almost exponential decay of periodic viscous surface waves without surface tension we consider a viscous fluid of finite depth below the air occupying a three dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary the fluid dynamics are governed by the gravity driven incompressible navier stokes equations and the effect of surface tension is neglected on the free surface the long time behavior of solutions near equilibrium has been an intriguing question since the work of beale commun pure appl math 34 3 359 392 1981 this paper is the third in a series of three guo in local well posedness of the viscous surface wave problem without surface tension anal pde 2012 to appear in decay of viscous surface waves without surface tension in horizontally infinite domains preprint 2011 that answers this question here we consider the case in which the free interface is horizontally periodic we prove that the problem is globally well posed and that solutions decay to equilibrium at an almost exponential rate in particular the free interface decays to a flat surface our framework contains several novel techniques which include 1 a priori estimates that utilize a geometric reformulation of the equations 2 a two tier energy method that couples the boundedness of high order energy to the decay of low order energy the latter of which is necessary to balance out the growth of the highest derivatives of the free interface 3 a localization procedure that is compatible with the energy method and allows for curved lower surface geometry our decay estimates lead to the construction of global in time solutions to the surface wave problem

a faffa mlfma algorithm for electromagnetic scattering based on the multilevel fast multipole algorithm mlfma an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation where the fast far field approximation faffa is combined with mlfma the translation between groups in mlfma is expensive because spherical hankel functions and legendre polynomials are involved and the translator is defined on an eward sphere with many k spl circ directions when two groups are in the far field region however the translation can be greatly simplified by faffa where only a single k spl circ direction is involved in the translator the condition for using faffa and the way to efficiently incorporate faffa with mlfma are discussed complexity analysis illustrates that the computational cost in faffa mlfma can be asymptotically cut by half compared to the conventional mlfma numerical results are given to verify the efficiency of the algorithm

zero surface tension limit of viscous surface waves we consider the free boundary problem for a layer of viscous incompressible fluid in a uniform gravitational field lying above a rigid bottom and below the atmosphere for the semi small initial data we prove the zero surface tension limit of the problem within a local time interval the unique local strong solution with surface tension is constructed as the limit of a sequence of approximate solutions to a special parabolic regularization for the small initial data we prove the global in time zero surface tension limit of the problem

krawtchouk polynomials and universal bounds for codes and designs in hamming spaces universal bounds for the cardinality of codes in the hamming space f sub r sup n with a given minimum distance d and or dual distance d are stated a self contained proof of optimality of these bounds in the framework of the linear programming method is given the necessary and sufficient conditions for attainability of the bounds are found the parameters of codes satisfying these conditions are presented in a table a new upper bound for the minimum distance of self dual codes and a new lower bound for the crosscorrelation of half linear codes are obtained

an inverse fast multipole method for geometry reconstruction using scattered field information a novel inverse fast multipole method fmm application for accelerating inverse problem solution is presented the idea is based on the multipole expansion properties of the scattered fields and reconstructed equivalent currents which allow an easy inversion of the fmm operators resulting in a forward solution of the inverse problem i e without matrix inversion or cost function minimization in addition this technique allows the use of reconstruction domain discretization larger than half a wavelength and overcomes the restriction of having the entire target enclosed by a reconstruction domain features that also contribute to the reduction of calculation time two 3d application examples are presented highlighting the achieved inverse fmm speed up with respect to previous inverse scattering methods for geometry reconstruction

linear programming bounds for doubly even self dual codes using a variant of the linear programming method we derive a new upper bound on the minimum distance d of doubly even self dual codes of length n asymptotically for n growing it gives d n spl les 0 166315 spl middot spl middot spl middot o 1 thus improving on the mallows odlyzko sloane bound of 1 6 to establish this we prove that in any doubly even self dual code the distance distribution is asymptotically upper bounded by the corresponding normalized binomial distribution in a certain interval

well posedness for the motion of an incompressible liquid with free surface boundary we study the motion of an incompressible perfect liquid body in vacuum this can be thought of as a model for the motion of the ocean or a star the free surface moves with the velocity of the liquid and the pressure vanishes on the free surface this leads to a free boundary problem for euler s equations where the regularity of the boundary enters to highest order we prove local existence in sobolev spaces assuming a physical condition related to the fact that the pressure of a fluid has to be positive

a bound for divisible codes a divisible code is a linear code whose word weights have a common divisor larger than one if the divisor is a power of the field characteristic there is a simple bound on the dimension of the code in terms of its weight range when this bound is applied to the subcode of words with weight divisible by four in a type i binary self dual code it yields an asymptotic improvement of the conway sloane bound for self dual codes

zero surface tension limit of the free surface incompressible euler equations with damping abstract we consider the free boundary problem for a layer of an incompressible inviscid fluid in a uniform gravitational field lying above a rigid bottom and below the atmosphere in a horizontally periodic setting we establish the global in time zero surface tension limit of the problem with damping for the small initial data

