the motivic nearby fiber and degeneration of stable rationality we prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities our proof is based on motivic specialization techniques and the criterion of larsen and lunts for stable rationality in the grothendieck ring of varieties

grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

on conservation at grid interfaces this paper considers the solution of hyperbolic systems of conservation laws on discontinuous grids in particular we consider what happens to conservation at grid interfaces a procedure is presented to derive conservative difference approximations at the grid interfaces for two dimensional grids which overlap in an arbitrary configuration the same procedures are applied to compute interface formulas for grids which are refined in space and or time and for continuous grids where a switch in the scheme causes the discontinuity

multigrid acceleration of a relaxation procedure for the reduced navier stokes equations on applique la methode multigrille pour ameliorer la convergence d une methode de relaxation iterative pour la resolution numerique des equations de navier stokes reduites

a conservative treatment of zonal boundaries for euler equation calculations finite difference calculations require the generation of a grid for the region of interest a zonal approach wherein the given region is subdivided into zones and the grid for each zone is generated independently makes the grid generation process for complicated topologies and for regions requiring selective grid refinement a fairly simple task this approach results in new boundaries within the given region that is zonal boundaries at the interfaces of the various zones the zonal boundary scheme the integration scheme used to update the points on the zonal boundary for the euler equations must be conservative accurate stable and applicable to general curvilinear coordinate systems a zonal boundary scheme with these desirable properties is developed in this study the scheme is designed for explicit first order accurate integration schemes but can be modified to accommodate second order accurate explicit and implicit integration schemes results for inviscid flow including supersonic flow over a cylinder blast wave diffraction by a ramp and one dimensional shock tube flow are obtained on zonal grids the conservative nature of the zonal boundary scheme permits the smooth transition of the discontinuities associated with these flows from one zone to another the calculations also demonstrate the continuity of contour lines across zonal boundaries that can be achieved with the present zonal scheme

nonequilibrium statistical thermodynamics of second order stochastic processes in the limit of large resistance the phase space generalization of the kinetic analog of boltzmann s principle is derived a kinetic criterion for the contraction of a second order ornstein uhlenbeck to a first order einstein smoluchowski stochastic process is advanced on the basis of an asymptotic expansion of the joint entropy in the limit of large resistance the kinetic criterion is shown to be the stationary solution to the first velocity moment of the phase space fokker planck equation the stratonovich criterion for the validity of the einstein smoluchowski description is corroborated from the asymptotic expansion of the joint entropy second order gaussian processes are used for illustration where it is shown that i the principles of least dissipation of energy and maximum joint entropy are equivalent and ii the observed local velocity arises from an exact balance between rates of growth and decay of velocity fluctuations

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

anisotropic grid adaptation for navier stokes equations navier stokes equations are discretized in space by a finite volume method error equations are derived which are approximately satisfied by the errors in the solution the dependence of the solution errors on the discretization errors is analyzed in certain flow cases the grid is adapted based on the estimated discretization errors the refinement and coarsening of the grid are anisotropic in the sense that it is different in different directions in the computational domain the adaptation algorithm is applied to laminar viscous flow over a flat plate in a channel with a bump and around a cylinder and an airfoil

birational automorphisms of fano hypersurfaces v v y v 0 between smooth three dimensional quartics v v4 v 0 v 0 4 in p is a projective isomorphism this is the original wording of their theorem in fact the arguments of im give a much stronger result namely they actually prove that smooth quartics are birationally superrigid the concept of birational rigidity is not visual being rather technical it makes little impression it is immediate implications of the property of being birationally super rigid that are really impressive for a projective variety x smooth in codimension 1 and a linear system jdj free from xed components we de ne the threshold of canonical adjunction or brie y just threshold of the pair x d setting

stably irrational hypersurfaces of small slopes we show that over any uncountable field of characteristic different from two a very general hypersurface of dimension n 2 and degree at least log 2 n 2 is not stably rational this significantly improves earlier results of kollar and totaro as a byproduct of our proof we obtain new counterexamples to the integral hodge conjecture answering a question of voisin and colliot thelene voisin

