an operational measure for squeezing we propose and analyse a mathematical measure for the amount of squeezing contained in a continuous variable quantum state we show that the proposed measure operationally quantifies the minimal amount of squeezing needed to prepare a given quantum state and that it can be regarded as a squeezing analogue of the entanglement of formation we prove that the measure is convex and subadditive and we provide analytic bounds as well as a numerical convex optimisation algorithm for its computation by example we then show that the amount of squeezing needed for the preparation of certain multi mode quantum states can be significantly lower than naive state preparation suggests

computation of three dimensional multiphase flow dynamics by fully coupled immersed flow fcif solver abstract this work presents a fully coupled immersed flow fcif solver for the three dimensional simulation of fluid fluid interaction by coupling two distinct flow solvers using an immersed boundary ib method the fcif solver captures dynamic interactions between two fluids with disparate flow properties while retaining the desirable simplicity of non boundary conforming grids for illustration we couple an ib based unsteady reynolds averaged navier stokes urans simulator with a depth integrated long wave solver for the application of slug development with turbulent gas and laminar liquid we perform a series of validations including turbulent laminar flows over prescribed wavy boundaries and freely evolving viscous fluids these confirm the effectiveness and accuracy of both one way and two way coupling in the fcif solver finally we present a simulation example of the evolution from a stratified turbulent laminar flow through the initiation of a slug that nearly bridges the channel the results show both the interfacial wave dynamics excited by the turbulent gas forcing and the influence of the liquid on the gas turbulence these results demonstrate that the fcif solver effectively captures the essential physics of gas liquid interaction and can serve as a useful tool for the mechanistic study of slug generation in two phase gas liquid flows in channels and pipes

renormalized meshfree schemes i consistency stability and hybrid methods for conservation laws this paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives the renormalized meshfree derivatives which improve the consistency of the original weighted particle methods the weak renormalized meshfree scheme built from the weak formulation of general conservation laws turns out to be l 2 stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field a time discretization is then performed by analogy with finite volume methods and the l 1 l infty and bv stabilities of the obtained time discretized scheme are studied from the same analogy with finite volume methods a hybrid particle scheme is built using the godunov method and is numerically compared to the weak renormalized scheme

an accurate low mach scheme for a compressible two fluid model applied to free surface flows classical approximate riemann solvers are known to be too much dissipative in the low mach number regime for this reason since the mach number in liquids is generally very small usual upwind schemes may provide inaccurate solutions when applied to the simulation of two phase flows in this paper to circumvent this difficulty while keeping a compressible model for the description of both gas and liquid an original accurate low mach scheme is introduced and theoretically studied extending some ideas already used for the gas dynamics system the proposed scheme is based on a centred formulation for the pressure gradient term in the momentum equation and on the introduction of a stabilising term proportional to the pressure difference between two neighbouring cells the scheme stability is ensured and theoretically proved under a convective cfl like condition by using a semi implicit time discretisation algorithm finally the correct asymptotic behaviour of the scheme in the limit of small mach numbers is assessed on several academic test cases

convexity with respect to holder mean involving zero balanced hypergeometric functions in this note we investigate the convexity of zero balanced hypergeometric functions with respect to holder mean

functional inequalities for the quotients of hypergeometric functions letf a b c x be the gaussian hypergeometric series and for 0 r 1 let formula g d anderson m k vamanamurthy and m vuorinen raised recently the following problem for whicha b 0 1 does formula hold for allr s 0 1 they also proved this inequality fora b 1 2 the main purpose of this paper is to give an answer to this problem fora b 1 and to find a lower bound for the summ r m s fora 0 2 andb 0 2 a

stability theory for difference approximations of euler korteweg equations and application to thin film flows we study the stability of various difference approximations of the euler korteweg equations this system of evolutionary pdes is a classical isentropic euler system perturbed by a dispersive third order term the euler equations are discretized with a classical scheme e g roe rusanov or lax friedrichs scheme whereas the dispersive term is discretized with centered finite differences we first prove that a certain amount of numerical viscosity is needed for a difference scheme to be stable in the von neumann sense then we consider the entropy stability of difference approximations for that purpose we introduce an additional unknown the gradient of a function of the density the euler korteweg system is transformed into a hyperbolic system perturbed by a second order skew symmetric term we prove entropy stability of lax friedrichs type schemes under a suitable courant friedrichs levy condition in addition we propose a spatial discretization of the euler korteweg system seen as a hamil

functional inequalities for the ratio of complete p elliptic integrals abstract in this paper we show monotonicity and convexity properties of a function involving the ratio of complete p elliptic integrals which reduces to the modulus of the grotzsch ring as applications we obtain several sharp functional inequalities

turan type inequalities for generalized complete elliptic integrals in this paper our aim is to establish some turan type inequalities for gaussian hypergeometric functions and for generalized complete elliptic integrals these results complete the earlier result of p turan proved for legendre polynomials moreover we show that there is a close connection between a turan type inequality and a sharp lower bound for the generalized complete elliptic integral of the first kind at the end of this paper we prove a recent conjecture of t sugawa and m vuorinen related to estimates of the hyperbolic distance of the twice punctured plane

concavity of the complete elliptic integrals of the second kind with respect to holder means abstract in this paper we establish a necessary and sufficient condition for the concavity of the complete elliptic integrals of the second kind with respect to holder means

geometrically concave univariate distributions in this paper our aim is to show that if a probability density function is geometrically concave convex then the corresponding cumulative distribution function and the survival function are geometrically concave convex too under some assumptions the proofs are based on the so called monotone form of l hospital s rule and permit us to extend our results to the case of the concavity convexity with respect to holder means to illustrate the applications of the main results we discuss in details the geometrical concavity of the probability density function cumulative distribution function and survival function of some common continuous univariate distributions moreover at the end of the paper we present a simple alternative proof to schweizer s problem related to the mulholland s generalization of minkowski s inequality

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

an accurate multi regime sph scheme for barotropic flows abstract this paper focuses on the use of a mesh less numerical method to solve barotropic fluid flows smooth particle hydrodynamics sph such methods suffer from a severe lack of accuracy when evaluating state variables as the pressure field sph ale methods based on riemann solvers significantly improve this evaluation but increase the scheme complexity and low mach issues are difficult to prevent we propose an alternative scheme called s p h a l e relying on the combination of the sph ale formalism and a finite volume stabilizing low mach scheme applied to monophasic barotropic euler equations its characteristics are detailed and evaluated through a nonlinear stability analysis highlighting cfl like conditions on the scheme parameters as far as we know it is the first time such nonlinear analysis is performed on a sph ale scheme finally its implementation on several academic test cases reveals that the proposed scheme actually increases both stability and accuracy in reduced computation time with respect to sph ale riemann solvers

generalized hersch pfluger distortion function and complete elliptic integrals abstract in this paper we study the relationship between the generalized hersch pfluger distortion function k a r and complete elliptic integrals of the second kind e r and establish several inequalities for k a r and e r

some properties of a generalized hamy symmetric function and its applications abstract this paper is concerned with the generalized hamy symmetric function n x r f 1 i 1 i 2 i r n f j 1 r x i j 1 r where f is a positive function defined in a subinterval of 0 some properties including schur convexity geometric schur convexity and harmonic schur convexity are investigated as applications several inequalities are obtained some of which extend the known ones

functional inequalities involving special functions ii this paper is motivated by an open problem of anderson vamanamurthy and vuorinen we prove a chain of inequalities for hypergeometric functions generalized and normalized bessel functions kummer functions and for some general power series some particular cases and refinements are given

concavity with respect to holder means involving the generalized grotzsch function the generalized grotzsch function has numerous applications in geometric function theory and analytic number theory and its properties have been investigated by many authors in this paper we study the concavity of the generalized grotzsch function with respect to holder means

