global strong solutions to incompressible ericksen leslie system in r3 abstract in this paper we consider the cauchy problem to the ericksen leslie system of liquid crystals in r 3 global well posedness of strong solutions are obtained under the condition that the product of u 0 2 d 0 2 and u 0 2 2 d 0 2 is suitably small this result can be viewed as a supplement to the local existence and blow up criteria recently established in hong et al 2014

homothermal acceleration waves in nematic liquid crystals abstract the aim of this paper is the study of propagation of acceleration waves of arbitrary shape in nematic liquid crystals the development of balance equation reduced to singular surface and the application of hadamard s theorem permit to obtain the speeds and the conditions of propagation of the acceleration waves differential equations that describe the modifications of the metric and topological properties of the wave during the propagation are deduced in function of kinematical descriptors of the continuum and its thermodynamical state the deduction of the coefficients of evolution equation for the amplitude of the jump concludes the paper

regularity criteria for the three dimensional ericksen leslie system in homogeneous besov spaces in this paper we establish some regularity criteria involving homogeneous besov spaces for both the simplified and the general three dimensional ericksen leslie system this improves many previous results and can be viewed as the ultimate optimal regularity criterion in the besov space framework

best linear unbiased design hyetograph under the conditions of system linearity and stationarity of the precipitation process we derive the hyetograph associated with any given flood discharge q using best linear unbiased estimation blue theory the blue hyetograph depends explicitly on the correlation characteristics of the rainfall process and the instantaneous unit hydrograph iuh of the basin when the correlation time of the rainfall process is short relative to the dispersion of the iuh the shape of the blue hyetograph is the mirror image of the iuh itself in the opposite case the design hyetograph is the mirror image of the rainfall correlation function the procedure is extended from lumped to semidistributed and distributed basins in the latter case we obtain simultaneous design hyetographs for each subbasin or each site in the basin the analytical findings and the possibility of regionalization are verified using synthetic and recorded rainfall time series with excellent agreement in both cases because of its simplicity robustness and theoretical basis the proposed procedure should be appealing for practical use particularly when not only the peak but the entire flood hydrograph is required

two new regularity criteria for nematic liquid crystal flows abstract in this study we present two new regularity criteria for three dimensional nematic liquid crystal flows more precisely we show that if 3 u l 0 t l r 3 with 2 3 3 2 4 2 or u 3 d l 0 t l r 3 with 2 3 3 4 1 2 10 3 then the corresponding weak solution u d can be extended beyond t

multi value microstructural descriptors for complex materials analysis of ground states we propose and analyze a multi scale and multi field description of complex materials in which we consider every material element as a system composed by q in mathbb n indistinct substructures we pay attention to the equilibrium configurations of such bodies we consider first rigid bodies with microstructure represented by means of q valued maps from the reference place to the manifold of microstructural shapes in that case just microenergetics appears then we enlarge the stage considering large strains and energies of ginzburg landau type with respect to the microstructural descriptor fields in both cases we provide conditions for semicontinuity of the relevant energies and the existence of ground states

liquid crystal flow dynamic and static configurations we consider a system modeling the flow of nematic liquid crystals with variable degrees of orientation although the set of constitutive equations involves many different parameters the flow behavior is determined mostly by three nondimensional parameters i e the ericksen number the reynolds number and the interface number we establish a dissipative relation of the system in general domains in the case of plane poiseuille flow we prove existence and regularity of solutions moreover we discuss the stationary configurations with a large number of defects due to the large ericksen number of the flow

approximation of liquid crystal flows the numerical solution of the flow of a liquid crystal governed by a particular instance of the ericksen leslie equations is considered convergence of finite element approximations is established under appropriate regularity hypotheses and numerical experiments exhibiting the interaction of singularities and the coupling of the director and momentum equations are presented

partial regularity for minimizers of singular energy functionals with application to liquid crystal models where f is quasiconvex in the gradient variables and the convex function f blows up to infinity at the boundary of a given bounded open set k r as we will explain later in section 5 this sort of energy functional arises in some recently proposed models in nematic liquid crystal theory we assume hereafter that u r is bounded smooth domain and that k is a bounded open convex subset of r our assumptions are these h1 hypotheses on f the given function f r 0 is nonnegative convex and smooth on k r we will write f f z we further require that

a coupled ericksen allen cahn model for liquid crystal droplets abstract we present a model and discretization that couples the ericksen model of liquid crystals with variable degree of orientation to the allen cahn equations with a mass constraint the coupled system models liquid crystal droplets with anisotropic surface tension effects due to the liquid crystal molecular alignment the total energy consists of the ericksen energy phase field allen cahn energy and a weak anchoring energy that couples the liquid crystal to the diffuse interface we describe our discretization of the total energy along with a method to compute minimizers via a discrete gradient flow algorithm which has a strictly monotone energy decreasing property numerical experiments are given in three dimensions that illustrate a wide variety of droplet shapes that result from their interaction with defects

dynamic solid solid transitions with phase characterized by an order parameter abstract we develop a thermodynamically consistent continuum theory for the study of solid solid phase transitions where deformation dominates heat and mass transfer we use an order parameter to characterize the notion of phase and identify phase interfaces with thin transition zones within which the strain and order parameter exhibit large gradients to model the growth of one phase at the expense of another we introduce configurational forces subject to their own balance that work against changes in the order parameter by studying traveling waves and the asymptotics of a transition layer we establish connections between our theory and more standard approaches that identify phase interfaces with surfaces of strain discontinuity

global weak solution and blow up criterion of the general ericksen leslie system for nematic liquid crystal flows abstract in this paper we investigate the three dimensional general ericksen leslie e l system with ginzburg landau type approximation modeling nematic liquid crystal flows first by overcoming the difficulties from lack of maximum principle for the director equation and high order nonlinearities for the stress tensor we prove existence of global in time weak solutions under physically meaningful boundary conditions and suitable assumptions on the leslie coefficients which ensures that the total energy of the e l system is dissipated moreover for the e l system with periodic boundary conditions we prove the local well posedness of classical solutions under the so called parodi s relation and establish a blow up criterion in terms of the temporal integral of both the maximum norm of the curl of the velocity field and the maximum norm of the gradient of the liquid crystal director field

nonlinear theory of defects in nematic liquid crystals phase transition and flow phenomena this is a summary of some recent mathematical advances in the theory of defects in nematic liquid crystals it also includes some new results concerning disclinations line defects which have not been published elsewhere

nonparabolic dissipative systems modeling the flow of liquid crystals we study a simplified system which retains most of the interesting mathematical properties of the original ericksen leslie equations for the flow of liquid crystals this is a coupled nonparabolic dissipative dynamic system we derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions we also discuss uniqueness and some stability properties of the system 1995 john wiley sons inc

the small deborah number limit of the doi onsager equation to the ericksen leslie equation we present a rigorous derivation of the ericksen leslie equation starting from the doi onsager equation as in the fluid dynamic limit of the boltzmann equation we first make the hilbert expansion for the solution of the doi onsager equation the existence of the hilbert expansion is connected to an open question whether the energy of the ericksen leslie equation is dissipated we show that the energy is dissipated for the ericksen leslie equation derived from the doi onsager equation the most difficult step is to prove a uniform bound for the remainder in the hilbert expansion this question is connected to the spectral stability of the linearized doi onsager operator around a critical point by introducing two important auxiliary operators the detailed spectral information is obtained for the linearized operator around all critical points however these are not enough to justify the small deborah number limit for the inhomogeneous doi onsager equation since the elastic stress in the velocity equation is also strongly singular for this we need to establish a precise lower bound for a bilinear form associated with the linearized operator in the bilinear form the interactions between the part inside the kernel and the part outside the kernel of the linearized operator are very complicated we find a coordinate transform and introduce a five dimensional space called the maier saupe space such that the interactions between two parts can been seen explicitly by a delicate argument of completing the square however the lower bound is very weak for the part inside the maier saupe space in order to apply them to the error estimates we have to analyze the structure of the singular terms and introduce a suitable energy functional

a stochastic model of dimensionless thunderstorm rainfall a concise stochastic model for the nondimensional thunderstorm rainfall process at a point is proposed the accumulated precipitation process for individual thunderstorms is nondimensionalized by dividing the precipitation at any time by the total precipitation and the elapsed time by the total duration the dimensionless process is divided into 100 equal time increments and the depth increments are rescaled to range between 0 and 1 the sequence of rescaled increments z1 z2 z9 are assumed to represent a nonhomogeneous markov process in discrete time with continuous state space the expected value of the kth rescaled increment given the k 1st increment is assumed to be a linear function of that increment and the marginal distribution of the first increment and the conditional distributions are assumed to be described by the beta distribution an analyses of data for 275 thunderstorms observed at the walnut gulch experimental watershed in southeastern arizona showed that the proposed model structure is a good approximation for this region the number of model parameters can be reduced from 26 to a minimum of 10 by approximating the 2 parameters in the conditional expectation function and the conditional beta parameter as polynomial functions of the dimensionless time likelihood ratio tests and the akaike information criterion suggest that the dependence parameters are independent of storm amount and duration but the conditional beta parameter k is larger for short duration storms than for long duration storms a 13 parameter model is recommended for disaggregating thunderstorm rainfall in southeastern arizona

asymptotics of minimizers of variational problems involving curl functional in this paper we are concerned with singularly perturbed variational problems involving the curl functional which arise in the mathematical theory of liquid crystals the asymptotic behavior of the minimizers in the singular limiting process is discussed which is closely related to the variational problems for curl functional under various constraints

a stochastic model of dimensionless hyetograph a very simple statistical model is proposed to describe the time distribution of rainfall within a rainy event the modeled process is the dimensionless hyetograph h tj that represents the fraction of rainfall accumulated over the time interval 0 tj where tj is a fraction of the total duration in any rainy episode lasting n 1 units of time the sequence h t1 h tn is described as an ordered sample from the beta distribution dimensionless rainfall from hourly data at three stations in southern spain show little dependence on rainfall duration amount of precipitation or period of the year these results though not essential to the model structure simplify its formulation reducing the number of parameters other features of the historical records such as correlations maximum dimensionless hourly precipitation or frequency curves are reasonably well reproduced by the model