function method with the energy method we overcome the weakly dissipative structure of the equation for the case of s 1 and obtain the global existence and optimal l p norm time decay rates of solutions in the case of regularity gain pointwise estimates of solutions are shown by using the refined analysis on the green function

global existence and optimal temporal decay estimates for systems of parabolic conservation laws ii the multidimensional case this paper is a continuation of our previous paper it is concerned with the global existence and the optimal temporal decay estimates for the cauchy problem of the following multidimensional parabolic conservation laws

analysis of the viscous cahn hilliard equation in r n abstract solvability of cauchy s problem in r n for an extended viscous cahn hilliard equation is studied the problem is considered first in a standard sobolev space h 1 r n next a notion of the h solution is introduced that is well adapted to the structure of the viscous cahn hilliard equation several properties of the solutions are reported in particular those connected with their asymptotic behavior we collect here also known properties of the unbounded operator 1 in r n that are needed in our considerations

numerical approximations for a phase field moving contact line model with variable densities and viscosities we consider the numerical approximations of a two phase hydrodynamics coupled phase field model that incorporates the variable densities viscosities and moving contact line boundary conditions the model is a nonlinear coupled system that consists of incompressible navierstokes equations with the generalized navier boundary condition and the cahnhilliard equations with moving contact line boundary conditions by some subtle explicitimplicit treatments to nonlinear terms we develop two efficient unconditionally energy stable numerical schemes in particular a linear decoupled energy stable scheme for the system with static contact line condition and a nonlinear energy stable scheme for the system with dynamic contact line condition an efficient spectral galerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes various numerical results show that the proposed schemes are efficient and accurate

noise in gene regulatory networks life processes in single cells and at the molecular level are inherently stochastic quantifying the noise is however far from trivial as a major contribution comes from intrinsic fluctuations arising from the randomness in the times between discrete jumps it is shown in this paper how a noise filtering setup with an operator theoretic interpretation can be relevant for analyzing the intrinsic stochasticity in jump processes described by master equations such interpretation naturally exists in linear noise approximations but it also provides an exact description of the jump process when the transition rates are linear as an important example it is shown in this paper how by addressing the proximity of the underlying dynamics in an appropriate topology a sequence of coupled birth death processes which can be relevant in gene expression tends to a pure delay this implies important limitations in noise suppression capabilities despite the exactness in a linear regime of the analysis of noise in conjunction with the network dynamics we emphasize in this paper the importance of also analyzing dynamic behavior when transition rates are highly nonlinear otherwise steady state solutions can be misinterpreted the examples are taken from systems with macroscopic models leading to bistability it is discussed that bistability in the deterministic mass action kinetics and bimodality in the steady state solution of the master equation neither always imply one another nor do they necessarily lead to efficient switching behaviours the underlying dynamics need to be taken into account finally we explore some of these issues in relation to a model of the lac operation

efficiently computing and representing aspect graphs of polyhedral objects an efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented the aspect graph is an approach to representing 3 d objects by a set of 2 d views for the purpose of object recognition in this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change the viewing data of an object is the partition of the viewpoint space together with a representative view in each region the algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection

a case study of global stability of strong rarefaction waves for 2 2 hyperbolic conservation laws with artificial viscosity this paper is concerned with the global stability of strong rarefaction waves for a class of 2 x 2 hyperbolic conservation laws with artificial viscosity i e the p system with artificial viscosity

fat triangles determine linearly many holes the authors show that for every fixed delta 0 the following holds if f is a union of n triangles all of whose angles are at least delta then the complement of f has o n connected components and the boundary of f consists of o n log log n straight segments where the constants of proportionality depend on delta this latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges