exact static solutions of a generalized discrete φ 4 model including short periodic solutions we carry out a comprehensive analysis of a generalized discrete 4 model of which virtually all 4 models discussed in the literature are particular cases for this model we construct the exact solutions in the form of the basic jacobi elliptic hyperbolic and sine functions and also give a list of short periodic and even aperiodic solutions some of those solutions coincide with the known ones others generalize the existing solutions and the rest of them are new we then discuss the relation between the models supporting exact static solutions and the two point maps in particular we show that some of the short periodic and sine solutions can be found from factorized difference equations and even from a set of two difference equations one of the first and another of the second order particular attention is paid to the discussion of the exceptional discrete ed models defined as models supporting the translationally invariant ti static solutions that can be placed arbitrarily with respect to the lattice we show that some of the derived short periodic solutions are ti ones while the others are not for the ti static solutions we demonstrate the existence of the translational goldstone mode for any location of the solution with respect to the lattice we then analyze numerically the stability and other properties of the ti kink solutions in conclusion we divide the ed models into two classes the ed i models support a two parameter set of ti static solutions while the ed ii models support only a one parameter set of such solutions

a new barrier to the existence of moving kinks in frenkel kontorova lattices an explanation is offered for an observed lower bound on the wave speed of travelling kinks in frenkel kontorova lattices kinks exist at discrete wavespeeds within a parameter regime where there is a resonance with linear waves phonons however they fail to exist even in this codimension one sense whenever there is more than one phonon branch in the dispersion relation inside such bands only quasi kinks with nondecaying oscillatory tails are possible the results are presented for a discrete sine gordon lattice with an onsite potential that has a tunable amount of anharmonicity novel numerical methods are used to trace kinks with topological charge q 1 and 2 in three parameters representing the propagation speed lattice discreteness and anharmonicity although none of the analysis is presented as rigorous mathematics numerical results suggest that the bound on allowable wavespeeds is sharp the results also explain why the vanishing at discrete values of anharmonicity of the peierls nabarro barrier between stationary kinks as discovered by savin et al does not lead to bifurcation of kinks with small wave speed 2003 elsevier b v all rights reserved

exact static solutions for discrete ϕ 4 models free of the peierls nabarro barrier discretized first integral approach we propose a generalization of the discrete klein gordon models free of the peierls nabarro barrier derived in spreight nonlinearity 12 1373 1999 and barashenkov et al phys rev e 72 035602 r 2005 such that they support not only kinks but a one parameter set of exact static solutions these solutions can be obtained iteratively from a two point nonlinear map whose role is played by the discretized first integral of the static klein gordon field as suggested by dmitriev et al j phys a 38 7617 2005 we then discuss some discrete ensuremath phi 4 models free of the peierls nabarro barrier and identify for them the full space of available static solutions including those derived recently by cooper et al phys rev e 72 036605 2005 but not limited to them these findings are also relevant to standing wave solutions of discrete nonlinear schr odinger models we also study stability of the obtained solutions as an interesting aside we derive the list of solutions to the continuum ensuremath phi 4 equation that fill the entire two dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models

a parameter estimation framework for patient specific hemodynamic computations we propose a fully automated parameter estimation framework for performing patient specific hemodynamic computations in arterial models to determine the personalized values of the windkessel models which are used as part of the geometrical multiscale circulation model a parameter estimation problem is formulated clinical measurements of pressure and or flow rate are imposed as constraints to formulate a nonlinear system of equations whose fixed point solution is sought a key feature of the proposed method is a warm start to the optimization procedure with better initial solution for the nonlinear system of equations to reduce the number of iterations needed for the calibration of the geometrical multiscale models to achieve these goals the initial solution computed with a lumped parameter model is adapted before solving the parameter estimation problem for the geometrical multiscale circulation model the resistance and the compliance of the circulation model are estimated and compensated the proposed framework is evaluated on a patient specific aortic model a full body arterial model and multiple idealized anatomical models representing different arterial segments for each case it leads to the best performance in terms of number of iterations required for the computational model to be in close agreement with the clinical measurements

on the zeta function regularization of a two dimensional series of epstein hurwitz type as a further step in the general program of zeta function regularization of multiseries expressions some original formulas are provided for the analytic continuation to any value of s of two dimensional series of epstein hurwitz type namely n1 n2 0 a1 n1 c1 2 a2 n2 c2 2 s where the aj are positive reals and the cj are not simultaneously nonpositive integers they come out from a generalization to hurwitz functions of the zeta function regularization theorem of the author and romeo phys rev d 40 436 1989 for ordinary zeta functions for s k 0 2 with k 1 2 3 the final results are in fact expressed in terms of hurwitz zeta functions only for general s they also involve bessel functions a partial numerical investigation of the different terms of the exact algebraic equations is also carried out as a by product the series n 0exp a n c 2 a c 0 is conveniently calculated in terms of them

exact static solutions to a translationally invariant discrete phi4 model for a discrete translationally invariant 4 model introduced by barashenkov et al 2005 phys rev e 72 35602r we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a jacobi elliptic function jef solution the first integral can be written in the form of a nonlinear map from which the static solution supported by the model can be constructed a set of jef solutions including the staggered ones is derived we also report on the stability analysis for the static bounded solutions and exemplify the dynamical behaviour of the unstable solutions this work provides a road map through this illustrative example on how to fully analyse translationally invariant models in terms of their static problem its first integral their full set of static solutions and associated conservation laws

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

moving kinks and nanopterons in the nonlinear klein gordon lattice we study moving topological solitons kinks and antikinks in the nonlinear klein gordon chain these solitons are shown to exist with both monotonic non oscillating and oscillating asymptotics tails using the pseudo spectral method the anti kink solutions with oscillating background so called nanopterons are found as travelling waves of permanent profile propagating with constant velocity each of these solutions may be considered as a bound state of an anti kink with a background nonlinear periodic wave so that the wave pushes the anti kink over the peierls nabarro barrier the stability of these bound states is confirmed numerically travelling wave solutions of permanent profile are shown to exist depending on the convexity of the on site substrate potential the set of velocities at which the anti kinks with monotonic asymptotics propagate freely is calculated we also find moving non oscillating anti kink profiles with higher topological charges each of which appears to be the bound state of anti kinks with lower topological charge jq jd 1 2000 elsevier science b v all rights reserved

dynamical transitions between equilibria in a dissipative klein gordon lattice abstract we consider the energy landscape of a dissipative klein gordon lattice with a 4 on site potential our analysis is based on suitable energy arguments combined with a discrete version of the ojasiewicz inequality in order to justify the convergence to a single nontrivial equilibrium for all initial configurations of the lattice then global bifurcation theory is explored to illustrate that in the discrete regime all linear states lead to nonlinear generalizations of equilibrium states direct numerical simulations reveal the rich structure of the equilibrium set consisting of non trivial topological kink shaped interpolations between the adjacent minima of the on site potential and the wealth of dynamical convergence possibilities these dynamical evolution results also provide insight on the potential stability of the equilibrium branches and glimpses of the emerging global bifurcation structure elucidating the role of the interplay between discreteness nonlinearity and dissipation

exact stationary solutions for the translationally invariant discrete nonlinear schrodinger equations from a wide class of translationally invariant discrete nonlinear schrodinger dnls equations we extract a two parameter subclass corresponding to kerr nonlinearity for which any stationary solution can be derived recurrently from a quadratic equation this subclass which incorporates the integrable ablowitz ladik lattice as a special case admits exact stationary solutions that are derived in terms of the jacobi elliptic functions exact moving solutions for the discrete equations are also obtained in the continuum limit the constructed stationary solutions reduce to the exact moving solutions to the continuum nls equation with kerr nonlinearity numerical results are also presented for the special case of localized solutions including sech pulse or bright soliton tanh kink or dark soliton and 1 tanh called here inverted kink profiles for these solutions we discuss their linearization spectra and their mobility particularly we demonstrate that discrete dark solitons are dynamically stable for a wide range of lattice spacings contrary to what is the case for their standard dnls counterparts furthermore the bright and dark solitons in the non integrable translationally invariant lattices can propagate at slow speed without any noticeable radiation