the fast multipole method we study integral methods applied to the resolution of the maxwell equations where the linear system is solved using an iterative method which requires only matrix vector products the fast multipole method fmm is one of the most efficient methods used to perform matrix vector products and accelerate the resolution of the linear system a problem involving n degrees of freedom may be solved in cniternlogn floating operations where c is a constant depending on the implementation of the method in this article several techniques allowing one to reduce the constant c are analyzed this reduction implies a lower total cpu time and a larger range of application of the fmm in particular new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms several numerical tests are also described these confirm the efficiency and the theoretical complexity of the fmm

convolutional and tail biting quantum error correcting codes rate n 2 n unrestricted and css type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self orthogonal rate 1 n f4 linear and binary linear convolutional codes respectively these codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes rate n 2 n block stabilizer codes with the same rate and error correction capability and essentially the same decoding complexity are derived from these convolutional codes via tail biting

an improved upper bound on the minimum distance of doubly even self dual codes we derive a new upper bound on the minimum distance d of doubly even self dual codes of length n asymptotically for n growing it gives lim sub n spl rarr spl infin sup d n spl les 5 5 sup 3 4 10 0 165630 thus improving on the mallows odlyzko sloane bound of 1 6 and our recent bound of 0 166315

multilevel fast multipole accelerated inverse equivalent current method employing rao wilton glisson discretization of electric and magnetic surface currents the radiation of any object in a homogeneous environment can be described by a set of equivalent sources different types of equivalent sources are feasible and all of them have their own benefits equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if a priori information about the object shall be used also they can immediately provide diagnostic information about the object in this paper a very flexible equivalent current method is presented which has been derived from a general purpose boundary integral equation solver as such the method works with arbitrary triangular surface meshes and rao wilton glisson basis functions where electric and or magnetic surface current densities can be assumed high efficiency is achieved since the multilevel fast multipole method has been adapted to speed up the inverse solution process results obtained from simulations and measurements are presented where large scale problems with dimensions up to 75 wavelengths are considered

the zero surface tension limit of two dimensional water waves we consider two dimensional water waves of infinite depth periodic in the horizontal direction it has been proven by wu in the slightly different nonperiodic setting that solutions to this initial value problem exist in the absence of surface tension recently ambrose has proven that solutions exist when surface tension is taken into account in this paper we provide a shorter more elementary proof of existence of solutions to the water wave initial value problem both with and without surface tension our proof requires estimating the growth of geometric quantities using a renormalized arc length parametrization of the free surface and using physical quantities related to the tangential velocity of the free surface using this formulation we find that as surface tension goes to 0 the water wave without surface tension is the limit of the water wave with surface tension far from being a simple adaptation of previous works our method requires a very original choice of variables these variables turn out to be physical and well adapted to both cases c

global wellposedness of the 3 d full water wave problem we consider the problem of global in time existence and uniqueness of solutions of the 3 d infinite depth full water wave problem in the setting that the interface tends to the horizontal plane the velocity and acceleration on the interface tend to zero at spatial infinity we show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders for any initial interface that is sufficiently small in its steepness and velocity we show that there exists a unique smooth solution of the full water wave problem for all time and the solution decays at the rate 1 t

uniform regularity and vanishing viscosity limit for the free surface navier stokes equations we study the inviscid limit of the free boundary navier stokes equations we prove the existence of solutions on a uniform time interval by using a suitable functional framework based on sobolev conormal spaces this allows us to use a strong compactness argument to justify the inviscid limit our approach does not rely on the justification of asymptotic expansions in particular we get a new existence result for the euler equations with free surface from the one for navier stokes

global solutions for the gravity water waves system in 2d we consider the gravity water waves system in the case of a one dimensional interface for sufficiently smooth and localized initial data and prove global existence of small solutions this improves the almost global existence result of wu invent math 177 1 45 135 2009 we also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear unlike the three dimensional case germain et al ann math 175 2 691 754 2012 wu invent math 184 1 125 220 2011 in particular we identify a suitable nonlinear logarithmic correction and show modified scattering the solutions we construct in this paper appear to be the first global smooth nontrivial solutions of the gravity water waves system in 2d

weights modulo a prime power in divisible codes and a related bound in this paper we generalize the theorem given by r m wilson about weights modulo pt in linear codes to a divisible code version using a similar idea we give an upper bound for the dimension of a divisible code by some divisibility property of its weight enumerator modulo pe we also prove that this bound implies ward s bound for divisible codes moreover we see that in some cases our bound gives better results than ward s bound

shadow bounds for self dual codes conway and sloane 1990 have previously given an upper bound on the minimum distance of a singly even self dual binary code using the concept of the shadow of a self dual code we improve their bound finding that the minimum distance of a self dual binary code of length n is at most 4 n 24 4 except when n mod 24 22 when the bound is 4 n 24 6 we also show that a code of length a multiple of 24 meeting the bound cannot be singly even the same technique gives similar results for additive codes over gf 4 relevant to quantum coding theory

inverse scattering for conductors by the equivalent source method the inverse scattering for two dimensional conductors is investigated assume that an incident wave is incident upon conducting cylinders of unknown shape and the scattered field is measured outside by properly processing the scattering data the position and shape of the conducting scatterers can then be reconstructed the proposed theory of inverse scattering is a combination of the diffraction tomography and the equivalent source method to overcome the ill posedness the condition of the measured scattered field and the boundary condition on the conductor surfaces are combined and recast into an optimization problem using the least squares concept by comparing the reconstructed and the prescribed results the inversion algorithms are numerically examined note that if a priori information of the shape is sufficient and the equivalent sources are properly placed the algorithms can be flexibly applied to the cases of multiple conductors also the effects of noise contamination and multiple scattering on the reconstruction result are numerically investigated

well posedness of the free surface incompressible euler equations with or without surface tension we provide a new method for treating free boundary problems in perfect fluids and prove local in time well posedness in sobolev spaces for the free surface incompressible 3d euler equations with or without surface tension for arbitrary initial data and without any irrotationality assumption on the fluid this is a free boundary problem for the motion of an incompressible perfect liquid in vacuum wherein the motion of the fluid interacts with the motion of the free surface at highest order

reconstructing distortions on reflector antennas with the iterative field matrix method using near field observation data this work extends the mathematical formulation of the iterative field matrix method for observed data from the near field region of a perfect electric conductor the method is used as a diagnosis tool for reflector antennas to determine the positions and extent of distortions from their idealized shapes the new formulation is tested on a reflector antenna with several significant bumps and excellent results are achieved this work also presents an example where the method of moments is used to generate the synthetic data and the inversion is performed using physical optics such a configuration ensures that the forward model is unbiased with respect to the inversion model demonstrating that the new formulation is also robust for these realistic scenarios

on the free boundary problem of three dimensional incompressible euler equations in this paper we consider in three dimensions the motion of a general inviscid incompressible fluid with a free interface that separates the fluid region from the vacuum we assume that the fluid region is below the vacuum and that there is no surface tension on the free surface then we prove the local well posedness of the free boundary problem in sobolev space provided that there is no self intersection point on the initial surface and under the stability assumption that with being restricted to the initial surface 2007 wiley periodicals inc

well posedness in sobolev spaces of the full water wave problem in 3 d we consider the motion of the interface separating an inviscid incompressible irrotational fluid from a region of zero density in three dimensional space we assume that the fluid region is below the vacuum the fluid is under the influence of gravity and the surface tension is zero assume that the density of mass of the fluid is one the gravitational field is 0 0 1 the free interface is t at time t 0 and the fluid occupies the region t the motion of the fluid is described by vt v v 0 0 1 p on t t 0 euler s equation 1 1 div v 0 on t t 0 incompressible 1 2 curl v 0 on t t 0 irrotational 1 3 where v v1 v2 v3 is the fluid velocity p is the fluid pressure since we neglect the surface tension the pressure is zero on the interface so on the interface p 0 on t 1 4 1 v is tangent to the free surface t t 1 5 we want to find solutions of system 1 1 1 5 taking prescribed initial data such that for every fixed t 0 t approaches the xy plane at infinity and v x y z t 0 vt x y z t 0 as x y z since the fluid is assumed irrotational incompressible we can reduce the study of the entire motion to the motion of the free surface the above model is a 3 d water wave model it is generally known that when surface tension is neglected the motion of the interface between an inviscid fluid and vacuum under the influence of gravity can be subject to taylor instability 8 22 in a previous work 24 we studied the 2 dimensional water wave model we showed that for a 2 d water wave the sign condition relating to taylor instability always holds for nonself intersecting interface that is the motion of the interface is not subject to taylor instability we showed further that the 2 d full nonlinear water wave problem is uniquely solvable in sobolev spaces locally in time for any initially nonself intersecting interface earlier works on the well posedness in sobolev spaces of the 2 d water wave problem include nalimov 18 yosihara 25 and walter craig 6 where the main results concern the well posedness of the

geometry and a priori estimates for free boundary problems of the euler s equation in this paper we derive estimates to the free boundary problem for the euler equation with surface tension and without surface tension provided the rayleigh taylor sign condition holds we prove that as the surface tension tends to 0 when the rayleigh taylor condition is satisfied solutions converge to the euler flow with zero surface tension 2007 wiley periodicals inc

global existence for capillary water waves consider the capillary water waves equations set in the whole space with infinite depth and consider small data i e sufficiently close to zero velocity and constant height of the water we prove global existence and scattering the proof combines in a novel way the energy method with a cascade of energy estimates the space time resonance method and commuting vector fields 2015 wiley periodicals inc

fast inverse scattering solutions using the distorted born iterative method and the multilevel fast multipole algorithm the distorted born iterative method dbim computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations by decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation large or high contrast variations in medium properties can be imaged through iterations that are each subject to the distorted born approximation however the need to repeatedly compute forward solutions still imposes a very heavy computational burden to ameliorate this problem the multilevel fast multipole algorithm mlfma has been applied as a forward solver within the dbim the mlfma computes forward solutions in linear time for volumetric scatterers the typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive mlfma setup additional benefits are gained by employing kaczmarz like iterations where partial measurements are used to accelerate convergence numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen