16 research outputs found
Location of Zeros in the Complex Temperature Plane: Absence of Lee-Yang Theorem, J
Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe
Surface Instability in Windblown Sand
We investigate the formation of ripples on the surface of windblown sand
based on the one-dimensional model of Nishimori and Ouchi [Phys. Rev. Lett. 71,
197 (1993)], which contains the processes of saltation and grain relaxation. We
carry out a nonlinear analysis to determine the propagation speed of the
restabilized ripple patterns, and the amplitudes and phases of their first,
second, and third harmonics. The agreement between the theory and our numerical
simulations is excellent near the onset of instability. We also determine the
Eckhaus boundary, outside which the steady ripple patterns are unstable.Comment: 23 pages, 8 figure
Fat Fisher Zeroes
We show that it is possible to determine the locus of Fisher zeroes in the
thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs
and their dual quadrangulations by matching up the real part of the high and
low temperature branches of the expression for the free energy. The form of
this expression for the free energy also means that series expansion results
for the zeroes may be obtained with rather less effort than might appear
necessary at first sight by simply reverting the series expansion of a function
g(z) which appears in the solution and taking a logarithm.
Unlike regular 2D lattices where numerous unphysical critical points exist
with non-standard exponents, the Ising model on planar phi4 graphs displays
only the physical transition at c = exp (- 2 beta) = 1/4 and a mirror
transition at c=-1/4 both with KPZ/DDK exponents (alpha = -1, beta = 1/2, gamma
= 2). The relation between the phi4 locus and that of the dual quadrangulations
is akin to that between the (regular) triangular and honeycomb lattices since
there is no self-duality.Comment: 12 pages + 6 eps figure
Bifurcations of a driven granular system under gravity
Molecular dynamics study on the granular bifurcation in a simple model is
presented. The model consists of hard disks, which undergo inelastic
collisions; the system is under the uniform external gravity and is driven by
the heat bath. The competition between the two effects, namely, the
gravitational force and the heat bath, is carefully studied. We found that the
system shows three phases, namely, the condensed phase, locally fluidized
phase, and granular turbulent phase, upon increasing the external control
parameter. We conclude that the transition from the condensed phase to the
locally fluidized phase is distinguished by the existence of fluidized holes,
and the transition from the locally fluidized phase to the granular turbulent
phase is understood by the destabilization transition of the fluidized holes
due to mutual interference.Comment: 35 pages, 17 figures, to be published in PR
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
De toekomst van het arbeidsovereenkomstenrecht
diminishing the discrimination between white collars and blue collars. Temporary gap in the legislation. Responsability of the state
Front Propagation in Self-Sustained and Laser Driven Explosive Crystal Growth: Stability Analysis and Morphological Aspects
Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe