optimal phase control for equal gain transmission in mimo systems with scalar quantization complexity and algorithms the complexity of the optimal phase control problem in wireless mimo systems with scalar feedback quantization and equal gain transmission is studied the problem is shown to be np hard when the number of receive antennas grows linearly with the number of transmit antennas for the case where the number of receive antennas is constant the problem can be solved in polynomial time an optimal algorithm is explicitly constructed for practical purposes a low complexity algorithm based on local search is presented simulation results show that its performance is nearly optimal

probability of error for equal gain combiners over rayleigh channels some closed form solutions the probability of error of a general equal gain combiner eg in closed form is not available in the literature by formulating the problem in the framework of signal detection and evaluating the probability of error directly from the characteristic function cf of the signal at the combiner output we obtain closed form solutions for the probability of error of the eg combiner with two or three branches operating over a rayleigh fading channel

adaptive biorthogonal spline schemes for advection reaction equations in this paper based on eulerian lagrangian localized adjoint method ellam we use biorthogonal spline wavelets to develop numerical schemes for multidimensional advection reaction equations the derived schemes produce accurate numerical solutions even if large time steps are used these schemes are explicit but unconditionally stable they also have the ability to carry out adaptive compression while preserving the total mass numerical experiments including observations on their convergence rates are presented to show the strong potential of these methods

sensitivity to timing errors in egc and mrc techniques the effect of imperfect timing is analyzed in equal gain combining egc and maximal ratio combining mrc techniques over rayleigh and nakagami m fading channels with binary phase shift keying modulation in the case of egc the bit error probability is derived while in the case of mrc error rate bounds are presented theoretical results are justified by computer simulation numerical results demonstrate that both egc and mrc are fairly sensitive to timing errors and comparatively mrc is more sensitive

the reversing of interfaces in slow diffusion processes with strong absorption this paper considers a family of one dimensional nonlinear diffusion equations with absorption in particular the solutions that have interfaces that change their direction of propagation are examined although this phenomenon of reversing interfaces has been seen numerically and some special exact solutions have been obtained there was previously no analytical insight into how this occurs in the general case the approach taken here is to seek self similar solutions local to the interface and local to the reversing time the analysis is split into two parts one for the solution prior to the reversing time and the other for the solution after the reversing time in each case the governing pde is reduced to an ode by introducing a self similar coordinate system these odes do not readily admit any nontrivial exact solutions and so the asymptotic behavior of solutions is studied by doing this the adjustable parameters or degrees of freedom which may be used in a numerical shooting scheme are determined a numerical algorithm is then proposed to furnish solutions to the odes and hence the pde in the limit of interest as examples of physical problems in which a pde of this type may be used as a model the authors study the spreading of a viscous film under gravity and subject to evaporation the dispersion of a population and a nonlinear heat conduction problem the numerical algorithm is demonstrated using these examples results are also given on the possible existence of self similar solutions and types of reversing behavior that can be exhibited by pdes in the family of interest

on the design of general purpose flux limiters for finite element schemes i scalar convection the algebraic flux correction afc paradigm is extended to finite element discretizations with a consistent mass matrix it is shown how to render an implicit galerkin scheme positivity preserving and remove excessive artificial diffusion in regions where the solution is sufficiently smooth to this end the original discrete operators are modified in a mass conserving fashion so as to enforce the algebraic constraints to be satisfied by the numerical solution a node oriented limiting strategy is employed to control the raw antidiffusive fluxes which consist of a convective part and a contribution of the consistent mass matrix the former offsets the artificial diffusion due to upwinding of the spatial differential operator and lends itself to an upwind biased flux limiting the latter eliminates the error induced by mass lumping and calls for the use of a symmetric flux limiter the concept of a target flux and a new definition of upper lower bounds make it possible to combine the advantages of algebraic fct and tvd schemes introduced previously by the author and his coworkers unlike other high resolution schemes for unstructured meshes the new algorithm reduces to a consistent high order galerkin scheme in smooth regions and is designed to provide an optimal treatment of both stationary and time dependent problems its performance is illustrated by application to the linear advection equation for a number of 1d and 2d configurations

regularity of the free boundary for the porous medium equation with r m 1 m 1 when u 0 then f 0 and both of the above equations become degenerate this degeneracy results in the interesting phenomenon of the finite speed of propagation if the initial data u is compactly supported in 1ztn the solution u t will remain compactly supported for all time t in this work we will show that under rather general assumptions on the initial data the free boundary

exact evaluation of maximal ratio and equal gain diversity receivers for m ary qam on nakagami fading channels exact integral expressions are derived for calculating the symbol error rate ser of multilevel quadrature amplitude modulation mqam in conjunction with l fold antenna diversity on arbitrary nakagami fading channel both maximal ratio combining mrc in independent and correlated fading and equal gain combining egc predetection in independent fading diversity techniques have been considered exact closed form ser expressions for two restricted nakagami fading cases mrc reception are also derived an exact analysis of egc for mqam has not been reported previously despite its practical interest remarkably the exact ser integrals can also be replaced by a finite series approximation formula a useful procedure for computing the confluent hypergeometric series is also presented

from a discrete to a continuum model of cell dynamics in one dimension multiscale modeling is emerging as one of the key challenges in mathematical biology however the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions for example at the cellular scale how can the appropriate discrete cell level model be identified in a given context additionally how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior in order to begin to address such questions we consider a discrete one dimensional cell based model in which cells are assumed to interact via linear springs from the discrete equations of motion the continuous rouse p e rouse j chem phys 21 1272 1953 model is obtained this formalism readily allows the definition of a cell number density for which a nonlinear fast diffusion equation is derived excellent agreement is demonstrated between the continuum and discrete models subsequently via the incorporation of cell division we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail in the limit of stiff springs where cells can be considered to be incompressible we show that cell velocity can be directly related to cell production this assumption is frequently made in the literature but our derivation places limits on its validity finally the model is compared with a model of a similar form recently derived for a different discrete cell based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models

eventual c regularity and concavity for flows in one dimensional porous media we study the regularity and the asymptotic behavior of the solutions of the initial value problem for the porous medium equation u t eft u m ight xx inq r imes eft 0 nfty ight ueft x 0 ight u 0 eft x ight forx n r

on some differential invariants for a family of diffusion equations the equivalence transformation algebra le and some of its differential invariants for the class of equations ut h u ux x f x u ux h 0 are obtained using these invariants we characterize subclasses which can be mapped by means of an equivalence transformation into the well studied family of equations vt vkvx x

self similar solution in the leith model of turbulence anomalous power law and asymptotic analysis we consider a leith model of turbulence leith c 1967 phys fluids 10 1409 in which the energy spectrum obeys a nonlinear diffusion equation we analytically prove the existence of a self similar solution with a power law asymptotic on the low wavenumber end and a sharp boundary on the high wavenumber end which propagates to infinite wavenumbers in a finite time t we prove that this solution has a power law asymptotic with an anomalous exponent x which is less than the kolmogorov value x 5 3 this is a result that was previously discovered by numerical simulations in connaughton and nazarenko 2004 phys rev lett 92 044501 we also prove the convergence to this self similar solution of the spectrum evolving from an arbitrary finitely supported initial data as t t

interfaces with a corner point in one dimensional porous medium flow we prove that for a large class of initial distributions the solutions of the initial value problem for the one dimensional porous medium equation have interfaces which start to move abruptly after a positive waiting time this happens for example if the initial pressure is o x 2 as x 0 we also give sufficient conditions for the smoothness of the interface which improve previous results

exact similarity solutions to some nonlinear diffusion equations the author gives new closed form similarity solutions to n dimensional radially symmetric nonlinear diffusion equations with power law and exponential diffusivities these solutions are generalisations of known similarity solutions

exact polynomial solutions to some nonlinear diffusion equations abstract a class of non group invariant exact solutions to a number of nonlinear diffusion equations is constructed expressed in the appropriate variables these solutions are polynomials in the spatial variable the method is mainly applicable to equations which may be written in an appropriate quadratically nonlinear form a number of equivalence transformations between various nonlinear diffusion equations are also derived

potential symmetries of a porous medium equation potential symmetries which are not local symmetries are carried out for the porous medium equation where when it can be written in a conserved form these symmetries are realized as local symmetries of a related auxiliary system and lead to the construction of corresponding invariant solutions as well as to the linearization of the equation by non invertible mappings

some non self similar solutions to a nonlinear diffusion equation the author generates exact solutions to the nonlinear diffusion equation ut del u 1 2 del u which are not similarity solutions some applications and generalizations are indicated

nonclassical symmetry reductions of a porous medium equation with convection in this paper new symmetry reductions and exact solutions are presented for the porous medium equation with convection those spatial forms for which the equation can be reduced to an ordinary differential equation are studied the symmetry reductions and exact solutions presented are derived by using the nonclassical method developed by bluman and cole and are unobtainable by lie classical method the asymptotic behaviour of some of the new solutions is analysed

