weak solutions for an initial boundary q tensor problem related to liquid crystals abstract the coupled navier stokes and q tensor system is considered in a bounded three dimensional domain under homogeneous dirichlet boundary conditions for the velocity u and either nonhomogeneous dirichlet or homogeneous neumann boundary conditions for the tensor q the corresponding initial value problem in the whole space r 3 was analyzed in paicu and zarnescu 2012 in this paper three main results concerning weak solutions will be proved the existence of global in time weak solutions bounded up to infinite time a uniqueness criteria and a maximum principle for q moreover we identify how to modify the system to deduce symmetry and traceless for q for any weak solution the presence of a stretching term in the q system plays a crucial role in all the analysis

the effect of attribute ranges on weights in multiattribute utility measurements multiattribute utility theory requires a specific relation between the range of outcomes of each attribute and the weight for that attribute the greater the range the greater the weight has to be experimental results show that subjects do not adjust their judgments properly if the range is varied for the two methods tested the adjustment is smaller than required by theory the bias was smaller for a regression procedure than for the direct ratio method weights based on an intuitive range were not found to be superior to those elicited over different ranges

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

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

global well posedness and decay for a q tensor model of incompressible nematic liquid crystals in rn abstract we consider the motion of a viscous incompressible liquid crystal flow in the n dimensional space r n we study the global well posedness of strong solutions in the l p l q maximal regularity class

global existence and regularity of solutions for active liquid crystals we study the hydrodynamics of active liquid crystals in the beris edwards hydrodynamic framework with the landau de gennes q tensor order parameter to describe liquid crystalline ordering the existence of global weak solutions in two and three spatial dimensions is established in the two dimensional case by the littlewood paley decomposition the higher regularity of the weak solutions and the weak strong uniqueness are also obtained

global well posedness and long time dynamics for a higher order quasi geostrophic type equation abstract in this paper we study a higher order viscous quasi geostrophic type equation this equation was derived in 11 as the limit dynamics of a singularly perturbed navier stokes korteweg system with coriolis force when the mach rossby and weber numbers go to zero at the same rate the scope of the present paper is twofold first of all we investigate well posedness of such a model on the whole space r 2 we prove that it is well posed in h s for any s 3 globally in time interestingly enough we show that this equation owns two levels of energy estimates for which one gets existence and uniqueness of weak solutions with different regularities namely h 3 and h 4 regularities this fact can be viewed as a remainder of the so called bd entropy structure of the original system in the second part of the paper we investigate the long time behavior of these solutions we show that they converge to the solution of the corresponding linear parabolic type equation with same initial datum and external force our proof is based on dispersive estimates both for the solutions to the linear and non linear problems

global strong solution to the three dimensional liquid crystal flows of q tensor model abstract a complex hydrodynamic system that models the fluid of nematic liquid crystals in a bounded domain in r 3 is studied the system is a forced incompressible navier stokes equation coupled with a parabolic type equation of q tensors we invoke the maximal regularity of the stokes operators and parabolic operators in besov spaces to obtain the local strong solution if the initial q tensor is not too wild in addition it is showed that such solution can be extended to a global one if the initial data is a sufficiently small perturbation around the trivial equilibrium state finally it is proved that the global strong solution obtained here is identical to those weak solutions obtained in paicu and zarnescu 26

from the q tensor flow for the liquid crystal to the harmonic map flow in this paper we consider the solutions of the relaxed q tensor flow in mathbb r 3 with small parameter epsilon we show that the limiting map is the so called harmonic map flow as a consequence we present a new proof for the global existence of a weak solution for the harmonic map flow in three dimensions as in 18 23 where the ginzburg landau approximation approach was used

global well posedness and twist wave solutions for the inertial qian sheng model of liquid crystals abstract we consider the inertial qian sheng model of liquid crystals which couples a hyperbolic type equation involving a second order material derivative with a forced incompressible navier stokes system we study the energy law and prove a global well posedness result we further provide an example of twist wave solutions that is solutions of the coupled system for which the flow vanishes for all times

a global 2d well posedness result on the order tensor liquid crystal theory abstract in 18 paicu and zarnescu have studied an order tensor system which describes the flow of a liquid crystal they have proven the existence of weak solutions the propagation of higher regularity namely h s with s 1 and the weak strong uniqueness in dimension two this paper is devoted to fill the gap of their results namely to propagate the low regularity namely h s for 0 s 1 and to prove the uniqueness of the weak solutions for the completeness of this research we also propose an alternative approach in order to prove the existence of weak solutions

global well posedness of the two dimensional beris edwards system with general laudau de gennes free energy abstract in this paper we consider the beris edwards system for incompressible nematic liquid crystal flows the system under investigation consists of the navier stokes equations for the fluid velocity u coupled with an evolution equation for the order parameter q tensor one important feature of the system is that its elastic free energy takes a general form and in particular it contains a cubic term that possibly makes it unbounded from below in the two dimensional periodic setting we prove that if the initial l norm of the q tensor is properly small then the system admits a unique global weak solution the proof is based on the construction of a specific approximating system that preserves the l norm of the q tensor along the time evolution

global weak solutions to the active hydrodynamics of liquid crystals abstract we consider the incompressible flow of the active hydrodynamics of liquid crystals with inhomogeneous density in the beris edwards hydrodynamics framework the landau de gennes q tensor order parameter is used to describe the liquid crystalline ordering faedo galerkin s method is adopted to construct the solutions for the initial boundary value problem two levels of approximations are used and the weak convergence is obtained through compactness estimates by new techniques due to the active terms the existence of global weak solutions in dimension two and three is established in a bounded domain

on the global well posedness of a class of 2d solutions for the rosensweig system of ferrofluids abstract we study a class of 2d solutions of a bloch torrey regularization of the rosensweig system in the whole space which arise when the initial data and the external magnetic field are 2d we prove that such solutions are globally defined if the initial data is in h k r 2 k 1

well posedness for the fene dumbbell model of polymeric flows we prove local and global well posedness for the fene dumbbell model for a very general class of potentials indeed in prior local or global well posedness results conditions on the strength of the singularity or on the parameter b were made here we give a proof in the general case we also prove global existence results if the data is small or if we restrict to the co rotational model in dimension 2 2008 wiley periodicals inc

a novel linear second order unconditionally energy stable scheme for a hydrodynamic q tensor model of liquid crystals abstract the hydrodynamic q tensor model has been used for studying flows of liquid crystals and liquid crystal polymers it can be derived from a variational approach together with the generalized onsager principle in which the total energy decreases in time in this paper we develop a novel linear second order semi discrete scheme in time to solve the governing system of equations in the model the scheme is developed following the novel energy quadratization strategy so that it is linear and unconditionally energy stable at the semi discrete level this scheme is further discretized in space using a second order finite difference method and implemented on a gpu for high performance computing the convergence rate in time is established using a mesh refinement test several numerical examples are presented to demonstrate the usefulness of the model and the effectiveness of the numerical scheme in simulating defect dynamics in flows of liquid crystals

liquid crystal flows in two dimensions this paper is concerned with a simplified hydrodynamic equation proposed by ericksen and leslie modeling the flow of nematic liquid crystals in dimension two we establish both interior and boundary regularity theorems for such a flow under smallness conditions as a consequence we establish the existence of global in time weak solutions on a bounded smooth domain in mathbb r 2 which are smooth everywhere with possible exceptions of finitely many singular times

smaa 2 stochastic multicriteria acceptability analysis for group decision making stochastic multicriteria acceptability analysis smaa is a multicriteria decision support method for multiple decision makers in discrete problems in smaa the decision makers need not express their preferences explicitly or implicitly instead the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one inaccurate or uncertain criteria values are represented by probability distributions from which the method computes confidence factors describing the reliability of the analysis in this paper we introduce the smaa 2 method which extends the original smaa by considering all ranks in the analysis in situations where the elitistic smaa may assess large acceptability only for extreme alternatives without sufficient majority support the more holistic smaa 2 analysis can be used to identify good compromise candidates the results are presented graphically we consider also situations where partial preference information is available we demonstrate the new method using a real life decision problem

comparison of weighting judgments in multiattribute utility measurement this paper compares four weighting methods in multiattribute utility measurement the ratio method the swing weighting method the tradeoff method and the pricing out method 200 subjects used these methods to weight attributes for evaluating nuclear waste repository sites in the united states the weighting methods were compared with respect to their internal consistency convergent validity and external validity internal consistency was measured by the degree to which ordinal and cardinal or ratio responses agreed within the same weighting method convergent validity was measured by the degree of agreement between the weights elicited with different methods external validity was determined by the degree to which weights elicited in this experiment agreed with weights that were elicited with managers of the department of energy in terms of internal consistency the tradeoff method fared worst in terms of convergent validity the pricing out method turned out to be an outlier in terms of external validity the pricing out method showed the best results while the ratio and swing methods are quite consistent and show a fair amount of convergent validity their external validity problems cast doubt on their usefulness the main recommendation for applications is to improve the internal consistency of the tradeoff method by careful interactive elicitation and to use it in conjunction with the pricing out method to enhance its external validity