transient behavior of supersonic flow through inlets a solution technique to compute inlet flow behavior is presented the phenomena of inlet unstart and restart are investigated using a flux split procedure applied to the euler and reduced navier stokes rns equations a time consisten t direct sparse matrix solver in conjunction with a domain decomposition strategy is applied to compute the transient flow behavior both internal and external to the inlet time varying shocks and timevarying recirculation regions are efficiently analyzed the code is quite general and is suitable for the computation of flow for a wide variety of geometries and over a wide range of mach and reynolds numbers

optimal control of the decay of nonequilibrium statistical correlations a quasithermodynamic interpretation of the stochastic control of irreversible thermodynamic diffusion processes is presented in which the drift is the control parameter the joint entropy considered as a function of the initial data is the negative of the optimal expected total cost and the generalized hamilton jacobi equation which it satisfies is the dynamic programming equation for the optimal stochastic drift control the two cost functions proposed by yasue are shown to differ by a stochastic gauge transformation and constitute equivalent variational problems yasue s results are shown to apply in two limiting cases the asymptotic time limit where the nonequilibrium statistical correlations have worn off or the weak noise limit where random thermal fluctuations have a negligible importance the asymptotic expected total cost is governed by a minimum relative entropy principle and the goodness of the thermodynamic drift control in the stochastic problem is determined

variational version of thermal conduction fluctuations in the context of the most probable route an expression for the square law fluctuation of internal energy is obtained in the framework of the local equilibrium approach with the aid of the non equilibrium distribution function presented by zubarev 1974 it is shown that this fluctuation satisfies the necessary conditions for its use as liapounov s function it is demonstrated that liapounov s stability requirement leads to a fluctuating functional which has a minimum for the hydrodynamic stage the infinitesimality estimates of the right parts are found for two balance equations energy and entropy it is shown that the local potential of prigogine and glansdorff 1971 can be derived from perturbed fluctuating functional obtained here with the aid of the well known formula of the onsager machlup postulate for the density probability transition of a thermodynamic system from some non equilibrium state the path integrals are obtained for the evolution of the system in the hydrodynamic stage

rationally isotropic quadratic spaces are locally isotropic let r be a regular local ring k its field of fractions and v a quadratic space over r assume that r contains a field of characteristic zero we show that if v r k is isotropic over k then v is isotropic over r this solves the characteristic zero case of a question raised by j l colliot thelene in 3 the proof is based on a variant of a moving lemma from 7 a purity theorem for quadratic spaces is proved as well it generalizes in the charactersitic zero case the main purity result from 9 and it is used to prove the main result in 2

varietes unirationnelles non rationnelles au dela de l exemple d artin et mumford keywords non rational but unirational variety grothendieck invariants rationality brauer invariants reference cma article 1989 001doi 10 1007 bf01850658 record created on 2008 12 16 modified on 2016 08 08

on the rationality problem for quadric bundles we classify all positive integers n and r such that stably nonrational complex r fold quadric bundles over rational n folds exist we show in particular that for any n and r a wide class of smooth r fold quadric bundles over pcn are not stably rational if r 2n 1 1 2n 2 in our proofs we introduce a generalization of the specialization method of voisin and of colliot thelene and pirutka which avoids universally ch0 trivial resolutions of singularities

time consistent pressure relaxation procedure for compressible reduced navier stokes equations a time consistent global pressure relaxation procedure for the unsteady compressible reduced navier stokes equations is presented the shock capturing capability of the procedure is investigated with different forms of pressure gradient splitting an efficient conservative method for capturing shocks is detailed the transient behaviour of laminar high reynolds number low subsonic flow past a sine wave airfoil geometry is analysed using the new reduced navier stokes based algorithm these solutions are compared with steady and unsteady results previously obtained with a modified interacting boundary layer procedure the strong influence of grid refinement and the type of differencing of the streamwise convection term on the existence or stability of separated laminar solutions is reaffirmed more stable turbulent flow results are also presented finally an unsteady solution for the flow past a finite flat plate at incidence is described in order to demonstrate the time accuracy of the algorithm

solution based grid adaptation through segmented multigrid domain decomposition a solution based grid adaptation method that combines elements of the multigrid method for solution acceleration and the domain decomposition philosophy for grid optimization is described unlike other solution based adaptive gridding schemes wherein the overhead of recomputing the grid and re evaluating the solution on the adapted grid leads to higher computational costs compared to a nonadapted calculation the present methodology reduces the computational time required to obtain the solution the computational effort involved in the present calculation is significantly lower than a nonadapted calculation that utilizes the multigrid method purely as a convergence acceleration tool in addition to convergence acceleration the multigrid framework provides a mechanism of information transfer from regions wherein grid refinement is specified to unrefined coarse grid regions the basis for domain decomposition in the current procedure is the variation in grid refinement requirements for each coordinate direction in different portions of the flow field the method is demonstrated herein on an efficient set of governing equations termed the reduced navier stokes equations applied in conjunction with a set of physical boundary conditions the governing equations are discretized through a pressure based flux splitting procedure that is uniformly applicable from incompressible to supersonic mach numbers

involution surface bundles over surfaces we construct models of involution surface bundles over algebraic surfaces degenerating over normal crossing divisors and with controlled singularities of the total space

thermodynamic criteria governing the stability of fluctuating paths in the limit of small thermal fluctuations critical paths in the limit of small thermal fluctuations critical paths and temporal bifurcations thermodynamic criteria for the stability of the most probable path for a fluctuation are derived in the limit of small thermal fluctuations the positive definiteness of the second frechet differential of the onsager machlup functional insures that the asymptotic probability distribution will be gaussian about the extremal path at which the onsager machlup functional is a proper minimum the vanishing of one of the eigenvalues of the second frechet differential of the onsager machlup functional indicates the presence of a critical path the lowest order term in the extended form of the taylor series expansion of the onsager machlup functions determines the stability characteristics of the critical path the cubic case is examined in detail

thermodynamic criteria governing irreversible processes under the influence of small thermal fluctuations the ventsel freidlin probability estimates for small random perturbations of dynamical systems are used to generalize and justify the onsager machlup irreversible thermodynamic variational description of gaussian statistical distributions in the limit where boltzmann s constant tends to zero for non gaussian diffusion processes a hamiltonian formulation is used to determine the maximum likelihood paths for the growth and decay of nonequilibrium fluctuations in the same limit subject to the imposed constraints the paths of maximum likelihood manifest a symmetry in past and future and are the stationary conditions of the constrained thermodynamic variational principle of least dissipation of energy the power balance equations supply the required constraints and the most likely path for the growth of a fluctuation is characterized by a negative entropy production the entropy plays the role of the quasipotential of ventsel and freidlin and exit from a bounded domain containing a deterministically stable steady state is made at that state on the boundary with maximum entropy

geometric criteria for tame ramification we prove an a campo type formula for the tame monodromy zeta function of a smooth and proper variety over a discretely valued field k as a first application we relate the orders of the tame monodromy eigenvalues on the l adic cohomology of a k curve to the geometry of a relatively minimal sncd model and we show that the semi stable reduction theorem and saito s criterion for cohomological tameness are immediate consequences of this result as a second application we compute the error term in the trace formula for smooth and proper k varieties we see that the validity of the trace formula would imply a partial generalization of saito s criterion to arbitrary dimension

hypersurfaces that are not stably rational a fundamental problem of algebraic geometry is to determine which varieties are rational that is isomorphic to projective space after removing lower dimensional subvarieties from both sides in particular we want to know which smooth hypersurfaces in projective space are rational an easy case is that smooth complex hypersurfaces of degree at least n 2 in p are not covered by rational curves and hence are not rational by far the most general result on rationality of hypersurfaces is kollar s theorem that for d at least 2d n 3 3e a very general complex hypersurface of degree d in p is not ruled and therefore not rational 13 theorem v 5 14 very little is known about rationality in lower degrees except for cubic 3 folds and quintic 4 folds 4 19 chapter 3 a rational variety is also stably rational meaning that some product of the variety with projective space is rational many techniques for proving non rationality give no information about stable rationality voisin made a breakthrough in 2013 by showing that a very general quartic double solid a double cover of p ramified over a quartic surface is not stably rational 23 these fano 3 folds were known to be non rational over the complex numbers but stable rationality was an open question voisin s method was to show that the chow group of zero cycles is not universally trivial that is the chow group becomes nontrivial over some extension of the base field by degenerating the variety to a nodal 3 fold which has a resolution of singularities x with nonzero torsion in h3 x z colliot thelene and pirutka simplified and generalized voisin s degeneration method they deduced that very general quartic 3 folds are not stably rational 6 this was striking in that non rationality of smooth quartic 3 folds was the original triumph of iskovskikh manin s work on birational rigidity while stable rationality of these varieties was unknown 11 beauville applied the method to prove that very general sextic double solids quartic double 4 folds and quartic double 5 folds are not stably rational 1 2 in this paper we show that a wide class of hypersurfaces in all dimensions are not stably rational namely for all d 2d n 2 3e and n 3 a very general complex hypersurface of degree d in p is not stably rational theorem 2 1 the theorem covers all the degrees in which kollar proved non rationality in fact we get a bit more since kollar assumed d 2d n 3 3e for example very general quartic 4 folds are not stably rational whereas it was not even known whether these varieties are rational the method applies to some smooth hypersurfaces over q in each even degree section 3 gives some examples over q which are not stably rational over c the idea is that the most powerful results are obtained by degenerating a smooth complex variety to a singular variety in positive characteristic rather than to a sin

the gersten conjecture for milnor k theory we prove that the n th milnor k group of an essentially smooth local ring over an infinite field coincides with the n n motivic cohomology of the ring this implies levine s generalized bloch kato conjecture

the stochastic h theorem the stochastic analogue of the generalized h theorem is formulated for multidimensional time homogeneous diffusion processes which asymptotically are characterized by an invariant probability distribution it applies to both isolated and open thermodynamic systems the latter being characterized by rotational probability currents the physical mechanism for the monotonic behavior of the stochastic h function in time is linked to the decay of statistical correlations between a given nonequilibrium state and those through which the system passes at successive instants in time

toroidal varieties and the weak factorization theorem we develop the theory of stratified toroidal varieties which gives together with the theory of birational cobordisms 73 a proof of the weak factorization conjecture for birational maps in characteristic zero a birational map between complete nonsingular varieties over an algebraically closed field k of characteristic zero is a composite of blow ups and blow downs with smooth centers

on the persistence of irreversible processes under the influence of random thermal fluctuations a thermodynamic criterion for the persistence of an irreversible process is derived from the method of associative distributions applied to the probability of large deviations in stochastic processes paths of relative maximum likelihood are determined from the condition that the distribution and associated distribution be non defective the latter predicts the threshold value of the noise strength and the paths are mirror images in time of one another based on the analogy with the central limit theorem and the method of associated distributions the technique is used to estimate the error in approximating the actual distribution by one that is obtained in the diffusion limit analogous to the normal distribution for large deviations the maximum power of the deviation is discussed in terms of the fractal dimension

an adaptive multigrid technique for the incompressible navier stokes equations an automatic adaptive refinement technique has been coupled to the multigrid approach to produce an efficient and stable solution strategy for solving the steady state incompressible navier stokes equations solutions have been obtained for the driven cavity and flow over a backward facing step for reynolds numbers up to 5000 and 800 respectively the refinement criterion is based on the local truncation error the solution error is monitored and automatic refinement can continue until it is reduced to a satisfactory level for driven cavity flow at re 1000 the adaptive refinement approach reduced the computer memory and cpu time to 20 and 40 of the requirements of the pure multigrid method the primitive variable formulation of the navier stokes equations is used so the method can be extended easily to three dimensions application to other nonlinear elliptic problems is equally possible

semiorthogonal decompositions and birational geometry of del pezzo surfaces over arbitrary fields we study the birational properties of geometrically rational surfaces from a derived categorical perspective in particular we give a criterion for the rationality of a del pezzo surface s over an arbitrary field namely that its derived category decomposes into zero dimensional components when s has degree at least 5 we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of s from brauer classes and chern classes associated to these vector bundles

on the principle of minimal correlational entropy the onsager machlup approximation for a discrete markov chain representing multistationary state transitions is formulated in the limit of small thermal fluctuations the principle of minimal correlational entropy is used to determine the state in which the invariant probability measure tends to concentrate as the intensity of the fluctuations tends to zero it is this principle rather than that of maximum entropy which is valid in open systems without microscopic reversibility in systems characterised by microscopic reversibility the two principles give the same predictions the principle of minimal correlational entropy is shown to be the statistical analogue of the thermodynamic principle of least dissipation of energy the principle of minimal correlational entropy is applied to the problem of stochastic exit from domains enclosing multistationary states it reduces to a minimum entropy difference principle for systems satisfying microscopic reversibility