data assimilation and modelling of patient specific single ventricle physiology with and without valve regurgitation a closed loop lumped parameter model of blood circulation is considered for single ventricle shunt physiology its parameters are estimated by an inverse problem based on patient specific haemodynamics measurements as opposed to a black box approach maximizing the number of parameters that are related to physically measurable quantities motivates the present model heart chambers are described by a single fibre mechanics model and valve function is modelled with smooth opening and closure a model for valve prolapse leading to valve regurgitation is proposed the method of data assimilation in particular the unscented kalman filter is used to estimate the model parameters from time varying clinical measurements this method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements two patient specific cases one without regurgitation and one with atrioventricular valve regurgitation are presented pulmonary and systemic circulation parameters are successfully estimated without assumptions on their relationships parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics or estimated results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure the model and the estimation method are shown to successfully capture patient specific clinical observations even with regurgitation such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings lastly biomechanical implications of the results are discussed

translationally invariant discrete kinks from one dimensional maps for most discretizations of the phi4 theory the stationary kink can only be centered either on a lattice site or midway between two adjacent sites we search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites we show that this translational invariance of the kink implies the existence of an underlying one dimensional map phi n 1 f phi n a simple algorithm based on this observation generates three families of exceptional discretizations

high speed kinks in a generalized discrete phi 4 model we consider a generalized discrete ensuremath phi 4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity the constructed exact moving solutions are dependent on the specific value of the propagation velocity we demonstrate that in this class of models given a specific velocity the problem of finding the exact moving solution is integrable namely this problem originally expressed as a three point map can be reduced to a two point map from which the exact moving solutions can be derived iteratively it was also found that these high speed kinks can be stable and robust against perturbations introduced in the initial conditions

exceptional discretizations of the sine gordon equation the method of one dimensional maps was recently introduced as a means of generating exceptional discretizations of the phi 4 theory i e discrete phi 4 models which support kinks centered at a continuous range of positions relative to the lattice in this paper we employ this method to obtain exceptional discretizations of the sine gordon equation i e exceptional frenkel kontorova chains we also use one dimensional maps to construct a discrete sine gordon equation supporting kinks which move with arbitrary velocities without emitting radiation

standard nearest neighbour discretizations of klein gordon models cannot preserve both energy and linear momentum we consider nonlinear klein gordon wave equations and illustrate that standard discretizations thereof involving nearest neighbours may preserve either standardly defined linear momentum or standardly defined total energy but not both this has a variety of intriguing implications for the non potential discretizations that preserve only the linear momentum such as the self accelerating or self decelerating motion of coherent structures such as discrete kinks in these nonlinear lattices

zeta functions formulas and applications abstract the existence conditions of the zeta function of a pseudodifferential operator and the definition of determinant thereby obtained are reviewed as well as the concept of multiplicative anomaly associated with the determinant and its calculation by means of the wodzicki residue exponentially fast convergent formulas valid in the whole of the complex plane and yielding the pole positions and residua that extend the ones by chowla and selberg for the epstein zeta function quadratic form and by barnes affine form are then given after briefly recalling the zeta function regularization procedure in quantum field theory some applications of these expressions in physics are described

some analytic continuations of the barnes zeta function in two and higher dimensions abstract formulas for the analytic continuation of the barnes zeta function and some affine extensions thereof in two and more dimensions are constructed the expressions are used to deal with determinants of multidimensional harmonic oscillators an example is therewith obtained of the multiplicative anomaly or defect associated with the most common definition due to ray and singer d b ray reidemeister torsion and the laplacian on lens spaces adv math 4 1970 109 126 d b ray i m singer r torsion and the laplacian on riemannian manifolds adv math 7 1971 145 201 d b ray i m singer analytic torsion for complex manifolds ann math 98 1973 154 177 of determinant of a pseudodifferential operator admitting a zeta function m kontsevich s vishik geometry of determinants of elliptic operators in functional analysis on the eve of the 21st century vol 1 1995 pp 173 197

normal form for travelling kinks in discrete klein gordon lattices abstract we study travelling kinks in the spatial discretizations of the nonlinear klein gordon equation which include the discrete 4 lattice and the discrete sine gordon lattice the differential advance delay equation for travelling kinks is reduced to the normal form a scalar fourth order differential equation near the quadruple zero eigenvalue we show numerically the non existence of monotonic kinks heteroclinic orbits between adjacent equilibrium points in the fourth order equation making generic assumptions on the reduced fourth order equation we prove the persistence of bounded solutions heteroclinic connections between periodic solutions near adjacent equilibrium points in the full differential advance delay equation with the technique of centre manifold reduction existence of multiple kinks in the discrete sine gordon equation is discussed in connection to recent numerical results of aigner et al a a aigner a r champneys v m rothos a new barrier to the existence of moving kinks in frenkel kontorova lattices physica d 186 2003 148 170 and results of our normal form analysis

explicit zeta functions for bosonic and fermionic fields on a non commutative toroidal spacetime explicit formulae for the zeta functions s corresponding to bosonic 2 and to fermionic 3 quantum fields living on a non commutative partially toroidal spacetime are derived formulae for the most general case of the zeta function associated with a quadratic linear constant form in z are obtained they provide the analytical continuation of the zeta functions in relation to the whole complex s plane in terms of series of bessel functions of fast exponential convergence thus being extended chowla selberg formulae as is well known this is the most convenient expression that can be found for the analytical continuation of a zeta function in particular the residua of the poles and their finite parts are explicitly given an important novelty is the fact that simple poles show up at s 0 as well as in other places simple or double depending on the number of compactified non compactified and non commutative dimensions of the spacetime where they had never appeared before this poses a challenge to the zeta function regularization procedure

on a class of discretizations of hamiltonian nonlinear partial differential equations abstract we present a new class of discretizations of partial differential equations pdes that preserve a momentum like integral of the motion this results in an effective translational invariance for the dynamical problem and the absence of a peierls nabarro barrier that is usually present in discretizations of hamiltonian pdes a general method to construct such discretizations for any nonlinearity is given and the properties of the resulting differential difference equations are analyzed in a number of different cases for nonlinear klein gordon as well for nonlinear schrodinger type systems while for the former nonintegrability of the dynamical problem is evident in the latter case numerical evidence suggests that the behavior is close to the one of integrable systems we also show how static solutions of the equations can be constructed for these discretizations and discuss the similarities and differences of the method with previously reported ones

adjoint based inverse analysis of windkessel parameters for patient specific vascular models a human circulatory system is composed of more than 50 000 miles of blood vessels such a huge network of vessels is responsible for the elevated pressure values within large arteries as such modeling of large blood arteries requires a full modeling of circulatory system this in turn is computationally not affordable thus a multiscale modeling of the arterial network is a necessity the multiscale approach is achieved through first modeling the arterial regions of interest with 3d models and the rest of the circulatory network with reduced dimensional reduced d models then coupling the multiscale domains together though reduced d models can well reproduce physiology calibrating them to fit 3d patient specific fluid structure interaction fsi geometries has received little attention for this reason this work develops calibration methods for reduced d models using adjoint based methods we also propose a reduced modeling complexity rmc approach that reduces the calibration cost of expensive fsi models using pure fluid modeling finally all of the developed calibration techniques are tested on patient specific arterial geometries showing the power and stability of the proposed calibration methods

analysis of an inhomogeneous generalized epstein hurwitz zeta function with physical applications the inhomogeneous generalized epstein hurwitz like multidimensional series em s a1 am c1 cm c2 n1 nm 0 a1 n1 c1 2 am nm cm 2 c2 s is investigated by means of a nontrivial asymptotic recurrence it is reduced to the one dimensional case f s a b2 n 0 n a 2 b2 s which is then studied in full detail in particular asymptotic expansions for f and its derivatives f s and f a together with analytical continuations of the same in the variable s are explicitly obtained using zeta function techniques several plots and tables of the numerical results are given some explicit applications to the regularization by means of hurwitz zeta functions of different problems that have appeared recently in the physical literature are considered