energy dissipation and regularity for a coupled navier stokes and q tensor system we study a complex non newtonian fluid that models the flowof nematic liquid crystals the fluid is described by a system that couples a forced navier stokes system with a parabolic type system we prove the existence of global weak solutions in dimensions two and three we show the existence of a lyapunov functional for the smooth solutions of the coupled system and use cancellations that allow its existence to prove higher global regularity in dimension two we also show the weak strong uniqueness in dimension two

landau de gennes theory of nematic liquid crystals the oseen frank limit and beyond we study global minimizers of a continuum landau de gennes energy functional for nematic liquid crystals in three dimensional domains subject to uniaxial boundary conditions we analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly in w1 2 to a global minimizer predicted by the oseen frank theory for uniaxial nematic liquid crystals with constant order parameter moreover the convergence is uniform in the interior of the domain away from the singularities of the limiting oseen frank global minimizer we obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the landau de gennes global minimizer we also study the interplay between biaxiality and uniaxiality in landau de gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions

strictly physical global weak solutions of a navier stokes q tensor system with singular potential we study the existence regularity and so called strict physicality of global weak solutions of a beris edwards system which is proposed as a model for the incompressible flow of nematic liquid crystal materials an important contribution to the dynamics comes from a singular potential introduced by john ball and apala majumdar which replaces the commonly employed landau de gennes bulk potential this is built into our model to ensure that a natural physical constraint on the eigenvalues of the q tensor order parameter is respected by the dynamics of this system moreover by a maximum principle argument we are able to construct global strong solutions in dimension two

existence of solutions for the ericksen leslie system we study the general ericksen leslie system which describes the flow of liquid crystal materials the dissipation property of the system is established and is used to prove the global existence of weak solutions we also study the existence of classical solutions and the asymptotic stability of the solutions

on q gaussians and exchangeability the q gaussian distributions introduced by tsallis are discussed from the point of view of variance mixtures of normals and exchangeability for each there is a q gaussian distribution that maximizes the tsallis entropy under suitable constraints this paper shows that q gaussian random variables can be represented as variance mixtures of normals when q 1 these variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables thereby providing a possible model that has been extensively studied in probability theory the formulation provided has the additional advantage of yielding for each q a process which is naturally the q analog of the brownian motion explicit mixing distributions for q gaussians should facilitate applications to areas such as option pricing the model might provide insight into the study of superstatistics

optimal boundary control of a simplified ericksen leslie system for nematic liquid crystal flows in 2d in this paper we investigate an optimal boundary control problem for a two dimensional simplified ericksen leslie system modelling the incompressible nematic liquid crystal flows the hydrodynamic system consists of the navier stokes equations for the fluid velocity coupled with a convective ginzburg landau type equation for the averaged molecular orientation the fluid velocity is assumed to satisfy a no slip boundary condition while the molecular orientation is subject to a time dependent dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals we first establish the existence of optimal boundary controls then we show that the control to state operator is frechet differentiable between appropriate banach spaces and derive first order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables

on hydrodynamics of viscoelastic fluids in this paper we study a hydrodynamic system describing fluids with viscoelastic properties after a brief examination of the relations between several models we shall concentrate on a few analytical issues concerning them in particular we establish local existence and global existence with small initial data of classical solutions for an oldroyd system without an artificially postulated damping mechanism

smaa stochastic multiobjective acceptability analysis stochastic multiobjective acceptability analysis smaa is a multicriteria decision support technique for multiple decision makers based on exploring the weight space inaccurate or uncertain input data can be represented as probability distributions in smaa the decision makers need not express their preferences explicitly or implicitly instead the technique analyses what kind of valuations would make each alternative the preferred one the method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative a central weight vector representing the typical valuations resulting in that decision and a confidence factor measuring whether the input data is accurate enough for making an informed decision

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

decision quality using ranked attribute weights three published approximation formulae for selecting the best multiattribute alternative based on rank ordered weights are evaluated all formulae are surprisingly efficacious in determining the best multiattribute alternative rank order centroid roc weights are more accurate than the other rank based formulae furthermore the roc formula generalizes to incorporate both other forms of partial information about attribute weights and partial rank order information as well because a roc based analysis is so straightforward and efficacious it provides an appropriate implementation tool

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions