colored group field theory random matrix models generalize to group field theories gft whose feynman graphs are dual to higher dimensional topological spaces the perturbative development of the usual gft s is rather involved combinatorially and plagued by topological singularities which we discuss in great detail in this paper thus very difficult to control and unsatisfactory

persistence exponents and scaling in two dimensional xy model and a nematic model the persistence exponents associated with the t 0 quenching dynamics of the two dimensional xy model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation the site persistence or the probability that the sign of a local spin component does not change starting from initial time t 0 up to a certain time t is found to decay as l t l t is the linear domain length scale with 0 305 0 020 for the two dimensional xy model and 0 199 0 009 for the two dimensional uniaxial spin nematic model we have also investigated the scaling at the late time of phase ordering associated with the correlated persistent sites in both models the persistence correlation length was found to grow in the same way as l t

addendum to a renormalizable 4 dimensional tensor field theory this note fills a gap in the article ben geloun and rivasseau commun math phys 318 69 109 2013 we provide the proof of eq 82 of lemma 5 in ben geloun and rivasseau commun math phys 318 69 109 2013 and thereby complete its power counting analysis with a more precise next to leading order estimate

the 1 n expansion of tensor models beyond perturbation theory we analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor using a version of the loop vertex expansion which we call the mixed expansion we show that the cumulants write as explicit series in 1 n plus bounded rest terms the mixed expansion recasts the problem of determining the subleading corrections in 1 n into a simple combinatorial problem of counting trees decorated by a finite number of loop edges

integral representation for the dimensionally renormalized feynman amplitude a compact convergent integral representation for dimensionally renormalized feynman amplitudes is explicitly constructed the subtracted integrand is expressed as a distribution in the schwinger parametric space and is obtained by applying upon the bare integrand a new subtraction operatorr which respects zimmermann s forest structure

dynamic correlations in domain growth a 1 n expansion the authors consider the dynamics of the n component ginzburg landau model with nonconserved order parameter model a following a quench from a high temperature equilibrium state to zero temperature the two time correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the form of the new exponent lambda which is a non trivial function of n and d was given explicitly to o 1 n in a recent letter the purpose of this study is to present a more detailed account of the calculation leading to the o 1 n form for lambda they also examine the role of thermal fluctuations in the ordered phase and the effect of long range initial correlations on the ordering process

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

growth of order in vector spin systems scaling and universality the growth of order in vector spin systems with nonconserved order parameter model a is considered following an instantaneous quench from infinite to zero temperature the results of numerical simulations in spatial dimension d 2 and spin dimension 2n5 are presented for n4 a scaling regime where a characteristic length scale l t emerges is entered for sufficiently long times with l t t12 the autocorrelation function a t decays with time as a t t d lambda 2 and the exponent lambda n agrees well with the predictions of the 1 n expansion the cases n 2 and 3 are more complicated due to the non trivial role played by topological singularities i e vortices n 2 and polyakov solitons n 3 for n4 universal amplitudes and scaling functions characterizing the energy relaxation and the equal time correlation function are identified it is argued that for d3 where an ordered phase exists at low temperature such universal quantities characterize the entire ordered phase

on motives associated to graph polynomials the appearance of multiple zeta values in anomalous dimensions and functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions in this paper we start to hunt the motive restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions

possibilities and limitations of gaussian closure approximations for phase ordering dynamics the nonlinear equations describing phase ordering dynamics can be closed by assuming the existence of an underlying gaussian stochastic field which is nonlinearly related to the observable order parameter field we discuss the relation between different implementations of the gaussian assumption and consider the limitations of this assumption for phase ordering dynamics the fact that the different approaches gives different results is a sign of the breakdown of the gaussian assumption we concentrate on the non conserved order parameter case but also touch on the conserved order parameter case we demonstrate that the gaussian assumption is fundamentally flawed in the latter case

the fate of the wilson fisher fixed point in non commutative ϕ4 in this article we study non commutative vector sigma model with the most general 4 interaction on moyal weyl spaces we compute the 2 and 4 point functions to all orders in the large n limit and then apply the approximate wilson renormalization group recursion formula to study the renormalized coupling constants of the theory the non commutative wilson fisher fixed point interpolates between the commutative wilson fisher fixed point of the ising universality class which is found to lie at zero value of the critical coupling constant a of the zero dimensional reduction of the theory and a novel strongly interacting fixed point which lies at infinite value of a corresponding to maximal non commutativity beyond which the two sheeted structure of a as a function of the dilation parameter disappears

parametric representation of covariant noncommutative qft models we extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call covariant because their power counting is definitely more difficult to obtain this class of theories is important since it includes gauge theories which should be relevant for the quantum hall effect

on the finite amplitudes for open graphs in abelian dynamical colored boulatov ooguri models in the work ben geloun and bonzom 2011 int j theor phys 50 2819 it has been proved that the radiative corrections of the 2 point function in the su 2 boulatov tensor model generates a marginal in the renormalization group sense contribution of the form of a laplacian such a term which was missing in the initial boulatov model action should be added in that action before discussing the renormalization analysis of this model in this work by linearizing the group manifold we prove that the amplitudes associated with feynman graphs with external legs of the colored boulatov model over u 1 3 endowed with a laplacian dynamics are all convergent we conjecture that the same feature happens for the corresponding boulatov model over su 2 higher rank models are also discussed

an optimal galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere the kinematic dynamo approximation describes the generation of magnetic field in a prescribed flow of electrically conducting liquid one of its main uses is as a proof of concept tool to test hypotheses about self exciting dynamo action indeed it provided the very first quantitative evidence for the possibility of the geodynamo despite its utility due to the requirement of resolving fine structures historically numerical work has proven difficult and reported solutions were often plagued by poor convergence in this paper we demonstrate the numerical superiority of a galerkin scheme in solving the kinematic dynamo eigenvalue problem in a full sphere after adopting a poloidal toroidal decomposition and expanding in spherical harmonics we express the radial dependence in terms of a basis of exponentially convergent orthogonal polynomials each basis function is constructed from a terse sum of one sided jacobi polynomials that not only satisfies the boundary conditions of matching to an electrically insulating exterior but is everywhere infinitely differentiable including at the origin this galerkin method exhibits more rapid convergence for a given problem size than any other scheme hitherto reported as demonstrated by a benchmark of the magnetic diffusion problem and by comparison to numerous kinematic dynamos from the literature in the axisymmetric flows we consider in this paper at a magnetic reynolds number of o 100 a convergence of 9 significant figures in the most unstable eigenvalue requires only 40 radial basis functions alternatively 4 significant figures requires 20 radial functions the terse radial discretization becomes particularly advantageous when considering flows whose associated numerical solution requires a large number of coupled spherical harmonics we exploit this new method to confirm the tentatively proposed positive growth rate of the planar flow of bachtiar et al 4 thereby verifying a counter example to the zel dovich anti dynamo theorem in a spherical geometry

on noncommutative quantum field theories and dimensionless insertions in this paper we discuss the precise definition of the tree level action for the noncommutative scalar and gauge field theories on four dimensional canonically deformed euclidean space as tools to achieve this goal we employ power counting and normalization conditions

phase ordering dynamics of a vector order parameter mazenko s theory of phase ordering dynamics is generalized to an n component nonconserved vector order parameter the scaling functions for the equal time and two time correlation functions are calculated as well as the exponent characterizing the decay of autocorrelations the equal time correlation function is numerically quite close to that recently calculated by bray and puri 1991 and by toyoki 1991 and exhibits the same power law tail in its fourier transform the time dependent structure factor

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

a polynomial invariant of graphs on orientable surfaces we consider cyclic graphs that is graphs with cyclic orders at the vertices corresponding to 2 cell embeddings of graphs into orientable surfaces or combinatorial maps we construct a three variable polynomial invariant of these objects the cyclic graph polynomial which has many of the useful properties of the tutte polynomial although the cyclic graph polynomial generalizes the tutte polynomial its definition is very different and it depends on the embedding in an essential way 2000 mathematical subject classification 05c10

constructive renormalization for φ24 theory with loop vertex expansion in this paper we construct the two dimensional euclidean 4 quantum field theory using the method of loop vertex expansion we reproduce the results of standard constructive theory for example the borel summability of the schwinger functions in the coupling constant our method should be also suitable for the future construction of grosse wulkenhaar models on non commutative space time

translation invariant models for non commutative gauge fields motivated by the recent construction of a translation invariant renormalizable non commutative model for a scalar field 1 we introduce models for non commutative u 1 gauge fields along the same lines more precisely we include some extra terms into the action with the aim of getting rid of the uv ir mixing