finite temperature casimir energy in closed rectangular cavities a rigorous derivation based on a zeta function technique we derive rigorously explicit formulae of the casimir free energy at finite temperature for massless scalar field and electromagnetic field confined in a closed rectangular cavity with different boundary conditions by a zeta regularization method we study both the low and high temperature expansions of the free energy in each case we write the free energy as a sum of a polynomial in temperature plus exponentially decay terms we show that the free energy is always a decreasing function of temperature in the cases of massless scalar field with the dirichlet boundary condition and electromagnetic field the zero temperature casimir free energy might be positive in each of these cases there is a unique transition temperature as a function of the side lengths of the cavity where the casimir energy changes from positive to negative when the space dimension is equal to two and three we show graphically the dependence of this transition temperature on the side lengths of the cavity finally we also show that we can obtain the results for a non closed rectangular cavity by letting the size of some directions of a closed cavity go to infinity and we find that these results agree with the usual integration prescription adopted by other authors

an extension of the chowla selberg formula useful in quantizing with the wheeler de witt equation the two dimensional inhomogeneous zeta function series with homogeneous part of the most general epstein type sigma m n in z am2 bmn cn2 q s is analytically continued in the variable s using zeta function techniques a simple formula is obtained which extends the chowla selberg formula to inhomogeneous epstein zeta functions the new expression is then applied to solve the problem of computing the determinant of the basic differential operator that appears in an attempt at quantizing gravity by using the wheeler de witt equation in 2 1 dimensional spacetime with the torus topology

jacobian elliptic function solutions of the discrete cubic quintic nonlinear schrodinger equation the study of solitary wave solutions is of prime significance for the nonlinear schrodinger equation with higher order dispersion and or higher degree nonlinearities in nonlinear physical systems we derive the discrete cubic quintic nonlinear schrodinger equation from a hamiltonian using different poisson brackets by using the extended jacobian elliptic function approach we investigate the abundant exact stationary solitons and periodic waves solution of this equation these solutions include jacobian periodic solutions alternating phase jacobi periodic solution kink and bubble soliton solutions alternating phase kink soliton solution and alternating phase bubble soliton solution provided that coefficients are bound by special relation and then with the aid of symbolic computation we present in explicit form these solutions the stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated

on the issue of imposing boundary conditions on quantum fields an interesting example of the deep interrelation between physics and mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields this procedure has recently been re examined with care comments on that and previous analysis are provided here together with considerations on the results of the purely mathematical zeta function method in an attempt at clarifying the issue hadamard regularization is invoked in order to fill the gap between the infinities appearing in the qft renormalized results and the finite values obtained in the literature with other procedures

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

kink dynamics in the highly discrete sine gordon system abstract we study kink dynamics in a very discrete sine gordon system where the kink width is of the order of the lattice spacing numerical simulations exhibit new properties of kinks in this case they lose the memory of their initial velocity and propagate preferentially at well defined velocities which correspond to quasi steady states while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations when a small external driving force is applied to the system the same velocities appear as plateus in the strongly nonlinear mobility of the kink the energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system and the preferential velocities for the kink are obtained to good accuracy similar results may be expected to be valid for other discrete systems manifesting topological solitons the numerical simulations reveal also new stable multiple kink excitations which can propagate almost freely in extremely discrete systems where ordinary simple kinks are pinned to the lattice by discreteness the stability of the multiple kinks is discussed

exact static solutions of a two dimensional discrete ϕ4 model for a two dimensional scalar discrete 4 model we obtain several exact static solutions in the form of the jacobi elliptic functions jef with arbitrary shift along the lattice the quispel roberts thompson type quadratic maps are identified for the considered two dimensional model by using a jef solution we also show that many of the static solutions can be constructed iteratively from these quadratic maps by starting from an admissible initial value the kink solution having the form of tanh is numerically demonstrated to be generically stable

discrete klein gordon models with static kinks free of the peierls nabarro potential for the nonlinear klein gordon type models we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice these discrete models are therefore free of the peierls nabarro potential previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method a relevant physical consequence of our findings is the existence of a wide class of discrete klein gordon models where slow kinks practically do not experience the action of the peierls nabarro potential such kinks are not trapped by the lattice and they can be accelerated by even weak external fields