724 research outputs found
A monopole solution from noncommutative multi-instantons
We extend the relation between instanton and monopole solutions of the
selfduality equations in SU(2) gauge theory to noncommutative space-times.
Using this approach and starting from a noncommutative multi-instanton solution
we construct a U(2) monopole configuration which lives in 3 dimensional
ordinary space. This configuration resembles the Wu-Yang monopole and satisfies
the selfduality (Bogomol'nyi) equations for a U(2) Yang-Mills-Higgs system.Comment: 19 pages; title and abstract changed, brane interpretation corrected.
Version to appear in JHE
Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems
Computer modeling of multicellular systems has been a valuable tool for
interpreting and guiding in vitro experiments relevant to embryonic
morphogenesis, tumor growth, angiogenesis and, lately, structure formation
following the printing of cell aggregates as bioink particles. Computer
simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in
explaining and predicting the resulting stationary structures (corresponding to
the lowest adhesion energy state). Here we present two alternatives to the MMC
approach for modeling cellular motion and self-assembly: (1) a kinetic Monte
Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC,
both KMC and CPD methods are capable of simulating the dynamics of the cellular
system in real time. In the KMC approach a transition rate is associated with
possible rearrangements of the cellular system, and the corresponding time
evolution is expressed in terms of these rates. In the CPD approach cells are
modeled as interacting cellular particles (CPs) and the time evolution of the
multicellular system is determined by integrating the equations of motion of
all CPs. The KMC and CPD methods are tested and compared by simulating two
experimentally well known phenomena: (1) cell-sorting within an aggregate
formed by two types of cells with different adhesivities, and (2) fusion of two
spherical aggregates of living cells.Comment: 11 pages, 7 figures; submitted to Phys Rev
Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect
A flux line in a Type-II superconductor with a single nonuniform columnar
defect is studied by a perturbative diagrammatic expansion around an annealed
approximation. The system undergoes a finite temperature depinning transition
for the (rather unphysical) on-the-average repulsive columnar defect, provided
that the fluctuations along the axis are sufficiently large to cause some
portions of the column to become attractive. The perturbative expansion is
convergent throughout the weak pinning regime and becomes exact as the
depinning transition is approached, providing an exact determination of the
depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st
Quantum interface unbinding transitions
We consider interfacial phenomena accompanying bulk quantum phase transitions
in presence of surface fields. On general grounds we argue that the surface
contribution to the system free energy involves a line of singularities
characteristic of an interfacial phase transition, occurring below the bulk
transition temperature T_c down to T=0. This implies the occurrence of an
interfacial quantum critical regime extending into finite temperatures and
located within the portion of the phase diagram where the bulk is ordered. Even
in situations, where the bulk order sets in discontinuously at T=0, the
system's behavior at the boundary may be controlled by a divergent length scale
if the tricritical temperature is sufficiently low. Relying on an effective
interfacial model we compute the surface phase diagram in bulk spatial
dimensionality and extract the values of the exponents describing the
interfacial singularities in
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
Network formation of tissue cells via preferential attraction to elongated structures
Vascular and non-vascular cells often form an interconnected network in
vitro, similar to the early vascular bed of warm blooded embryos. Our
time-lapse recordings show that the network forms by extending sprouts, i.e.,
multicellular linear segments. To explain the emergence of such structures, we
propose a simple model of preferential attraction to stretched cells. Numerical
simulations reveal that the model evolves into a quasi-stationary pattern
containing linear segments, which interconnect above the critical volume
fraction of 0.2. In the quasi-stationary state the generation of new branches
offset the coarsening driven by surface tension. In agreement with empirical
data, the characteristic size of the resulting polygonal pattern is
density-independent within a wide range of volume fractions
Non-locality and short-range wetting phenomena
We propose a non-local interfacial model for 3D short-range wetting at planar
and non-planar walls. The model is characterized by a binding potential
\emph{functional} depending only on the bulk Ornstein-Zernike correlation
function, which arises from different classes of tube-like fluctuations that
connect the interface and the substrate. The theory provides a physical
explanation for the origin of the effective position-dependent stiffness and
binding potential in approximate local theories, and also obeys the necessary
classical wedge covariance relationship between wetting and wedge filling.
Renormalization group and computer simulation studies reveal the strong
non-perturbative influence of non-locality at critical wetting, throwing light
on long-standing theoretical problems regarding the order of the phase
transition.Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Let
Kinetics of catalysis with surface disorder
We study the effects of generalised surface disorder on the monomer-monomer
model of heterogeneous catalysis, where disorder is implemented by allowing
different adsorption rates for each lattice site. By mapping the system in the
reaction-controlled limit onto a kinetic Ising model, we derive the rate
equations for the one and two-spin correlation functions. There is good
agreement between these equations and numerical simulations. We then study the
inclusion of desorption of monomers from the substrate, first by both species
and then by just one, and find exact time-dependent solutions for the one-spin
correlation functions.Comment: LaTex, 19 pages, 1 figure included, requires epsf.st
State Differentiation by Transient Truncation in Coupled Threshold Dynamics
Dynamics with a threshold input--output relation commonly exist in gene,
signal-transduction, and neural networks. Coupled dynamical systems of such
threshold elements are investigated, in an effort to find differentiation of
elements induced by the interaction. Through global diffusive coupling, novel
states are found to be generated that are not the original attractor of
single-element threshold dynamics, but are sustained through the interaction
with the elements located at the original attractor. This stabilization of the
novel state(s) is not related to symmetry breaking, but is explained as the
truncation of transient trajectories to the original attractor due to the
coupling. Single-element dynamics with winding transient trajectories located
at a low-dimensional manifold and having turning points are shown to be
essential to the generation of such novel state(s) in a coupled system.
Universality of this mechanism for the novel state generation and its relevance
to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres
New axially symmetric Yang-Mills-Higgs solutions with negative cosmological constant
We construct numerically new axially symmetric solutions of SU(2)
Yang-Mills-Higgs theory in anti-de Sitter spacetime. Two types of
finite energy, regular configurations are considered: multimonopole solutions
with magnetic charge and monopole-antimonopole pairs with zero net
magnetic charge. A somewhat detailed analysis of the boundary conditions for
axially symmetric solutions is presented. The properties of these solutions are
investigated, with a view to compare with those on a flat spacetime background.
The basic properties of the gravitating generalizations of these configurations
are also discussed.Comment: 18 pages, 7 figures; v2: typos correcte
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