renormalization in quantum field theory and the riemann hilbert problem i the hopf algebra structure of graphs and the main theorem this paper gives a complete selfcontained proof of our result announced in 6 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the riemann hilbert problem we shall first show that for any quantum field theory the combinatorics of feynman graphs gives rise to a hopf algebra which is commutative as an algebra it is the dual hopf algebra of the enveloping algebra of a lie algebra whose basis is labelled by the one particle irreducible feynman graphs the lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa the corresponding lie group g is the group of characters of we shall then show that using dimensional regularization the bare unrenormalized theory gives rise to a loop where c is a small circle of complex dimensions around the integer dimension d of space time our main result is that the renormalized theory is just the evaluation at z d of the holomorphic part of the birkhoff decomposition of we begin to analyse the group g and show that it is a semi direct product of an easily understood abelian group by a highly non trivial group closely tied up with groups of diffeomorphisms the analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title

a remark on possible violations of the pauli principle recently ignatiev and kuzmin 1988 developed a theoretical model to implement small violations of the pauli principle the authors remark that the pauli principle is unique among discrete symmetries and that in consequence any apparent violation actually signals new physical degrees of freedom with no violation of the pauli principle they construct an algebraic model which incorporates the algebra of ignatiev and kuzmin and leads to the same apparent violations yet preserves the pauli principle their algebra is that of a jordan pair an algebraic concept which provides a natural framework for structures that do not assume bilinear commutation relations

a spectral method for the wave equation of divergence free vectors and symmetric tensors inside a sphere the wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence free constraint we describe a numerical method based on the spectral decomposition of vector tensor components onto spherical harmonics that allows for the evolution of only those scalar fields which correspond to the divergence free degrees of freedom of the vector tensor the full vector tensor field is recovered at each time step from these two in the vector case or three symmetric tensor case scalar fields through the solution of a first order system of ordinary differential equations ode for each spherical harmonic the correspondence with the poloidal toroidal decomposition is shown for the vector case numerical tests are presented using an explicit chebyshev tau method for the radial coordinate

inertial manifolds and completeness of eigenmodes for unsteady magnetic dynamos we prove the emergence of asymptotic spatial patterns in magnetic dynamos generated by unsteady fluid flows the patterns emerge because solutions of the dynamo equation converge exponentially to a time dependent inertial manifold this inertial manifold exists for general time aperiodic velocity fields under a spectral gap condition on the associated stokes operator for time periodic velocity fields we show that the inertial manifold is spanned by floquet eigenmodes that are analogous to the strange eigenmodes observed in the mixing of diffusive tracers this result gives an affirmative answer to the long standing question of completeness of floquet solutions in time periodic dynamo problems

new exponent for dynamic correlations in domain growth the dynamics of the n component ginzburg landau model with non conserved order parameter model a are considered following a quench to zero temperature the correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the new exponent lambda is calculated to o 1 n for general space dimension d and has a non trivial dependence on n and d

some classes of renormalizable tensor models we identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property mainly a version of the rank 3 tensor model as defined by ben geloun and samary ann henri poincare 14 1599 2013 e print arxiv 1201 0176 hep th 10 1007 s00023 012 0225 5 and the grosse wulkenhaar model in 4d and 2d generate three different classes of renormalizable models the proof of the renormalizability is fully performed for the first reduced model the same procedure can be applied for the remaining cases interestingly we find that due to the peculiar behavior of anisotropic wave function renormalizations the rank 3 tensor model reduced to a matrix model generates a simple super renormalizable vector model

a polynomial of graphs on surfaces i e graphs realized as disks vertices joined together by strips edges glued to their boundaries corresponding to neighbourhoods of graphs embedded into surfaces we construct a four variable polynomial invariant of these objects the ribbon graph polynomial which has all the main properties of the tutte polynomial although the ribbon graph polynomial extends the tutte polynomial its definition is very different and it depends on the topological structure in an essential way

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

renormalization in the complete mellin representation of feynman amplitudes the feynman amplitudes are renormalized in the formalism of the cm representation this mellin barnes type integral representation previously introduced for the study of asymptotic behaviours is shown to have the following interesting property in contrast with the usual subtraction procedures the renormalization leaves the cm integrand unchanged and only results into translations of the integration path the explicit cm representation of the renormalized amplitudes is given in addition the dimensional regularization and the extension to spinor amplitudes are sketched

generalization of the bollobas riordan polynomial for tensor graphs tensor models are used nowadays for implementing a fundamental theory of quantum gravity we define here a polynomial t encoding the supplementary topological information this polynomial is a natural generalization of the bollobas riordan polynomial used to characterize matrix graphs and is different from the gur u polynomial r gur u ann henri poincare 11 565 2010 10 1007 s00023 010 0035 6 defined for a particular class of tensor graphs the colorable ones the polynomial t is defined for both colorable and non colorable graphs and it is proved to satisfy the deletion contraction relation a non trivial example of a non colorable graphs is analyzed

an application of one sided jacobi polynomials for spectral modeling of vector fields in polar coordinates a spectral tau method is proposed for solving vector field equations defined in polar coordinates the method employs one sided jacobi polynomials as radial expansion functions and fourier exponentials as azimuthal expansion functions all the regularity requirements of the vector field at the origin and the physical boundary conditions at a circumferential boundary are exactly satisfied by adjusting the additional tau coefficients of the radial expansion polynomials of the highest order the proposed method is applied to linear and nonlinear dispersive time evolution equations of hyperbolic type describing internal kelvin and poincare waves in a shallow stratified lake on a rotating plane

equation free implementation of statistical moment closures we present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex large scale nonlinear systems building on recently developed equation free methods this approach numerically integrates the closure dynamics the equations of which may not even be available in closed form although closure dynamics introduce statistical assumptions of unknown validity they can have significant computational advantages as they typically have fewer degrees of freedom and may be much less stiff than the original detailed model the numerical closure approach can in principle be applied to a wide class of nonlinear problems including strongly coupled systems either deterministic or stochastic for which there may be no scale separation we demonstrate the equation free approach for implementing entropy based eyink levermore closures on a nonlinear stochastic partial differential equation

a spectral method for polar coordinates a new set of polynomial functions that can be used in spectral expansions of c functions in polar coordinates r is defined by a singular sturm liouville equation with the use of the basis functions the spectral representations remain analytic at the pole despite the coordinate singularity because the pole condition is exactly satisfied at the origin for ag azimuthal modes not just a few of the gravest modes which is the usual case based on recurrence relations fast and stable numerical operators for 1 r r d dr the laplacian and helmholtz operators and their inverses are developed although the spacings in the azimuthal direction of the collocation points near the origin are small i e 1 m2 where m is the number of radial modes the explicit numerical method for euler s equation is not stiff at the origin namely the cfl number is o 1 where the grid size in is defined as m i e the maximum allowable timestep is proportional to 1 m not 1 m2

renormalization group study of thea b diffusion limited reaction thea b diffusion limited reaction with equal initial densitiesa 0 b 0 n0 is studied by means of a field theoretic renormalization group formulation of the problem for dimensiond 2 an effective theory is derived from which the density and correlation functions call be calculated we find the density decays in time as a b sim c sqrt delta dt d 4 ford 4 with n0 c n 0 d 2 wherec is a universal constant andc is nonuniversal the calculation is extended to the case of unequal diffusion constantsd a d b resulting in a new amplitude but the same exponent ford 2 a controlled calculation is not possible but a heuristic argument is presented that the results above give at least the leading term in an e 2 d expansion finally we address reaction zones formed in the steady state by opposing currents ofa andb particles and derive scaling properties

dynamic correlations in phase ordering the 1 n expansion reconsidered the ordering dynamics of a system with a non conserved order parameter is considered following a quench into the ordered phase from high temperature newman and bray 1990 have set up an expansion in powers of 1 n for the o n model to obtain correlation functions and the two time exponent lambda but their calculation contains a simplifying assumption which is incorrect tight upper and lower bounds for lambda are obtained as a function of the space dimension d these bounds exclude the result of newman and bray although the dependence of lambda on d is qualitatively very similar comparison with simulations shows that the first order 1 n calculation does not agree with numerical results as well as previously thought

