7,973 research outputs found
Persistence of Randomly Coupled Fluctuating Interfaces
We study the persistence properties in a simple model of two coupled
interfaces characterized by heights h_1 and h_2 respectively, each growing over
a d-dimensional substrate. The first interface evolves independently of the
second and can correspond to any generic growing interface, e.g., of the
Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2,
however, is coupled to h_1 via a quenched random velocity field. In the limit
d\to 0, our model reduces to the Matheron-de Marsily model in two dimensions.
For d=1, our model describes a Rouse polymer chain in two dimensions advected
by a transverse velocity field. We show analytically that after a long waiting
time t_0\to \infty, the stochastic process h_2, at a fixed point in space but
as a function of time, becomes a fractional Brownian motion with a Hurst
exponent, H_2=1-\beta_1/2, where \beta_1 is the growth exponent characterizing
the first interface. The associated persistence exponent is shown to be
\theta_s^2=1-H_2=\beta_1/2. These analytical results are verified by numerical
simulations.Comment: 15 pages, 3 .eps figures include
Exact Phase Diagram of a model with Aggregation and Chipping
We revisit a simple lattice model of aggregation in which masses diffuse and
coalesce upon contact with rate 1 and every nonzero mass chips off a single
unit of mass to a randomly chosen neighbour with rate . The dynamics
conserves the average mass density and in the stationary state the
system undergoes a nonequilibrium phase transition in the plane
across a critical line . In this paper, we show analytically that in
arbitrary spatial dimensions, exactly and hence,
remarkably, independent of dimension. We also provide direct and indirect
numerical evidence that strongly suggest that the mean field asymptotic answer
for the single site mass distribution function and the associated critical
exponents are super-universal, i.e., independent of dimension.Comment: 11 pages, RevTex, 3 figure
Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra
We derive a lower bound for energies of harmonic maps of convex polyhedra in
to the unit sphere with tangent boundary conditions on the
faces. We also establish that maps, satisfying tangent boundary
conditions, are dense with respect to the Sobolev norm, in the space of
continuous tangent maps of finite energy.Comment: Acknowledgment added, typos removed, minor correction
Magnetic behavior of single crystalline HoPdSi
The magnetic behavior of single-crystal HoPdSi, crystallizing in an
AlB-derived hexagonal structure, is investigated by magnetic susceptibility
() and electrical resistivity () measurements along two directions.
There is no dramatic anisotropy in the high temperature Curie-Weiss parameter
or in the and isothermal magnetization data, though there is a
noticeable anisotropy in the magnitude of between two perpendicular
orientations. The degree of anisotropy is overall less prominent than in the Gd
(which is an S-state ion!) and Tb analogues. A point of emphasis is that this
compound undergoes long range magnetic ordering below 8 K as in the case of
analogous Gd and Dy compounds. Considering this fact for these compounds with
well-localised f-orbital, the spin glass freezing noted for isomorphous U
compounds in the recent literature could be attributed to the role of the
f-ligand hybridization, rather than just Pd-Si disorder.Comment: Physical Review B, in pres
Spatial survival probability for one-dimensional fluctuating interfaces in the steady state
We report numerical and analytic results for the spatial survival probability
for fluctuating one-dimensional interfaces with Edwards-Wilkinson or
Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are
obtained from analysis of steady-state profiles generated by integrating a
spatially discretized form of the Edwards-Wilkinson equation to long times. We
show that the survival probability exhibits scaling behavior in its dependence
on the system size and the `sampling interval' used in the measurement for both
`steady-state' and `finite' initial conditions. Analytic results for the
scaling functions are obtained from a path-integral treatment of a formulation
of the problem in terms of one-dimensional Brownian motion. A `deterministic
approximation' is used to obtain closed-form expressions for survival
probabilities from the formally exact analytic treatment. The resulting
approximate analytic results provide a fairly good description of the numerical
data.Comment: RevTeX4, 21 pages, 8 .eps figures, changes in sections IIIB and IIIC
and in Figs 7 and 8, version to be published in Physical Review
Persistence and the Random Bond Ising Model in Two Dimensions
We study the zero-temperature persistence phenomenon in the random bond Ising model on a square lattice via extensive numerical simulations. We find
strong evidence for ` blocking\rq regardless of the amount disorder present in
the system. The fraction of spins which {\it never} flips displays interesting
non-monotonic, double-humped behaviour as the concentration of ferromagnetic
bonds is varied from zero to one. The peak is identified with the onset of
the zero-temperature spin glass transition in the model. The residual
persistence is found to decay algebraically and the persistence exponent
over the range . Our results are
completely consistent with the result of Gandolfi, Newman and Stein for
infinite systems that this model has ` mixed\rq behaviour, namely positive
fractions of spins that flip finitely and infinitely often, respectively.
[Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]Comment: 9 pages, 5 figure
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