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

some notes on the fourier transform methods for error rate analysis of equal gain combining transform techniques based on moment generating functions mgfs and characteristic functions chfs have recently provided efficient analytical tools for the performance evaluation of digital communication systems over fading channels more recently the convolution theorem of the fourier transform has been employed to obtain unified expressions for the average error probabilities of equal gain combining egc diversity reception in terms of the chfs of the branches amplitude gains in this paper we prove that these expressions include redundant terms furthermore simpler analytical expressions for the average error rates of egc diversity reception can be obtained when the convolutional theorem of the sine and cosine transforms are used instead of the conventional fourier transform

flux correction tools for finite elements flux correction in the finite element context is addressed criteria for positivity of the numerical solution are formulated and the low order transport operator is constructed from the discrete high order operator by adding modulated dissipation so as to eliminate negative off diagonal entries the corresponding antidiffusive terms can be decomposed into a sum of genuine fluxes rather than element contributions which represent bilateral mass exchange between individual nodes thereby essentially one dimensional flux correction tools can be readily applied to multidimensional problems involving unstructured meshes the proposed methodology guarantees mass conservation and makes it possible to design both explicit and implicit fct schemes based on a unified limiting strategy numerical results for a number of benchmark problems illustrate the performance of the algorithm

new exact closed form pdf of the sum of nakagami m random variables with applications an exact closed form expression is developed for the probability density function pdf of the sum of independent but not necessarily identically distributed nakagami m random variables by utilizing the newly developed pdf and the associated developments new exact expressions of the bit error probability are presented for predetection equal gain combining diversity

classical point symmetries of a porous medium equation the lie group formalism is applied to deduce symmetries of the porous medium equation we study those spatial forms that admit the classical symmetry group the reduction obtained from the optimal system of subalgebras are derived some new exact solutions can be obtained

a novel extension to craig s q function formula and its application in dual branch egc performance analysis a novel identity for the gaussian q function of the sum of two non negative variables is introduced as an extension of craig s q function formula it is shown that this new identity provides a unified framework in the performance analysis of dual branch equal gain combining egc diversity similar to that of craig s q function formula for maximum ratio combining diversity then the performance of dual correlated branch egc in nakagami m fading is studied using this novel approach for coherent modulations with error probabilities in terms of the gaussian q function it is shown that the average error probability of the dual correlated branch egc in nakagami m fading is the same as the average error probability of a modeled single channel receiver in the same fading environment using this fact simple exact and approximate closed form expressions for this average error probability are derived the analytical results are verified and illustrated by numerical results and computer simulations

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

large time solution of an inhomogeneous nonlinear diffusion equation the paper considers the large time solution of the nonlinear diffusion equation x u t x c x u u x 0 for initial data with compact support the asymptotic behaviour of x and c x as x defines a parameter space and the nature of the solution at large time depends crucially on the location therein the paper examines the nature and uniformity of the asymptotic solutions for x in a restricted region of the entire parameter space and in certain cases gives the leading error terms a new integral invariant of the solution is also given

on lagrangian schemes for porous medium type generalized diffusion equations a discrete energetic variational approach abstract in this paper we present a systematic framework to derive a variational lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach such discrete energetic variational approaches are analogous to energetic variational approaches 39 25 in a semidiscrete level which provide a basis of deriving the semi discrete equations and can be applied to a large class of partial differential equations with energy dissipation laws and kinematic relations the numerical schemes derived by this framework can inherit the variational structure from the continuous energy dissipation law as an illustration we develop two variational lagrangian schemes for the multidimensional porous medium equations pme based on two different energy dissipation laws we focus on the numerical scheme based on the energy dissipation law with 1 2 u 2 d x as the dissipation functional several numerical experiments demonstrate the accuracy of this scheme as well as its ability in capturing the free boundary and estimating the waiting time for the pme in both 1d and 2d

the non classical solution of the inhomogeneous non linear diffusion equation a complete classification of the symmetry reductions of the inhomogeneous nonlinear diffusion inld equation using the non classical method leads to one family of symmetry generators the resulting ordinary differential equation is of second order and non linear new solutions are obtained for some physical processes corresponding to particular values of n and p m

nonclassical symmetry solutions and the methods of bluman cole and clarkson kruskal nonclassical symmetry solutions of physically relevant partial differential equations are considered via the reduction methods of bluman and cole and clarkson and kruskal consistency conditions will be provided to show that if satisfied these two methods are equivalent in the sense that they lead to the same symmetry solutions the boussinesq equation and burgers equation are used as illustrative examples exact solutions one of which is new will be presented for burgers equation obtained from the bluman and cole method yet not obtainable by clarkson and kruskal s method

finite element formulation for advection reaction equations with change of variable and discontinuity capturing abstract we propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection reaction equations discretized by the finite element method this change of variable confines the concentration below an upper bound in a very natural way for the non negativity constraint we propose to use a discontinuity capturing method defined on the reference element that is combined with an anisotropic crosswind dissipation operator this discontinuity capturing cannot completely eliminate negative values but effectively minimizes their occurrence the proposed methods are applied to different biophysical models and show a good agreement with experimental results for the fda benchmark blood pump for a physiological red blood cell pore formation model

equal gain transmission in multiple input multiple output wireless systems multiple input multiple output mimo wireless systems are of interest due to their ability to provide substantial gains in capacity and quality the paper proposes equal gain transmission egt to provide diversity advantage in mimo systems experiencing rayleigh fading the applications of egt with selection diversity combining equal gain combining and maximum ratio combining are addressed it is proven that systems using egt with any of these combining schemes achieve full diversity order when transmitting over a memoryless flat fading rayleigh matrix channel with independent entries since in practice full channel knowledge at the transmitter is difficult to realize a quantized version of egt is proposed an algorithm to construct a beamforming vector codebook that guarantees full diversity order is presented monte carlo simulation comparisons with various beamforming and combining systems illustrate the performance as a function of quantization

similarity reductions of partial differential equations the author determine the relation between two methods of reduction the similarity reduction method using nonclassical symmetry groups and the direct approach used by clarkson and kruskal 1989 they prove that the solutions which are obtained by similarity in correspondence to nonclassical groups constitute a larger family than the one obtained by the method of clarkson and kruskal the two procedures are equivalent only if the generators zeta x t u tau x t u eta x t u of the nonclassical groups are such that zeta tau is independent of u to explain these results he proves the existence of families of solutions of the burgers equation which are found by means of nonclassical symmetry reduction and which cannot be determined via the general reduction form of clarkson and kruskal

regularity of solutions and interfaces of the porous medium equation via local estimates on demontre la regularite c pour des interfaces mobiles de solutions locales de l equation de milieu poreux

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

space time discretizations using constrained first order system least squares cfosls abstract this paper studies finite element discretizations for three types of time dependent pdes namely heat equation scalar conservation law and wave equation which we reformulate as first order systems in a least squares setting subject to a space time conservation constraint coming from the original pde available piecewise polynomial finite element spaces in n 1 dimensions for functional spaces from the n 1 dimensional de rham sequence for n 2 3 are used for the implementation of the method computational results illustrating the error behavior iteration counts and performance of block diagonal and monolithic geometric multigrid preconditioners are presented for the discrete cfosls system the results are obtained from a parallel implementation of the methods for which we report reasonable scalability

regularity of the free boundary in parabolic phase transition problems in this paper we start the study of the regularity properties of the free boundary for parabolic two phase free boundary problems may be the best known example of a parabolic two phase free boundary problem is the stefan problem a simplified model describing the melting or solidification of a material with a solid liquid interphase the concept of solution can be stated in several ways classical solution weak so lution on divergence form or viscosity solution and as usual one would like to prove that the weak solutions that may be constructed are in fact as smooth and classical as possible locally a classical solution of the stefan problem may be described as following on the unit cylinder q1 b1 1 1 we have two complementary domains and qi separated by a smooth surface s oi2 nq1 in fl and qi we have two smooth solutions ul and u2 of the heat equations

on the distribution of the sum of nakagami m random variables in this paper we investigate the classical problem of finding the probability density function pdf of the sum of nakagami m random variables exact infinite series representations are derived for the sum of three and four identically and independently distributed i i d nakagami m random variables and subsequently it is extended to the sum of general number of random variables a useful pattern emerged as a result of these extensions and a new fourier transform pair that involves parabolic cylinder function and gauss hypergeometric function is obtained bounds on the error resulting from truncation of the infinite series of pdfs are also presented these pdfs are used to analyze the performance of dual triple and quadruple branch predetection equal gain combining egc receivers over nakagami m fading environment furthermore a hypergeometric relation is derived as a result of those derivations subsequently the analysis is extended to the case of l branch egc receiver performance as well selected simulation plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the formulation

an implicit level set method for modeling hydraulically driven fractures we describe a novel implicit level set algorithm to locate the free boundary for a propagating hydraulic fracture a number of characteristics of the governing equations for hydraulic fractures and their coupling present considerable challenges for numerical modeling namely the degenerate lubrication equation the hypersingular elastic integral equation the indeterminate form of the velocity of the unknown fracture front which precludes the implementation of established front evolution strategies that require an explicit velocity field and the computationally prohibitive cost of resolving all the length scales an implicit algorithm is also necessary for the efficient solution of the stiff evolution equations that involve fully populated matrices associated with the coupled non local elasticity and degenerate lubrication equations the implicit level set algorithm that we propose exploits the local tip asymptotic behavior applicable at the computational length scale in order to locate the free boundary local inversion of this tip asymptotic relation yields the boundary values for the eikonal equation whose solution gives the fracture front location as well as the front velocity field the efficacy of the algorithm is tested by comparing the level set solution to analytic solutions for hydraulic fractures propagating in a number of distinct regimes the level set algorithm is shown to resolve the free boundary problem with first order accuracy further it captures the field variables such as the fracture width with the first order accuracy that is consistent with the piecewise constant discretization that is used