renormalisation of noncommutative ϕ 4 theory by multi scale analysis in this paper we give a much more efficient proof that the real euclidean 4 model on the four dimensional moyal plane is renormalisable to all orders we prove rigorous bounds on the propagator which complete the previous renormalisation proof based on renormalisation group equations for non local matrix models on the other hand our bounds permit a powerful multi scale analysis of the resulting ribbon graphs here the dual graphs play a particular role because the angular momentum conservation is conveniently represented in the dual picture choosing a spanning tree in the dual graph according to the scale attribution we prove that the summation over the loop angular momenta can be performed at no cost so that the power counting is reduced to the balance of the number of propagators versus the number of completely inner vertices in subgraphs of the dual graph

planar velocity dynamos in a sphere the earth9s main magnetic field is generally believed to be due to a self exciting dynamo process in the earth9s fluid outer core a variety of antidynamo theorems exist that set conditions under which a magnetic field cannot be indefinitely maintained by dynamo action against ohmic decay one such theorem the planar velocity antidynamo theorem precludes field maintenance when the flow is everywhere parallel to some plane e g the equatorial plane this paper shows that the proof of the planar velocity theorem fails when the flow is confined to a sphere due to diffusive coupling at the boundary then the theorem reverts to a conjecture there is a need to either prove the conjecture or find a functioning planar velocity dynamo to the latter end this paper formulates the toroidal poloidal spectral form of the magnetic induction equation for planar flows as a basis for a numerical investigation we have thereby determined magnetic field growth rates associated with various planar flows in spheres for most flows the induced magnetic field decays with time supporting a planar velocity antidynamo conjecture for a spherical conducting fluid however one flow is exceptional indicating that magnetic field growth can occur we also re examine some classical kinematic dynamo models converting the flows where possible to planar flows for the flow of pekeris et al pekeris c l accad y shkoller b 1973 kinematic dynamos and the earth9s magnetic field phil trans r soc a 275 425 461 this conversion dramatically reduces the critical magnetic reynolds number

renormalization in quantum field theory and the riemann hilbert problem ii the β function diffeomorphisms and the renormalization group we showed in part i that the hopf algebra of feynman graphs in a given qft is the algebra of coordinates on a complex infinite dimensional lie group g and that the renormalized theory is obtained from the unrenormalized one by evaluating at 0 the holomorphic part of the riemann hilbert decomposition 1 of the loop g provided by dimensional regularization we show in this paper that the group g acts naturally on the complex space x of dimensionless coupling constants of the theory more precisely the formula g 0 gz 1 z 3 3 2 for the effective coupling constant when viewed as a formal power series does define a hopf algebra homomorphism between the hopf algebra of coordinates on the group of formal diffeomorphisms to the hopf algebra this allows first of all to read off directly without using the group g the bare coupling constant and the renormalized one from the riemann hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms this shows that renormalization is intimately related with the theory of non linear complex bundles on the riemann sphere of the dimensional regularization parameter it also allows to lift both the renormalization group and the function as the asymptotic scaling in the group g this exploits the full power of the riemann hilbert decomposition together with the invariance of under a change of unit of mass this not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group g for the full higher pole structure of minimal subtracted counterterms in terms of the residue

upper bound on the coarsening rate for an epitaxial growth model we study a specific example of energy driven coarsening in two space dimensions the energy is u 2 1 u 2 2 the evolution is the fourth order pde representing steepest descent this equation has been proposed as a model of epitaxial growth for systems with slope selection numerical simulations and heuristic arguments indicate that the standard deviation of u grows like t1 3 and the energy per unit area decays like t 1 3 we prove a weak one sided version of the latter statement the time averaged energy per unit area decays no faster than t 1 3 our argument follows a strategy introduced by kohn and otto in the context of phase separation combining i a dissipation relation ii an isoperimetric inequality and iii an ode lemma the interpolation inequality is new and rather subtle our proof is by contradiction relying on recent compactness results for the aviles giga energy 2003 wiley periodicals inc

on magnetic energy instability in spherical stationary flows eigenmode or linear analysis of the induction equation yields magnetic field structures which grow or decay exponentially in time under the influence of a prescribed flow geometry however due to

energy scaling approach to phase ordering growth laws we present a simple unified approach to determining the growth law for the characteristic length scale l t in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase this approach based on a scaling assumption for pair correlations determines l t self consistently for purely dissipative dynamics by computig the time dependence of the energy in two ways we derive growth laws for conserved and nonconserved o n models including two dimensional xy models and systems with textures we demonstrate that the growth laws for other systems such as liquid crystals and potts models are determined by the type of topological defect in the order parameter field that dominates the energy we also obtain generalized porod laws for systems with topological textures

time dependent kinematic dynamos with stationary flows numerical solutions to the magnetic induction equation in a sphere have been obtained for a number of stationary velocity models by searching for non steady magnetic fields and in some circumstances showing that all magnetic field modes decay the inability of several earlier researchers to find convergent steady solutions is explained results of previous authors are generally confirmed but also extended to cover non steady fields different values of magnetic reynolds number and other parameters and higher truncation limits some non decaying fields are found where only decaying or non convergent results have previously been reported two flows epsilon s 0 2 t 0 2 and epsilon s 0 2 t 0 1 each consisting of two very simple axisymmetric rolls are seen to sustain growing fields provided that i the magnetic reynolds number r and the poloidal to toroidal flow ratio epsilon are of appropriate magnitudes and ii the meridional s 0 2 flow is directed inwards along the equatorial plane and out towards the poles an even simpler axisymmetric single roll flow epsilon s 0 1 t 0 1 is also seen to support growing fields for appropriate epsilon and r these simple flows dispel the somewhat prevalent belief that dynamo maintenance relies on the supporting flow being complex and having length scale significantly less than that of the conducting fluid volume

algebras of distributions suitable for phase space quantum mechanics i the twisted product of functions on r2n is extended to a algebra of tempered distributions that contains the rapidly decreasing smooth functions the distributions of compact support and all polynomials and moreover is invariant under the fourier transformation the regularity properties of the twisted product are investigated a matrix presentation of the twisted product is given with respect to an appropriate orthonormal basis which is used to construct a family of banach algebras under this product

poloidal toroidal decomposition in a finite cylinder i influence matrices for the magnetohydrodynamic equations the navier stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder this formulation insures that the velocity and magnetic fields are divergence free by construction but leads to systems of partial differential equations of higher order whose boundary conditions are coupled the influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems the magnetic field in the induction equation is matched to that in an exterior vacuum by means of the dirichlet to neumann mapping thus eliminating the need to discretize the exterior the influence matrix is scaled in order to attain an acceptable condition number

theory of phase ordering kinetics the theory of phase ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken symmetry phase is reviewed with the emphasis on recent developments interest will focus on the scaling regime that develops at long times after the quench how can one determine the growth laws that describe the time dependence of characteristic length scales and what can be said about the form of the associated scaling functions particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered for example vector and tensor elds the latter are needed for example to describe phase ordering in nematic liquid crystals on which there have been a number of recent experiments the study of topological defects domain walls vortices strings and monopoles provides a unifying framework for discussing coarsening in these dia erent systems

coarsening dynamics of the one dimensional cahn hilliard model the dynamics of one dimensional cahn hilliard model is studied the stationary and particle type solutions the bubbles are perused as a function of initial conditions boundary conditions and system size we characterize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system a set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations we also compare these dynamics with the bubble dynamics deduced from the classical kink interaction computation where our model seems to be more appropriated in the case of two bubbles we deduce analytical expressions for the bubble s position and the bubble s width besides a simple description of the ulterior dynamics is presented

parametric representation of a translation invariant renormalizable noncommutative model we construct here the parametric representation of a translation invariant renormalizable scalar model on the noncommutative moyal space of even dimension d this representation of the feynman amplitudes is based on some integral form of the noncommutative propagator all types of graphs planar and non planar are analyzed the role played by noncommutativity is explicitly shown this parametric representation established allows us to calculate the power counting of the model furthermore the space dimension d is just a parameter in the formulae obtained this paves the road for the dimensional regularization of this noncommutative model

kinetics of phase ordering in the o n model with a conserved order parameter we study the phase ordering dynamics of the o n model with a conserved order parameter for systems with topological defects we present results from both cell dynamical simulations and predictions of a gaussian auxiliary field gaf approximation for the xy n 2 model in two and three dimensions and the heisenberg n 3 model in three dimensions we describe the results for the structure factor s q and growth law l t from simulations the growth laws obtained are consistent with theoretical predictions based on energy scaling arguments the structure factor shows good dynamical scaling using a length extracted from its first moment the simulations are compared with the theoretical predictions of the gaf for the scaling functions our results show that the gaf gives a good qualitative description of most features of the structure factor however it overestimates the amplitude of the porod tail in the large q limit moreover for small q the structure factor exhibits a q2 behaviour instead of the expected generalized yeung result of q4

dimensionally regularized tsallis statistical mechanics and two body newton s gravitation abstract typical tsallis statistical mechanics quantifiers like the partition function and the mean energy exhibit poles we are speaking of the partition function z and the mean energy u the poles appear for distinctive values of tsallis characteristic real parameter q at a numerable set of rational numbers of the q line these poles are dealt with dimensional regularization resources the physical effects of these poles on the specific heats are studied here for the two body classical gravitation potential

nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a fourier finite element technique and an interior penalty method the maxwell equations in the mhd limit in heterogeneous axisymmetric domains composed of conducting and non conducting regions are solved by using a mixed fourier lagrange finite element technique finite elements are used in the meridian plane and fourier modes are used in the azimuthal direction parallelization is made with respect to the fourier modes continuity conditions across interfaces are enforced using an interior penalty technique the performance of the method is illustrated on kinematic and full dynamo configurations

domain growth in weakly disordered magnets we present results from extensive numerical simulations of phase ordering dynamics in a mean field dynamical model of weakly disordered random magnets we apply a stringent test of dynamical scaling to confirm that the domain growth is superuniversal i e the scaling function for the disordered case is the same as for the pure case at least for the disorder amplitudes we consider however we are not able to ascertain a universal functional form for the domain growth law

quantum field theory on quantized bergman domain we present an oscillator realization of discrete series representations of group su 2 2 we give formulas for the coherent state star product quantization of a bergman domain d a formulation of a regularized noncommutative scalar field on a quantized d is given

on the renormalizability of noncommutative u 1 gauge theory an algebraic approach we investigate the quantum effects of the nonlocal gauge invariant operator in the noncommutative u 1 action and its consequences to the infrared sector of the theory nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the lorentz invariance more recently a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field and the first loop analysis was carried out blaschke et al 2009 eur phys j c 62 433 43 we will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only brst doublets this will allow us to conduct a complete brst algebraic study of the renormalizability of the theory following zwanziger s method of localization of nonlocal operators in qft

multi orientable group field theory group field theories gfts are quantum field theories over group manifolds they can be seen as a generalization of matrix models gft feynman graphs are tensor graphs generalizing ribbon graphs or combinatorial maps these graphs are not always dual to manifolds in order to simplify the topological structure of these various singularities colored gft was recently introduced and intensively studied we propose here a different simplification of gft which we call multi orientable gft we study the relation between multi orientable gft feynman graphs and colorable graphs we prove that tadfaces and some generalized tadpoles are absent some feynman amplitude computations are performed a few remarks on the renormalizability of both multi orientable and colorable gft are made a generalization from three dimensional to four dimensional theories is also proposed

the ponzano regge model and parametric representation we give a parametric representation of the effective noncommutative field theory derived from a kappa deformation of the ponzano regge model and define a generalized kirchhoff polynomial with kappa correction terms obtained in a kappa linear approximation we then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature we look in particular at the tetrahedron graph which is the basic case of relevance to quantum gravity with the help of computer calculations we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients hence the hypersurface of the tetrahedron is not polynomially countable this shows that the correction term can change significantly the motivic properties of the hypersurfaces with respect to the classical case

a soluble model of domain growth in one dimensional disordered systems we introduce a new algorithm for domain growth in disordered systems at low temperatures based on the tendency for such a system to freeze into metastable states we apply the algorithm to the d 1 random bond ising model for a variety of bond distributions the analytical forms we obtain for the two point correlation function and autocorrelation function agree well with numerical simulations of the model these forms are not the same as those of the pure ising model with glauber dynamics

noise induced jumps in two coupled duffing oscillators abstract we consider two coupled duffing oscillators with the coexistence of four attractors switching between the coexisting attractors by noises is investigated three types of noises such as gaussian amplitude dependent and dichotomous are used we observed noise induced extrinsic intermittency intermittent dynamics is characterized using power spectrum average and relative residence times on each precoupled attractors and probability distribution of time interval between successive switchings variation of probability distribution of state variables in poincare map is studied as a function of noise strength the effect of various noises is compared the occurrence of crisis induced and type i intermittencies are also presented

the massless higher loop two point function we introduce a new method for computing massless feynman integrals analytically in parametric form an analysis of the method yields a criterion for a primitive feynman graph g to evaluate to multiple zeta values the criterion depends only on the topology of g and can be checked algorithmically as a corollary we reprove the result due to bierenbaum and weinzierl that the massless 2 loop 2 point function is expressible in terms of multiple zeta values and generalize this to the 3 4 and 5 loop cases we find that the coefficients in the taylor expansion of planar graphs in this range evaluate to multiple zeta values but the non planar graphs with crossing number 1 may evaluate to multiple sums with 6th roots of unity our method fails for the five loop graphs with crossing number 2 obtained by breaking open the bipartite graph k3 4 at one edge

spectral method for matching exterior and interior elliptic problems a spectral method is described for solving coupled elliptic problems on an interior and an exterior domain the method is formulated and tested on the two dimensional interior poisson and exterior laplace problems whose solutions and their normal derivatives are required to be continuous across the interface a complete basis of homogeneous solutions for the interior and exterior regions corresponding to all possible dirichlet boundary values at the interface are calculated in a preprocessing step this basis is used to construct the influence matrix which serves to transform the coupled boundary conditions into conditions on the interior problem chebyshev approximations are used to represent both the interior solutions and the boundary values a standard chebyshev spectral method is used to calculate the interior solutions the exterior harmonic solutions are calculated as the convolution of the free space green s function with a surface density this surface density is itself the solution to an integral equation which has an analytic solution when the boundary values are given as a chebyshev expansion properties of chebyshev approximations insure that the basis of exterior harmonic functions represents the external near boundary solutions uniformly the method is tested by calculating the electrostatic potential resulting from charge distributions in a rectangle the resulting influence matrix is well conditioned and solutions converge exponentially as the resolution is increased the generalization of this approach to three dimensional problems is discussed in particular the magnetohydrodynamic equations in a finite cylindrical domain surrounded by a vacuum

loop vertex expansion for φ2k theory in zero dimension in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction

spectral solvers for spherical elliptic problems a new family of direct spectral solvers for the 3d helmholtz equation in a spherical gap and inside a sphere for nonaxisymmetric problems is presented a variational formulation no collocation is adopted based on the fourier expansion and the associated legendre functions to represent the angular dependence over the sphere and using basis functions generated by legendre or jacobi polynomials to represent the radial structure of the solution in the present method boundary conditions on the polar axis and at the sphere center are not required and never mentioned by construction the spectral solution of the vector dirichlet problem is also considered by employing a transformation that uncouples the spherical components of the fourier modes and that is implemented here for the first time the condition numbers of the matrices involved in the scalar solvers are computed and the spectral convergence of all the proposed solution algorithms is verified by numerical tests

parametric representation of noncommutative field theory in this paper we investigate the schwinger parametric representation for the feynman amplitudes of the recently discovered renormalizable phi 4 4 quantum field theory on the moyal non commutative mathbb r 4 space this representation involves new hyperbolic polynomials which are the non commutative analogs of the usual kirchoff or symanzik polynomials of commutative field theory but contain richer topological information

power counting theorem for non local matrix models and renormalisation solving the exact renormalisation group equation a la wilson polchinski perturbatively we derive a power counting theorem for general matrix models with arbitrarily non local propagators the power counting degree is determined by two scaling dimensions of the cut off propagator and various topological data of ribbon graphs as a necessary condition for the renormalisability of a model the two scaling dimensions have to be large enough relative to the dimension of the underlying space in order to have a renormalisable model one needs additional locality properties typically arising from orthogonal polynomials which relate the relevant and marginal interaction coefficients to a finite number of base couplings the main application of our power counting theorem is the renormalisation of field theories on noncommutative d in matrix formulation

renormalization of tensorial group field theories abelian u 1 models in four dimensions we tackle the issue of renormalizability for tensorial group field theories tgft including gauge invariance conditions with the rigorous tool of multi scale analysis to prepare the ground for applications to quantum gravity models in the process we define the appropriate generalization of some key qft notions including connectedness locality and contraction of high subgraphs we also define a new notion of wick ordering corresponding to the subtraction of maximal melonic tadpoles we then consider the simplest examples of dynamical 4 dimensional tgft with gauge invariance conditions for the abelian u 1 case we prove that they are super renormalizable for any polynomial interaction