2,203,816 research outputs found
Planar Harmonic Polynomials of Type B
The hyperoctahedral group is the Weyl group of type B and is associated with
a two-parameter family of differential-difference operators T_i, i=1,..,N (the
dimension of the underlying Euclidean space). These operators are analogous to
partial derivative operators. This paper finds all the polynomials in N
variables which are annihilated by the sum of the squares (T_1)^2+(T_2)^2 and
by all T_i for i>2 (harmonic). They are given explicitly in terms of a novel
basis of polynomials, defined by generating functions. The harmonic polynomials
can be used to find wave functions for the quantum many-body spin Calogero
model.Comment: 17 pages, LaTe
Elastic collapse in disordered isostatic networks
Isostatic networks are minimally rigid and therefore have, generically,
nonzero elastic moduli. Regular isostatic networks have finite moduli in the
limit of large sizes. However, numerical simulations show that all elastic
moduli of geometrically disordered isostatic networks go to zero with system
size. This holds true for positional as well as for topological disorder. In
most cases, elastic moduli decrease as inverse power-laws of system size. On
directed isostatic networks, however, of which the square and cubic lattices
are particular cases, the decrease of the moduli is exponential with size. For
these, the observed elastic weakening can be quantitatively described in terms
of the multiplicative growth of stresses with system size, giving rise to bulk
and shear moduli of order exp{-bL}. The case of sphere packings, which only
accept compressive contact forces, is considered separately. It is argued that
these have a finite bulk modulus because of specific correlations in contact
disorder, introduced by the constraint of compressivity. We discuss why their
shear modulus, nevertheless, is again zero for large sizes. A quantitative
model is proposed that describes the numerically measured shear modulus, both
as a function of the loading angle and system size. In all cases, if a density
p>0 of overconstraints is present, as when a packing is deformed by
compression, or when a glass is outside its isostatic composition window, all
asymptotic moduli become finite. For square networks with periodic boundary
conditions, these are of order sqrt{p}. For directed networks, elastic moduli
are of order exp{-c/p}, indicating the existence of an "isostatic length scale"
of order 1/p.Comment: 6 pages, 6 figues, to appear in Europhysics Letter
New conjecture for the Perk-Schultz models
We present a new conjecture for the Perk-Schultz models. This
conjecture extends a conjecture presented in our article (Alcaraz FC and
Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in
cond-mat/0204074).Comment: 3 pages 0 figure
Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations
We have developed a new technique to measure viscoelasticity in soft
materials such as polymer solutions, by monitoring thermal fluctuations of
embedded probe particles using laser interferometry in a microscope.
Interferometry allows us to obtain power spectra of fluctuating beads from 0.1
Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear response
theory, we determined the frequency-dependent loss and storage shear moduli up
to frequencies on the order of a kHz. Our technique measures local values of
the viscoelastic response, without actively straining the system, and is
especially suited to soft biopolymer networks. We studied semiflexible F-actin
solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter
close to their gelation threshold. With small particles, we could probe the
transition from macroscopic viscoelasticity to more complex microscopic
dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G'=0.11
+/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close to
the onset of the elastic plateau, and scaling behavior consistent with G(omega)
as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateau
moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5%
concentration (weight/volume) respectively, in agreement to within a factor of
two with values obtained from conventional rheology. We also found evidence for
scaling of G(omega) as \omega^(1/2), consistent with the predictions of the
Rouse model for flexible polymers.Comment: 16 pages, with 15 PostScript figures (to be published in
Macromolecules
Generalization of the matrix product ansatz for integrable chains
We present a general formulation of the matrix product ansatz for exactly
integrable chains on periodic lattices. This new formulation extends the matrix
product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo
J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004)
4149-4182.)Comment: 5 pages. to appear in J. Phys. A: Math. Ge
The effect of concurrent geometry and roughness in interacting surfaces
We study the interaction energy between two surfaces, one of them flat, the
other describable as the composition of a small-amplitude corrugation and a
slightly curved, smooth surface. The corrugation, represented by a spatially
random variable, involves Fourier wavelengths shorter than the (local)
curvature radii of the smooth component of the surface. After averaging the
interaction energy over the corrugation distribution, we obtain an expression
which only depends on the smooth component. We then approximate that functional
by means of a derivative expansion, calculating explicitly the leading and
next-to-leading order terms in that approximation scheme. We analyze the
resulting interplay between shape and roughness corrections for some specific
corrugation models in the cases of electrostatic and Casimir interactions.Comment: 14 pages, 3 figure
Vacuum fluctuations and generalized boundary conditions
We present a study of the static and dynamical Casimir effects for a quantum
field theory satisfying generalized Robin boundary condition, of a kind that
arises naturally within the context of quantum circuits. Since those conditions
may also be relevant to measurements of the dynamical Casimir effect, we
evaluate their role in the concrete example of a real scalar field in 1+1
dimensions, a system which has a well-known mechanical analogue involving a
loaded string.Comment: 8 pages, 1 figur
The derivative expansion approach to the interaction between close surfaces
The derivative expansion approach to the calculation of the interaction
between two surfaces, is a generalization of the proximity force approximation,
a technique of widespread use in different areas of physics. The derivative
expansion has so far been applied to seemingly unrelated problems in different
areas; it is our principal aim here to present the approach in its full
generality. To that end, we introduce an unified setting, which is independent
of any particular application, provide a formal derivation of the derivative
expansion in that general setting, and study some its properties. With a view
on the possible application of the derivative expansion to other areas, like
nuclear and colloidal physics, we also discuss the relation between the
derivative expansion and some time-honoured uncontrolled approximations used in
those contexts. By putting them under similar terms as the derivative
expansion, we believe that the path is open to the calculation of next to
leading order corrections also for those contexts. We also review some results
obtained within the derivative expansion, by applying it to different concrete
examples and highlighting some important points.Comment: Minor changes, version to appear in Phys. Rev.
Inertial forces and dissipation on accelerated boundaries
We study dissipative effects due to inertial forces acting on matter fields
confined to accelerated boundaries in , , and dimensions. These
matter fields describe the internal degrees of freedom of `mirrors' and impose,
on the surfaces where they are defined, boundary conditions on a fluctuating
`vacuum' field. We construct different models, involving either scalar or Dirac
matter fields coupled to a vacuum scalar field, and use effective action
techniques to calculate the strength of dissipation. In the case of massless
Dirac fields, the results could be used to describe the inertial forces on an
accelerated graphene sheet.Comment: 7 pages, no figure
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