exact results for the nonlinear diffusion equations delta u delta t delta delta x u 4 3 delta u delta x and delta u delta t delta delta x u 2 3 delta u delta x the author exploits local and non local symmetries of the two equations of the title and of some related equations some new exact solutions are derived and some specific boundary value problems of physical significance are considered

performance of dual diversity predetection egc in correlated rayleigh fading with unequal branch snrs the bit error probability bep for coherent detection of binary signals with dual diversity predetection equal gain combining is derived using the beaulieu 1991 series in particular we consider a correlated rayleigh fading channel with unequal branch signal to noise ratios the bep expression is in terms of the power correlation coefficient of the branches is easy to compute and depicts clearly the effect of correlated fading on the error performance

a general method for calculating error probabilities over fading channels signal fading is a ubiquitous problem in mobile and wireless communications in digital systems fading results in bit errors and evaluating the average error rate under fairly general fading models and multichannel reception is often required predominantly to date most researchers perform the averaging using the probability density function method or the moment generating function mgf method this paper presents a third method called the characteristic function chf method for calculating the average error rates and outage performance of a broad class of coherent differentially coherent and noncoherent communication systems with or without diversity reception in a myriad of fading environments unlike the mgf technique the proposed chf method based on parseval s theorem enables us to unify the average error rate analysis of different modulation formats and all commonly used predetection diversity techniques i e maximal ratio combining equal gain combining selection diversity and switched diversity within a single common framework the chf method also lends itself to the averaging of the conditional error probability involving the complementary incomplete gamma function and the confluent hypergeometric function over fading amplitudes which heretofore resisted to a simple form as an aside we show some previous results as special cases of our unified framework

development of an adaptive discontinuous galerkin finite element method for advection reaction equations abstract this paper presents an adaptive discontinuous galerkin finite element method to solve linear advection reaction equations the method was developed for the prediction of hemolysis in prosthetic devices where the flow may include recirculation zones to ensure the well posedness of the problem we solve the transient form of the pde time discretization is achieved with an implicit euler scheme in order to obtain the steady state solution rapidly linear interpolation functions are used to approximate the hemolysis field the a posteriori estimation of the error is obtained by solving an advection reaction equation for the error which is approximated with quadratic interpolation functions then elementary estimations of the error are computed using a semi norm developed to achieve the best possible results even in the presence of recirculation code verification to assess the convergence and conservation properties of the method is performed with the method of manufactured solutions and with a conservation test using a sharp gaussian function as a reaction term excellent results are obtained in both cases predictions of hemolysis in a dialysis cannula are presented as an engineering application of our method

small and waiting time behavior of the thin film equation we consider the small time behavior of interfaces of zero contact angle solutions to the thin film equation for a certain class of initial data through asymptotic analyses we deduce a wide variety of behavior for the free boundary point these are supported by extensive numerical simulations

group invariant solutions and optimal systems for multidimensional hydrodynamics the group properties of the three dimensional 3 d one temperature hydrodynamic equations including nonlinear conduction and a thermal source are presented a subgroup corresponding to axisymmetric geometry is chosen and the details of the construction of the one and two dimensional optimal systems are shown the two dimensional optimal system is used to generate 23 intrinsically different reductions of the 2 d partial differential equations to ordinary differential equations these ordinary differential equations can be solved to provide analytic solutions to the original partial differential equations two example analytic solutions are presented a 2 d axisymmetric flow with a p2 asymmetry and a 3 d spiraling flow

space time coupled spectral hp least squares finite element formulation for the incompressible navier stokes equations we consider least squares finite element models for the numerical solution of the non stationary navier stokes equations governing viscous incompressible fluid flows the paper presents a formulation where the effects of space and time are coupled resulting in a true space time least squares minimization procedure as opposed to a space time decoupled formulation where a least squares minimization procedure is performed in space at each time step the formulation is first presented for the linear advection diffusion equation and then extended to the navier stokes equations the formulation has no time step stability restrictions and is spectrally accurate in both space and time to allow the use of practical c0 element expansions in the resulting finite element model the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity as an additional independent variable and the least squares method is used to develop the finite element model of the governing equations high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix free form spectral convergence of the l2 least squares functional and l2 error norms in space time is verified using a smooth solution to the two dimensional non stationary incompressible navier stokes equations numerical results are presented for impulsively started lid driven cavity flow oscillatory lid driven cavity flow transient flow over a backward facing step and flow around a circular cylinder the results demonstrate the predictive capability and robustness of the proposed formulation even though the space time coupled formulation is emphasized we also present the formulation and numerical results for least squares space time decoupled finite element models the numerical results show that the space time coupled formulation has superior predictive capabilities for flows demanding high space time resolution exemplified here by the transient flow over a backward facing step

nonlinear galilei invariant pdes with infinite dimensional lie symmetry a class of nonlinear galilei invariant generalizations of the heat equation admitting infinite dimensional lie symmetry is presented lie symmetries and examples of exact solutions are found for some nonlinear equations generalizing the heat equation full sets of the absolute differential invariants for two non equivalent representations of the galilei algebra are constructed

moving finite element methods for evolutionary problems ii applications abstract in this the second of two papers on the subject we present applications of the moving finite element method to a number of test problems key features are linear elements a direct approach to parallelism and node overtaking avoiding penalty functions rapid inversion of the mass matrix by preconditioned conjugate gradients and explicit euler time stepping the resulting codes are fast and efficient and are able to follow fronts and similar features with great accuracy the paper includes a substantial section on changes of dependent variable and front tracking techniques for non linear diffusion problems test problems include non linear hyperbolic conservation laws and non linear parabolic equations in one and two dimensions

symmetries periodic plane waves and blow up of l ω systems abstract nonclassical symmetries of one dimensional reaction diffusion equations of the type have been studied the functional forms of and for which the system admits nonclassical symmetries have been determined and the corresponding reduced systems have been obtained some of these reduced systems admit symmetries which lead to further reductions among the several classes of exact solutions that have been obtained asymptotically periodic plane waves appear as similarity solutions of systems we also have obtained a family of solutions that exhibit a blow up process

algorithms for the nonclassical method of symmetry reductions in this article the authors first present an algorithm for calculating the determining equations associated with so called nonclassical method of symmetry reductions a la bluman and cole for systems of partial differential equations this algorithm requires significantly less computation time than that standardly used and avoids many of the difficulties commonly encountered the proof of correctness of the algorithm is a simple application of the theory of grobner bases in the second part they demonstrate some algorithms which may be used to analyse and often to solve the resulting systems of overdetermined nonlinear pdes the authors take as their principal example a generalised boussinesq equation which arises in shallow water theory although the equation appears to be nonintegrable the authors obtain an exact two soliton solution from a nonclassical reduction

the interfaces of one dimensional flows in porous media abstract a porous media equation pme has been used as a model for a number of physical phenomena heat diffusion at high temperatures boundary layer theory spread of a thin layer of viscous material and mainly the flow of gas in a porous medium the most distinctive characteristic of the solutions to pme as compared with the linear heat equation is the finite speed of propagation in this paper the properties of the interfaces are studied in terms of the initial data sometimes the interface is stationary for a certain time and then begins to move we characterize the existence of a positive waiting time and give bounds for it

waiting time solutions of a nonlinear diffusion equation similarity solutions of the equation partial c partial t partial partial x c n partial c partial x n 0 are studied for both t 0 and t 0 and there is a stationary free boundary at x 0 and for t 0 have support in x at beta where beta 1 a 0 i e there is a moving free boundary x at beta by prescribing appropriate initial data c c 0 x x 0 at t t 0 these solutions demonstrate the existence of a waiting time t 0 before the free boundary moves a comparison theorem then enables a number of results to be obtained and conjectures to be made about the existence and length of waiting times for general initial data a three parameter family of solutions which exhibit blow up at t 0 is also constructed applications of these results to models for the spreading of a viscous blob on a hor

analysis of equal gain diversity on nakagami fading channels an infinite series for the complementary probability distribution function cdf of the signal to noise ratio snr at the output of l branch equal gain eg diversity combiners in nakagami 1960 fading channels is derived the bit error rate for a matched filter receiver is analyzed for the l branch eg combiner and different fading parameters both coherent phase shift keying cpsk and differential coherent phase shift keying dcpsk are considered the effects of gain unbalance between branches on the probability distribution of the snr and on the bit error rates are investigated bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying fsk the effects of gain unbalances on fsk modulations are also investigated bit error rates for eg combining on rayleigh fading channels are obtained for l 2 these results are presented as a special case of the more generalized nakagami fading model

equal gain diversity receiver performance in wireless channels performance analysis of equal gain combining egc diversity systems is notoriously difficult only more so given that the closed form probability density function pdf of the egc output is only available for dual diversity combining in rayleigh fading a powerful frequency domain approach is therefore developed in which the average error rate integral is transformed into the frequency domain using parseval s theorem such a transformation eliminates the need for computing or approximating the egc output pdf which is unknown but instead requires the knowledge of the corresponding characteristic function which is readily available the frequency domain method also circumvents the need to perform multiple fold convolution integral operations usually encountered in the calculation of the pdf of the sum of the received signal amplitudes we then derive integral expressions for the average symbol error rate of an arbitrary two dimensional signaling scheme with egc reception in rayleigh rician nakagami m 1960 and nakagami q fading channels for practically important cases of second and third order diversity systems in nakagami fading both coherent and noncoherent detection methods for binary signaling are analyzed using the appell hypergeometric function a number of closed form solutions are derived in which the results put forward by zhang see ibid vol 45 p 270 73 1997 are shown to be special cases

the characterization of reaction convection diffusion processes by travelling waves it has long been known that the heat equation displays infinite speed of propagation this is to say that if the initial data are nonnegative and have nonempty compact support the solution of an initial value problem is positive everywhere after any infinitesimal time however since the nineteen fifties it has also been known that certain nonlinear diffusion equations of degenerate parabolic type do not display this phenomenon for these equations the generalized solution of an initial value problem with compactly supported initial data will have bounded support with respect to the spatial variable at all times in this paper the necessary and sufficient criterion for finite speed of propagation for the general nonlinear reaction convection diffusion equation formula is determined the assumptions on the coefficientsa bandcare such that the classification unifies and generalizes previously known results the technique employed is comparision of an arbitrary solution of the equation with suitably constructed travelling wave solutions and subsolutions basically the central conclusion is that the equation exhibits finite speed of propagation if and only if it admits a travelling wave solution with bounded support concurrently the search for a travelling wave solution with bounded support can be reduced to the study of a singular nonlinear integral equation whose solution must satisfy a certain constraint

infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains we study the positivity and regularity of solutions to the fractional porous me dium equations ut sum 0 in 0 for m 1 and s 0 1 with dirichlet boundary data u 0 in 0 n and nonnegative initial condition u 0 u0 0 our first result is a quantitative lower bound for solutions that holds for all positive times t 0 as a consequence we find a global harnack principle stating that for any t 0 solutions are comparable to ds m where d is the distance to this is in sharp contrast with the local case s 1 where the equation has finite speed of propagation after this we study the regularity of solutions we prove that solutions are classical in the interior c in x and c1 in t and establish a sharp cxs m regularity estimate up to the boundary our methods are quite general and can be applied to wider classes of nonlocal parabolic equations of the form ut f u 0 in both in bounded and unbounded domains 2016 wiley periodicals inc

non stationary spectra of local wave turbulence abstract the evolution of the kolmogorov zakharov k z spectrum of weak turbulence is studied in the limit of strongly local interactions where the usual kinetic equation describing the time evolution of the spectral wave action density can be approximated by a pde if the wave action is initially compactly supported in frequency space it is then redistributed by resonant interactions producing the usual direct and inverse cascades leading to the formation of the k z spectra the emphasis here is on the direct cascade the evolution proceeds by the formation of a self similar front which propagates to the right leaving a quasi stationary state in its wake this front is sharp in the sense that the solution remains compactly supported until it reaches infinity if the energy spectrum has infinite capacity the front takes infinite time to reach infinite frequency and leaves the k z spectrum in its wake on the other hand if the energy spectrum has finite capacity the front reaches infinity within a finite time t and the wake is steeper than the k z spectrum for this case the k z spectrum is set up from the right after the front reaches infinity the slope of the solution in the wake can be related to the speed of propagation of the front it is shown that the anomalous slope in the finite capacity case corresponds to the unique front speed which ensures that the front tip contains a finite amount of energy as the connection to infinity is made we also introduce for the first time the notion of entropy production in wave turbulence and show how it evolves as the system approaches the stationary k z spectrum

positivity versus localization in degenerate diffusion equations on considere le probleme de cauchy u t u m f u 0 dans s r n o u x o u 0 x x r n ou m 1 n 1 et les fonctions f et u 0 satisfont les hypotheses 1 f c 1 o f o 0 2 u 0 est une fonction continue non negative definie sur r n a support borne

some non local transformations between nonlinear diffusion equations generalized backlund transformations are applied to derive links between a large number of different types of nonlinear diffusion equations including many which are of physical significance some new exactly linearizable forms are determined

c regularity for the porous medium equation on etablit un resultat de regularite optimale pour l equation d un milieu poreux u t u m xx 0 x r t 0 u 0 u 0 pour m 1 et la donnee initiale u 0 positive continue a support compact connexe

a local space time discontinuous finite element method we present a locally enriched space time finite element method for solving hyperbolic problems with discontinuities the space time formulation is coupled to a standard semidiscrete finite element method the discontinuities are captured by a space time version of the extended finite element method which treats arbitrary moving discontinuities since the discontinuities are local the enriched space time method is only needed around the discontinuities which provides significant computational savings the coupling is implemented through a weak enforcement of the continuity of the flux between the space time and semidiscrete domains in a manner similar to discontinuous galerkin methods the method is illustrated through one dimensional problems it displays remarkable accuracy in capturing moving discontinuities both in their amplitude and speed

nonclassical symmetries of a porous medium equation with absorption in this paper new symmetry reductions and exact solutions are presented for the porous medium equation with absorption those spatial forms for which the equation can be reduced to an ordinary differential equation are studied the symmetry reductions and exact solutions presented are derived by using the nonclassical method developed by bluman and cole and are unobtainable by lie classical method

new classes of similarity solutions of the inhomogeneous nonlinear diffusion equations the lie similarity method has been used to extend the similarity solutions of the one dimensional inhomogeneous nonlinear diffusion equations we determine the lie point symmetry vector fields and calculate the similarity ansatz then we discuss the resulting nonlinear ordinary differential equations exact solutions are found and their relations to some real physical situations are discussed

performance analysis of predetection egc in exponentially correlated nakagami m fading channel using a gil palaez lemma based approach we derive a general expression for the bit error rate of a predetection equal gain combining receiver for coherent binary phase shift keying modulation in exponentially correlated nakagami m fading channel for an arbitrary number of branches the obtained expressions are different for even and odd numbers of branches numerical results have been corroborated with simulations

splitting based schemes for numerical solution of nonlinear diffusion equations on a sphere we provide an advanced study of our recently developed method for the numerical solution of nonlinear diffusion equations on a sphere in particular we analyse the method in detail when applied to solving diverse diffusion phenomena with specific conditions on the smoothness of the solution the degree of nonlinearity and the initial data and sources the main idea of the method consists in splitting the original differential operator by coordinates and subsequent constructing finite difference schemes for the split one dimensional problems using different coordinate maps for the sphere at the two split time intervals the essential advantage of this technique is that each split 1d equation can be equipped with a periodic boundary condition despite the sphere being not a doubly periodic domain therefore unlike the existing methods this one does not require applying special numerical procedures for careful computing the solution near the poles which is always a challenge each split 1d equation is approximated by a second or a fourth order finite difference scheme that keeps all the substantial properties of the differential problem it is balanced and dissipative since the spatial finite difference operator is negative definite the developed algorithm is cheap to implement from the computational point of view the theoretical results are confirmed numerically by simulating various nonlinear diffusion processes a numerical example in particular shows that the competition of the three basic mechanisms the nonlinear interaction forcing and dissipation can generate wave solutions whose spatial structures on the sphere are subjected to the alternating influence of the processes of self organisation and self destruction the accuracy of the method is evaluated by comparing the numerical solutions versus the analytical ones obtained with specially chosen forcings the convergence of the numerical solution to the analytics is verified by refining spatial grids

space time least squares finite element method for convection reaction system with transformed variables we present a method to solve a convection reaction system based on a least squares finite element method lsfem for steady state computations issues related to recirculation flow are stated and demonstrated with a simple example the method can compute concentration profiles in open flow even when the generation term is small this is the case for estimating hemolysis in blood time dependent flows are computed with the space time lsfem discretization we observe that the computed hemoglobin concentration can become negative in certain regions of the flow it is a physically unacceptable result to prevent this we propose a quadratic transformation of variables the transformed governing equation can be solved in a straightforward way by lsfem with no sign of unphysical behavior the effect of localized high shear on blood damage is shown in a circular couette flow with blade configuration and a physiological condition is tested in an arterial graft flow

invariant solutions for the nonlinear diffusion model of turbulence we study leith s model of turbulence represented by a nonlinear degenerate q1 diffusion equation leith 1967 phys fluids 10 1409 16 connaughton and nazarenko 2004 phys rev lett 92 044501 506 the model is constructed such that in the case of vanishing viscosity there are two steady state solutions the kolmogorov spectrum that corresponds to the cascade state and a thermodynamic equilibrium distribution using group analysis we have obtained integral equations which describe all essentially different invariant q2 solutions of the leith equation with or without viscosity the integral equations defining these solutions reveal new possibilities for analytical and numerical studies in these equations the presence of arbitrary constants allows one to solve them for different boundary conditions we have proved existence and uniqueness for such boundary value problems

lagrangian non oscillatory and fem schemes for the porous media equation abstract interface tracking schemes derived from a lagrangian formulation of the equation are considered existence and equivalence results valid even for the non smooth interface case are given and non oscillatory schemes needed in this case are discussed mixed euler lagrange fem discretization for mixed problems and numerical experiments are presented

group invariant solutions of differential equations we introduce the concept of a weak symmetry group of a system of partial differential equations that generalizes the nonclassical method introduced by bluman and cole for finding group invariant