stochastic eulerian lagrangian methods for fluid structure interactions with thermal fluctuations we present approaches for the study of fluid structure interactions subject to thermal fluctuations a mixed mechanical description is utilized combining eulerian and lagrangian reference frames we establish general conditions for operators coupling these descriptions stochastic driving fields for the formalism are derived using principles from statistical mechanics the stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes to cope with this issue we derive reduced stochastic differential equations for several physical regimes we also present stochastic numerical methods for each regime to approximate the fluid structure dynamics and to generate efficiently the required stochastic driving fields to validate the methodology in each regime we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid structure formalism we compare this analysis with results from statistical mechanics to further demonstrate the applicability of the methodology we perform computational studies for spherical particles having translational and rotational degrees of freedom we compare these studies with results from fluid mechanics the presented approach provides for fluid structure systems a set of rather general computational methods for treating consistently structure mechanics hydrodynamic coupling and thermal fluctuations

nonuniversality of front fluctuations for compact colonies of nonmotile bacteria the front of a compact bacterial colony growing on a petri dish is a paradigmatic instance of non equilibrium fluctuations in the celebrated eden or kardar parisi zhang kpz universality class while in many experiments the scaling exponents crucially differ from the expected kpz values the source of this disagreement has remained poorly understood we have performed growth experiments with b subtilis 168 and e coli atcc 25922 under conditions leading to compact colonies in the classically alleged eden regime where individual motility is suppressed non kpz scaling is indeed observed for all accessible times kpz asymptotics being ruled out for our experiments due to the monotonic increase of front branching with time simulations of an effective model suggest the occurrence of transient nonuniversal scaling due to diffusive morphological instabilities agreeing with expectations from detailed models of the relevant biological reaction diffusion processes

immersed boundary method for variable viscosity and variable density problems using fast constant coefficient linear solvers i numerical method and results we present a general variable viscosity and variable density immersed boundary method that is first order accurate in the variable density case and for problems possessing sufficient regularity second order accurate in the constant density case the viscosity and density are considered material properties and are defined by a dynamically updated tesselation empirical convergence rates are reported for a test problem of a two dimensional viscoelastic shell with spatially varying material properties the reduction to first order accuracy in the variable density case can be avoided by using an iterative scheme although this approach may not be efficient enough for practical use in our time stepping scheme both the inertial and viscous terms are split into two parts a constant coefficient part that is treated implicitly and a variable coefficient part that is treated explicitly this splitting allows the resulting equations to be solved efficiently using fast constant coefficient linear solvers and i

kardar parisi zhang universality class and the anchored toom interface we revisit the anchored toom interface and use kardar parisi zhang scaling theory to argue that the interface fluctuations are governed by the airy1 process with the role of space and time interchanged the predictions which contain no free parameter are numerically well confirmed for space time statistics in the stationary state in particular the spatial fluctuations of the interface computed numerically agree well with those given by the goe edge distribution of tracy and widom

exact solution for the stationary kardar parisi zhang equation we obtain the first exact solution for the stationary one dimensional kardar parisi zhang equation a formula for the distribution of the height is given in terms of a fredholm determinant which is valid for any finite time t the expression is explicit and compact enough so that it can be evaluated numerically furthermore by extending the same scheme we find an exact formula for the stationary two point correlation function

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

upper critical dimension of the kardar parisi zhang equation numerical results for the directed polymer model in 1 4 dimensions in various types of disorder are presented the results are obtained for a system size that is considerably larger than considered previously for the extreme strong disorder case min max system associated with the directed percolation model the expected value of the meandering exponent 0 5 is clearly revealed with very weak finite size effects for the weak disorder case associated with the kardar parisi zhang equation finite size effects are stronger but the value of is clearly seen in the vicinity of 0 57 in systems with strong disorder it is expected that the system will cross over sharply from min max behavior at short chains to weak disorder behavior at long chains our numerical results agree with that expectation to complete the picture we obtain the energy fluctuation exponent for weak disorder and we find that the value of is in the vicinity of 0 14 thus the meandering exponent and the energy fluctuation exponent obey the strong coupling scaling relation 2 1 our results indicate that 1 4 is not the upper critical dimension in the weak disorder case and thus 4 1 does not seem to be the upper critical dimension for the kardar parisi zhang equation

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

an immersed boundary method for simulating vesicle dynamics in three dimensions we extend our previous immersed boundary ib method for 3d axisymmetric inextensible vesicle in navier stokes flows hu et al 2014 17 to general three dimensions despite a similar spirit in numerical algorithms to the axisymmetric case the fully 3d numerical implementation is much more complicated and is far from straightforward a vesicle membrane surface is known to be incompressible and exhibits bending resistance as in 3d axisymmetric case instead of keeping the vesicle locally incompressible we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension lagrange multiplier for the incompressible constraint can be avoided nevertheless the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension the vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex lagrangian marker in the ib method of the triangulation a series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method we perform the convergence study for the immersed boundary forces and the fluid velocity field we then study the vesicle dynamics in various flows such as quiescent simple shear and gravitational flows our numerical results show good agreements with those obtained in previous theoretical experimental and numerical studies

numerical methods for the stochastic landau lifshitz navier stokes equations the landau lifshitz navier stokes llns equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes this paper examines explicit eulerian discretizations of the full llns equations several computational fluid dynamics approaches are considered including maccormack s two step lax wendroff scheme and the piecewise parabolic method and are found to give good results for the variance of momentum fluctuations however neither of these schemes accurately reproduces the fluctuations in energy or density we introduce a conservative centered scheme with a third order runge kutta temporal integrator that does accurately produce fluctuations in density energy and momentum a variety of numerical tests including the random walk of a standing shock wave are considered and results from the stochastic llns solver are compared with theory when available and with molecular simulations using a direct simulation monte carlo algorithm

a stochastic immersed boundary method for fluid structure dynamics at microscopic length scales in modeling many biological systems it is important to take into account flexible structures which interact with a fluid at the length scale of cells and cell organelles thermal fluctuations of the aqueous environment become significant in this work it is shown how the immersed boundary method of c s peskin the immersed boundary method acta num 11 2002 1 39 for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations a stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps an important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved partially resolved or fully resolved while retaining a good level of accuracy error estimates in each of these regimes are given for the method a number of theoretical and numerical checks are furthermore performed to assess its physical fidelity for a conservative force the method is found to simulate particles with the correct boltzmann equilibrium statistics it is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters the method is also shown to reproduce a well known hydrodynamic effect of a brownian particle in which the velocity autocorrelation function exhibits an algebraic 3 2 decay for long times b j alder t e wainwright decay of the velocity autocorrelation function phys rev a 1 1 1970 18 21 a few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method specifically we present simulations of osmotic effects of molecular dimers worm like chain polymer knots and a basic model of a molecular motor immersed in fluid subject to a hydrodynamic load force the theoretical analysis and numerical results show that the immersed boundary method with thermal fluctuations captures many important features of small length scale hydrodynamic systems and holds promise as an effective method for simulating biological phenomena on the cellular and subcellular length scales

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

exact solution for the kardar parisi zhang equation with flat initial conditions we provide the first exact calculation of the height distribution at arbitrary time t of the continuum kardar parisi zhang kpz growth equation in one dimension with flat initial conditions we use the mapping onto a directed polymer with one end fixed one free and the bethe ansatz for the replicated attractive boson model we obtain the generating function of the moments of the directed polymer partition sum as a fredholm pfaffian our formula valid for all times exhibits convergence of the free energy i e kpz height distribution to the gaussian orthogonal ensemble tracy widom distribution at large time

simulation of osmotic swelling by the stochastic immersed boundary method we develop computational methods for the simulation of osmotic swelling phenomena relevant to microscopic vesicles containing transformable solute molecules we introduce stochastic immersed boundary methods sibms that can capture osmotically driven fluid transport through semipermeable elastic membranes subject to thermal fluctuations we also develop numerical methods to handle within sibms an elastic shell model for a neo hookean material our extended sibm allows for capturing osmotic swelling phenomena driven by concentration changes and interactions between a discrete collection of confined particles while accounting for the thermal fluctuations of the semipermeable membrane and the hydrodynamic transport of solvent we use our computational methods to investigate osmotic phenomena in regimes that go beyond the classical van t hoff theory we develop statistical mechanics theories for osmotic swelling of vesicles when there are significant interactions between particles that can transform over tim

steady state scaling function of the 1 1 dimensional single step model the steady state height height correlation function for the 1 1 dimensional single step model is calculated in a large scale monte carlo simulation analysis of the data yields a universal ratio of scaling amplitudes which differs from the value obtained recently from a mode coupling calculation an empirical form for a universal scaling function is also presented

existence and uniqueness results for double phase problems with convection term abstract in this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient under quite general assumptions on the convection term we prove the existence of a weak solution by applying the theory of pseudomonotone operators imposing some linear conditions on the gradient variable the uniqueness of the solution is obtained

positive solutions to nonlinear nonhomogeneous inclusion problems with dependence on the gradient abstract the goal of the paper is to study a generalized elliptic inclusion problem driven by a nonhomogeneous partial differential operator with the dirichlet boundary condition and a convection multivalued term an existence theorem for positive solutions of the problem is established by applying the method of subsolution supersolution together with truncation and comparison techniques

universal fluctuations in kardar parisi zhang growth on one dimensional flat substrates we present a numerical study of the evolution of height distributions hds obtained in interface growth models belonging to the kardar parisi zhang kpz universality class the growth is done on an initially flat substrate the hds obtained for all investigated models are very well fitted by the theoretically predicted gaussian orthogonal ensemble goe distribution the first cumulant has a shift that vanishes as t 1 3 while the cumulants of order 2 n 4 converge to goe as t 2 3 or faster behaviors previously observed in other kpz systems these results yield evidences for the universality of the goe distribution in kpz growth on flat substrates finally we further show that the surfaces are described by the airy 1 process

positive and negative solutions of a quasi linear elliptic equation by a mountain pass method and truncature techniques abstract the existence of a positive and a negative solution of a problem of the type u f x u u 0 in u 0 on is proved when f has a growth at infinity depending both on u and on u the techniques are based on an iterative scheme of mountain pass approximated solutions and the use of a suitable truncature method

positive solutions for nonlinear elliptic problems with dependence on the gradient abstract we consider a quasilinear neumann problem with a differential operator and a reaction term both dependent on u and du using topological methods together with suitable truncation and comparison techniques we show that the problem has at least one positive smooth solution

existence of solutions for double phase obstacle problems with multivalued convection term abstract the main goal of this paper is the study of an elliptic obstacle problem with a double phase phenomena and a multivalued reaction term which also depends on the gradient of the solution such term is called multivalued convection term under quite general assumptions on the data we prove that the set of weak solutions to our problem is nonempty bounded and closed our proof is based on a surjectivity theorem for multivalued mappings generated by the sum of a maximal monotone multivalued operator and a bounded multivalued pseudomonotone mapping

nodal and multiple constant sign solutions for resonant p laplacian equations with a nonsmooth potential abstract in this paper we study a nonlinear dirichlet elliptic differential equation driven by the p laplacian and with a nonsmooth potential hemivariational inequality using a variational approach combined with suitable truncation techniques and the method of upper lower solutions we prove the existence of five nontrivial smooth solutions two positive two negative and the fifth nodal our hypotheses on the nonsmooth potential allow resonance at infinity with respect to the principal eigenvalue 1 0 of p w 0 1 p z

a kpz cocktail shaken not stirred the stochastic partial differential equation proposed nearly three decades ago by kardar parisi and zhang kpz continues to inspire intrigue and confound its many admirers here we i pay debts to heroic predecessors ii highlight additional experimentally relevant aspects of the recently solved 1 1 kpz problem iii use an expanding substrates formalism to gain access to the 3d radial kpz equation and lastly iv examining extremal paths on disordered hierarchical lattices set our gaze upon the fate of d infty kpz clearly there remains ample unexplored territory within the realm of kpz and for the hearty much work to be done especially in higher dimensions where numerical and renormalization group methods are providing a deeper understanding of this iconic equation

circular kardar parisi zhang equation as an inflating self avoiding ring polymer we consider the kardar parisi zhang equation for a circular interface in two dimensions unconstrained by the standard small slope and no overhang approximations numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short time regime with the interface fluctuations of a self avoiding ring or two dimensional vesicle and a long time regime governed by the tracy widom distribution expected for this geometry for small noise amplitudes scaling behavior is only of the latter type large noise is also seen to renormalize the bare physical parameters of the ring akin to analogous parameter renormalization for equilibrium three dimensional membranes our results bear particular importance on the relation between relevant universality classes of scale invariant systems in two dimensions

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process