time periodic solutions to the full navier stokes fourier system with radiation on the boundary the navier stokes fourier system is a well established model to describe motion of viscous compressible heat conducting fluids we study the existence of time periodic weak solutions and improve the result from 4 in the following sense we extend the class of pressure functions id est consider lower exponent and include also the effect of radiation on the boundary

null surgery on knots in l spaces let k be a knot in an l space y with a dehn surgery to a surface bundle over s 1 we prove that k is rationally fibered that is the knot complement admits a fibration over s 1 as part of the proof we show that if k c y has a dehn surgery to s 1 x s 2 then k is rationally fibered in the case that k admits some s 1 x s 2 surgery k is floer simple that is the rank of hfk y k is equal to the order of h 1 y by combining the latter two facts we deduce that the induced contact structure on the ambient manifold y is tight in a different direction we show that if k is a knot in an l space y then any thurston norm minimizing rational seifert surface for k extends to a thurston norm minimizing surface in the manifold obtained by the null surgery on k i e the unique surgery on k with b 1 0

mimetic discretization and higher order time integration for acoustic electromagnetic and elastodynamic wave propagation this paper is devoted to the simulation of acoustic electromagnetic and elastodynamic wave propagation problems in a unified manner we focus on the finite integration technique for the spatial discretization of the first order wave equation systems using lowest order elements a universal framework of staggered grids is set up in which the application of the finite integration technique for acoustics electromagnetics and elastodynamics can be combined this framework offers opportunities to get generic and more efficient implementations the mimetic properties of the discretization technique are outlined for the time integration the use of a class of higher order time integrators with close resemblance to the classical leapfrog method is discussed it is shown that for the considered wave propagation problems higher order time integrators compare favourably to the classical second leapfrog order scheme even in combination with a low order spatial discretization

coupled simulation of transient heat flow and electric currents in thin wires application to bond wires in microelectronic chip packaging abstract this work addresses the simulation of heat flow and electric currents in thin wires an important application is the use of bond wires in microelectronic chip packaging the heat distribution is modeled by an electrothermal coupled problem which poses numerical challenges due to the presence of different geometric scales the necessity of very fine grids is relaxed by solving and embedding a 1d sub problem along the wire into the surrounding 3d geometry the arising singularities are described using de rham currents it is shown that the problem is related to fluid flow in porous 3d media with 1d fractures c d angelo siam journal of numerical analysis 50 1 pp 194 215 2012 a careful formulation of the 1d 3d coupling condition is essential to obtain a stable scheme that yields a physical solution elliptic model problems are used to investigate the numerical errors and the corresponding convergence rates additionally the transient electrothermal simulation of a simplified microelectronic chip package as used in industrial applications is presented

ozsvath szabo invariants and tight contact three manifolds ii let s 3 k be the oriented 3 manifold obtained by rational r surgery on a knot k s 3 using the contact ozsv ath szab o invariants we prove for a class of knots k containing all the algebraic knots that s 3 k carries positive tight contact structures for every r 6 g s k 1 where gs k is the slice genus of k this implies in particular that the brieskorn spheres 2 3 4 and 2 3 3 carry tight positive contact structures as an application of our main result we show that for each m2n there exists a seifert bered rational homology 3 sphere mm carrying at least m pairwise non isomorphic tight nonllable contact structures

l2 estimates for the finite element method for the dirichlet problem with singular data in this paper we consider the approximation by the finite element method of second order elliptic problems on convex domains and homogeneous dirichlet condition on the boundary in these problems the data are borel measures using a quasiuniform mesh of finite elements and polynomials of degree 1 we prove that in two dimensions the convergence is of orderh inl 2 and in three dimensions of orderh 1 2

concentrations of solutions to time discretizied compressible navier stokes equations the compactness properties of solutions to time discretization of compressible navier stokes equations are investigated in three dimensions the existence of generalized solutions is established

the dirichlet problem for viscous compressible isothermal navier stokes equations in two dimensions we consider the navier stokes equations for compressible isothermal flow in the steady two dimensional case and show the existence of a weak solution for homogeneous dirichlet boundary conditions

handlebody construction of stein surfaces the topology of stein surfaces and contact 3 manifolds is studied by means of handle decompositions a simple characterization of homeomorphism types of stein surfaces is obtained they correspond to open handlebodies with all handles of index 2 an uncountable collection of exotic l4 s is shown to admit stein structures new invariants of contact 3 manifolds are produced including a complete and computable set of invariants for determining the homotopy class of a 2 plane field on a 3 manifold these invariants are applicable to seiberg witten theory several families of oriented 3 manifolds are examined namely the seifert fibered spaces and all surgeries on various links in s3 and in each case it is seen that most members of the family are the

discrete hodge operators many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms discrete differential forms provide a natural and canonical approach to their discretization however much freedom remains concerning the choice of discrete hodge operators that is discrete analogues of constitutive laws a generic discrete hodge operator is introduced and it turns out that most finite element and finite volume schemes emerge as its specializations we reap the possibility of a unified convergence analysis in the framework of discrete exterior calculus

on the classification of tight contact structures ii we present complete classification results for tight contact structures on two classes of 3 manifolds i torus bundles which fiber over the circle and ii circle bundles which fiber over closed surfaces

fractional step methods for index 1 differential algebraic equations in the numerical solution of ordinary differential systems the method of fractional steps also known as operator splitting yields high order accurate schemes based on separate computationally convenient treatments of distinct physical effects such schemes are equally desirable but much less accurate for semi explicit index 1 differential algebraic equations daes in the first half of this note it is shown that email protected ve application to daes of standard splitting schemes suffers from order reduction both first and second order schemes are only first order accurate for daes in the second half of this note a new family of higher order splitting schemes for semi explicit index 1 daes is developed the new schemes are based on a deferred correction paradigm in which an error equation is solved numerically and therefore inherit a simple computationally convenient structure higher order convergence of the new schemes is proved and numerical results confirm the expected order of accuracy in addition to establishing efficiency

weak and variational entropy solutions to the system describing steady flow of a compressible reactive mixture abstract we consider a system of partial differential equations which describes steady flow of a compressible heat conducting chemically reacting gaseous mixture we extend the result from giovangigli et al 2015 in the sense that we introduce the variational entropy solution for this model and prove existence of a weak solution for 4 3 and existence of a variational entropy solution for any 1 the proof is based on improved density estimates

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

a priori mesh grading for an elliptic problem with dirac right hand side the green function of the poisson equation in two dimensions is not contained in the sobolev space h 1 omega such that finite element error estimates for the discretization of a problem with the dirac measure on the right hand side are nonstandard and quasi uniform meshes are inappropriate by using graded meshes l 2 error estimates of almost optimal order are shown as a byproduct we show for the poisson equation with a right hand side in l 2 that appropriate mesh refinement near some interior point diminishes the error at this point by nearly one order

control of an elliptic problem with pointwise state constraints this paper deals with a quadratic control problem for elliptic equations with pointwise state constraints existence and uniqueness of the solution is proved optimality conditions are given and regularity of the optimal solution is investigated

tight contact structures on some small seifert fibered 3 manifolds we classify tight contact structures on the small seifert fibered 3 manifolds m 1 r1 r2 r3 with ri 0 1 q and r1 r2 the result is obtained by combining convex surface theory with computations of contact ozsvath szabo invariants we also show that some of the tight contact structures on the manifolds considered are nonfillable justifying the use of heegaard floer theory

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

convergence analysis of fully discrete finite volume methods for maxwell s equations in nonhomogeneous media we will consider both explicit and implicit fully discrete finite volume schemes for solving three dimensional maxwell s equations with discontinuous physical coefficients on general polyhedral domains stability and convergence for both schemes are analyzed we prove that the schemes are second order accurate in time both schemes are proved to be first order accurate in space for the voronoi delaunay grids and second order accurate for nonuniform rectangular grids we also derive explicit expressions for the dependence on the physical parameters in all estimates

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

steady compressible navier stokes fourier system for monoatomic gas and its generalizations we consider steady compressible navier stokes fourier system for a gas with pressure p and internal energy e related by the constitutive law p i 1 e 1 we show that for any 3 there exists a variational entropy solution i e solution satisfying the weak formulation of balance of mass and momentum entropy inequality and global balance of total energy this result includes the model for monoatomic gas 5 if 5 these solutions also fulfill the weak formulation of the pointwise total energy balance

on the steady compressible navier stokes fourier system we study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible navier stokes fourier system our main result is the existence of a weak solution to these equations for arbitrarily large data a key element of the proof is a special approximation of the original system guaranteeing pointwise uniform boundedness of the density as well as the positiveness of the temperature therefore the passage to the limit omits tedious technical tricks required by the standard theory basic estimates on the solutions are possible to obtain by a suitable choice of physically reasonable boundary conditions

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

finite element approximation of elliptic problems with dirac measure terms in weighted spaces applications to one and three dimensional coupled problems in this work we study the stability and the convergence rates of the finite element approximation of elliptic problems involving dirac measures using weighted sobolev spaces and weighted discrete norms our approach handles both the cases where the measure is simply a right hand side and where it represents an additional term i e solution dependent in the formulation of the problem the main motivation of this study is to provide a methodological tool to treat elliptic problems in fractured domains where the coupling terms are seen as dirac measures concentrated on the fractures we first establish a decomposition lemma which is our fundamental tool for the analysis of the considered problems in the nonstandard setting of weighted spaces then we consider the stability of the galerkin approximation with finite elements in weighted norms with uniform and graded meshes we introduce a discrete decomposition lemma that extends the continuous one and allows us to derive discrete inf sup conditions in weighted norms then we focus on the convergence of the finite element method due to the lack of regularity the convergence rates are suboptimal for uniform meshes we show that using graded meshes optimal rates are recovered our theoretical results are supported by several numerical experiments finally we show how our theoretical results apply to certain coupled problems involving fluid flow in porous three dimensional media with one dimensional fractures that are found in the analysis of microvascular flows

holomorphic triangles and invariants for smooth four manifolds abstract in earlier articles the authors introduced invariants for closed oriented three manifolds defined using a variant of lagrangian floer homology in the symmetric products of riemann surfaces the aim of this article is to introduce invariants of oriented smooth four manifolds built using these floer homology groups this four dimensional theory also endows the corresponding three dimensional theories with additional structure an absolute grading of certain of its floer homology groups

on the flow of chemically reacting gaseous mixture abstract we consider the cauchy problem for the system of equations governing flow of isothermal reactive mixture of compressible gases our main contribution is to prove sequential stability of weak solutions when the state equation essentially depends on the species concentration and the viscosity coefficients vanish on vacuum moreover under additional assumption on the cold component of the pressure in the regions of small density we prove the existence of weak solutions for arbitrary large initial data

weak solutions to the three dimensional steady full compressible navier stokes system abstract we study the motion of the steady compressible viscous heat conductive fluid in a bounded three dimensional domain governed by the full navier stokes system for the pressure law of the form p 1 e the existence of weak solutions for any 5 4 is obtained our method relies upon the weighted estimates of both pressure and kinetic energy for the approximate system other tools such as effective viscous flux and oscillation defect measure developed by lions and feireisl respectively are also needed

rationally convex domains and singular lagrangian surfaces in mathbb c 2 we give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in mathbb c 2 we recall some classical obstructions and prove some deeper ones related to symplectic and contact topology we explain the close connection to lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces our proof also gives a complete characterization of lagrangian surfaces with open whitney umbrellas answering a question first posed by givental in 1986

khovanov homology open books and tight contact structures abstract we define the reduced khovanov homology of an open book s and identify a distinguished contact element in this group which may be used to establish the tightness or non fillability of contact structures compatible with s our construction generalizes the relationship between the reduced khovanov homology of a link and the heegaard floer homology of its branched double cover as an application we give combinatorial proofs of tightness for several contact structures which are not stein fillable lastly we investigate a comultiplication structure on the reduced khovanov homology of an open book which parallels the comultiplication on heegaard floer homology defined in baldwin 2008 4

ozsvath szabo invariants and fillability of contact structures recently ozsvath and szabo defined an invariant of contact structures with values in the heegaard floer homology groups they also proved that a version of the invariant with twisted coefficients is non trivial for weakly symplectically fillable contact structures in this article we show that their non vanishing result does not hold in general for the contact invariant with untwisted coefficients as a consequence of this fact heegaard floer theory can distinguish between weakly and strongly symplectically fillable contact structures

calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity an efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave the method is based upon the finite difference time domain fd td formulation the concept of equivalent radius is used to replace wire bundles with single wires in the fd td model then the radius of the equivalent wire is accounted by a modified fd td time stepping expression based on a faraday s law contour path formulation for the looping magnetic fields adjacent to the wire fd td computed fields at a virtual surface fully enclosing the equivalent wire are then obtained permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation efie substantial analytical and experimental validations are reported for both time harmonic and broad band excitations of wires in free space and in a high q metal cavity