inequalities for means abstract a monotone form of l hospital s rule is obtained and applied to derive inequalities between the arithmetic geometric mean of gauss the logarithmic mean and stolarsky s identric mean some related inequalities are given for complete elliptic integrals

monotonicity criterion for the quotient of power series with applications abstract in this paper we present the necessary and sufficient condition for the monotonicity of the quotient of power series as applications some gaps and misquotations in certain published articles are pointed out and corrected and some known results involving the landen inequalities for zero balanced hypergeometric functions are improved

a numerical reduced model for thin liquid films sheared by a gas flow the non linear dynamics of thin liquid films sheared by a laminar gas flow in a channel is investigated such a two layer flow is driven by pressure gradient and possibly by the gravity force we describe the liquid phase with a long wave integral model with the aim to save computational cost with respect to the full direct numerical simulation dns of the navier stokes equations we derive this long wave model by the integration of the navier stokes equations over the film thickness and by an asymptotic expansion up to the first order in terms of a long wave parameter these depth integrated or shallow water equations are discretized by means of an augmented system which holds an evolution equation for the surface tension in order to avoid numerical instabilities of classical upwind and centered schemes on the other side we study the gas phase with compressible navier stokes equations and we discretize them by means of a low mach scheme accounting also for moving meshes ale in order to analyze liquid gas interactions we introduce then a coupling methodology between depth integrated equations and navier stokes equations this approach represents a compromise between the two existing methods the full dns and the full long wave model applied to both phases in order to validate this approach we present comparisons with dns showing a good agreement of spatio temporal evolutions of the film thickness and the stress field furthermore interfacial shear stress and pressure gradient evolutions are shown to be in accordance with those provided by two layer second order low dimensional models

generalized convexity and inequalities abstract let r 0 and let m be the family of all mean values of two numbers in r some examples are the arithmetic geometric and harmonic means given m 1 m 2 m we say that a function f r r is m 1 m 2 convex if f m 1 x y m 2 f x f y for all x y r the usual convexity is the special case when both mean values are arithmetic means we study the dependence of m 1 m 2 convexity on m 1 and m 2 and give sufficient conditions for m 1 m 2 convexity of functions defined by maclaurin series the criteria involve the maclaurin coefficients our results yield a class of new inequalities for several special functions such as the gaussian hypergeometric function and a generalized bessel function

the inverse hyperbolic tangent function and jacobian sine function abstract the holder convexity of the composition of inverse hyperbolic tangent function and jacobian sine function is investigated in this paper

inequalities for zero balanced hypergeometric functions the authors study certain monotoneity and convexity properties of the gaussian hypergeometric function and those of the euler gamma function

functional inequalities for modified struve functions in this paper by using a general result on the monotonicity of quotients of power series our aim is to prove some monotonicity and convexity results for the modified struve functions moreover as consequences of the above mentioned results we present some functional inequalities as well as lower and upper bounds for modified struve functions our main results complement and improve the results of joshi and nalwaya

an accurate adaptive solver for surface tension driven interfacial flows a method combining an adaptive quad octree spatial discretisation geometrical volume of fluid interface representation balanced force continuum surface force surface tension formulation and height function curvature estimation is presented the extension of these methods to the quad octree discretisation allows adaptive variable resolution along the interface and is described in detail the method is shown to recover exact equilibrium to machine accuracy between surface tension and pressure gradient in the case of a stationary droplet irrespective of viscosity and spatial resolution accurate solutions are obtained for the classical test case of capillary wave oscillations an application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method the source code of the implementation is freely available as part of the gerris flow solver

mills ratio monotonicity patterns and functional inequalities in this paper we study the monotonicity properties of some functions involving the mills ratio of the standard normal law from these we deduce some new functional inequalities involving the mills ratio and we show that the mills ratio is strictly completely monotonic at the end of this paper we present some turan type inequalities for mills ratio