264 research outputs found
Numerical Methods for Multilattices
Among the efficient numerical methods based on atomistic models, the
quasicontinuum (QC) method has attracted growing interest in recent years. The
QC method was first developed for crystalline materials with Bravais lattice
and was later extended to multilattices (Tadmor et al, 1999). Another existing
numerical approach to modeling multilattices is homogenization. In the present
paper we review the existing numerical methods for multilattices and propose
another concurrent macro-to-micro method in the numerical homogenization
framework. We give a unified mathematical formulation of the new and the
existing methods and show their equivalence. We then consider extensions of the
proposed method to time-dependent problems and to random materials.Comment: 31 page
Higher Spins from Tensorial Charges and OSp(N|2n) Symmetry
It is shown that the quantization of a superparticle propagating in an N=1,
D=4 superspace extended with tensorial coordinates results in an infinite tower
of massless spin states satisfying the Vasiliev unfolded equations for free
higher spin fields in flat and AdS_4 N=1 superspace. The tensorial extension of
the AdS_4 superspace is proved to be a supergroup manifold OSp(1|4). The model
is manifestly invariant under an OSp(N|8) (N=1,2) superconformal symmetry. As a
byproduct, we find that the Cartan forms of arbitrary Sp(2n) and OSp(1|2n)
groups are GL(2n) flat, i.e. they are equivalent to flat Cartan forms up to a
GL(2n) rotation. This property is crucial for carrying out the quantization of
the particle model on OSp(1|4) and getting the higher spin field dynamics in
super AdS_4, which can be performed in a way analogous to the flat case.Comment: LaTeX, 21 page (JHEP style), misprints corrected, added comments on
the relation of results of hep-th/0106149 with hep-th/9904109 and
hep-th/9907113, references adde
The SU(3) spin chain sigma model and string theory
The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous
dimension of single trace operators involving the three complex scalars of N=4
supersymmetric Yang-Mills. We construct the non-linear sigma model describing
the continuum limit of the SU(3) spin chain. We find that this sigma model
corresponds to a string moving with large angular momentum in the five-sphere
in AdS_5xS^5. The energy and spectrum of fluctuations for rotating circular
strings with angular momenta along three orthogonal directions of the
five-sphere is reproduced as a particular case from the spin chain sigma model.Comment: 14 pages. Latex.v2: Misprints corrected. v3: Minor changes and
improved details from journal versio
Absorbing boundary conditions for the Westervelt equation
The focus of this work is on the construction of a family of nonlinear
absorbing boundary conditions for the Westervelt equation in one and two space
dimensions. The principal ingredient used in the design of such conditions is
pseudo-differential calculus. This approach enables to develop high order
boundary conditions in a consistent way which are typically more accurate than
their low order analogs. Under the hypothesis of small initial data, we
establish local well-posedness for the Westervelt equation with the absorbing
boundary conditions. The performed numerical experiments illustrate the
efficiency of the proposed boundary conditions for different regimes of wave
propagation
Geometry and dynamics of higher-spin frame fields
We give a systematic account of unconstrained free bosonic higher-spin fields
on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism.
The generalized spin connections are determined by solving a chain of
torsion-like constraints. Via a generalization of the vielbein postulate these
allow to determine higher-spin Christoffel symbols, whose relation to the de
Wit--Freedman connections is discussed. We prove that the generalized Einstein
equations, despite being of higher-derivative order, give rise to the AdS
Fronsdal equations in the compensator formulation. To this end we derive
Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the
possibility of a geometrical and local action principle, which is manifestly
invariant under unconstrained higher-spin symmetries.Comment: 30 pages, uses youngtab.sty, v2: minor changes, references adde
On spin chains and field theories
We point out that the existence of global symmetries in a field theory is not
an essential ingredient in its relation with an integrable model. We describe
an obvious construction which, given an integrable spin chain, yields a field
theory whose 1-loop scale transformations are generated by the spin chain
Hamiltonian. We also identify a necessary condition for a given field theory to
be related to an integrable spin chain.
As an example, we describe an anisotropic and parity-breaking generalization
of the XXZ Heisenberg spin chain and its associated field theory. The system
has no nonabelian global symmetries and generally does not admit a
supersymmetric extension without the introduction of more propagating bosonic
fields. For the case of a 2-state chain we find the spectrum and the
eigenstates. For certain values of its coupling constants the field theory
associated to this general type of chain is the bosonic sector of the
Leigh-Strassler deformation of N=4 SYM theory.Comment: 22 pages, Latex; v2. typos correcte
A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
We probe the long-range spin chain approach to planar N=4 gauge theory at
high loop order. A recently employed hyperbolic spin chain invented by
Inozemtsev is suitable for the SU(2) subsector of the state space up to three
loops, but ceases to exhibit the conjectured thermodynamic scaling properties
at higher orders. We indicate how this may be bypassed while nevertheless
preserving integrability, and suggest the corresponding all-loop asymptotic
Bethe ansatz. We also propose the local part of the all-loop gauge transfer
matrix, leading to conjectures for the asymptotically exact formulae for all
local commuting charges. The ansatz is finally shown to be related to a
standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical
string theory uncovers a detailed, non-perturbative agreement between the
corresponding expressions for the infinite tower of local charge densities.
However, the respective Bethe equations differ slightly, and we end by refining
and elaborating a previously proposed possible explanation for this
disagreement.Comment: 48 pages, 1 figure. v2, further results added: discussion of the
relationship to an inhomogeneous spin chain, normalization in sec 3 unified,
v3: minor mistakes corrected, published versio
Matching Higher Conserved Charges for Strings and Spins
We demonstrate that the recently found agreement between one-loop scaling
dimensions of large dimension operators in N=4 gauge theory and energies of
spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite
number of hidden higher commuting charges. This dynamical agreement is of a
mathematically highly intricate and non-trivial nature. In particular, on the
gauge side the generating function for the commuting charges is obtained by
integrable quantum spin chain techniques from the thermodynamic density
distribution function of Bethe roots. On the string side the generating
function, containing information to arbitrary loop order, is constructed by
solving exactly the Backlund equations of the integrable classical string sigma
model. Our finding should be an important step towards matching the integrable
structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof
that the entire infinite towers of commuting gauge and string charges match);
references adde
On Integrability of Classical SuperStrings in AdS_5 x S^5
We explore integrability properties of superstring equations of motion in
AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges
and construct a Lax representation for the corresponding Hamiltonian dynamics
on subspace of physical superstring degrees of freedom. We present some
explicit results for the corresponding conserved charges by consistently
reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both
bosonic and fermionic fields.Comment: JHEP style, 32 pages; v2: refined discussion of monodromy, refs adde
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Is the Helmholtz equation really sign-indefinite?
The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts
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