353 research outputs found
Phase coexistence of gradient Gibbs states
We consider the (scalar) gradient fields --with denoting
the nearest-neighbor edges in --that are distributed according to the
Gibbs measure proportional to \texte^{-\beta H(\eta)}\nu(\textd\eta). Here
is the Hamiltonian, is a symmetric potential,
is the inverse temperature, and is the Lebesgue measure on the linear
space defined by imposing the loop condition
for each plaquette
in . For convex , Funaki and Spohn have shown that
ergodic infinite-volume Gibbs measures are characterized by their tilt. We
describe a mechanism by which the gradient Gibbs measures with non-convex
undergo a structural, order-disorder phase transition at some intermediate
value of inverse temperature . At the transition point, there are at
least two distinct gradient measures with zero tilt, i.e., .Comment: 3 figs, PTRF style files include
5-Fluorouracil-Loaded Transfersome as Theranostics in Dermal Tumor of Hypertrophic Scar Tissue
To investigate the ability of transfersomal gel carrying the antiscarring agent (5-FU) to permeate hypertrophic scars in vivo and in vitro, scar permeation studies were performed after the agent was labeled with the fluorescent agent, rhodamine 6GO. Laser confocal microscope was employed to dynamically observe the effects of transfersomal gel carrying 5-FU at different time points. High-performance liquid chromatography (HPLC) was used to analyze the contents of the agent in the scar tissues at different hours after administration. Scar elevation index (SEI) was used to evaluate the changes of the ear scar models in rabbits. Compared with the PBS gel of 5-FU, the transfersomal gel displayed greater permeation rate and depth, as well as a higher content retention of the agent in scar tissues. Local administrations of the agent for some certain periods effectively inhibited the hyperplasia of ear scars in rabbits. Transfersomes can be chosen as a potential transdermal drug delivery system
Mean-field driven first-order phase transitions in systems with long-range interactions
We consider a class of spin systems on with vector valued spins
(\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The
interactions are generally spread-out in the sense that the 's exhibit
either exponential or power-law fall-off. Under the technical condition of
reflection positivity and for sufficiently spread out interactions, we prove
that the model exhibits a first-order phase transition whenever the associated
mean-field theory signals such a transition. As a consequence, e.g., in
dimensions , we can finally provide examples of the 3-state Potts model
with spread-out, exponentially decaying interactions, which undergoes a
first-order phase transition as the temperature varies. Similar transitions are
established in dimensions for power-law decaying interactions and in
high dimensions for next-nearest neighbor couplings. In addition, we also
investigate the limit of infinitely spread-out interactions. Specifically, we
show that once the mean-field theory is in a unique ``state,'' then in any
sequence of translation-invariant Gibbs states various observables converge to
their mean-field values and the states themselves converge to a product
measure.Comment: 57 pages; uses a (modified) jstatphys class fil
Optimal designs for rational function regression
We consider optimal non-sequential designs for a large class of (linear and
nonlinear) regression models involving polynomials and rational functions with
heteroscedastic noise also given by a polynomial or rational weight function.
The proposed method treats D-, E-, A-, and -optimal designs in a
unified manner, and generates a polynomial whose zeros are the support points
of the optimal approximate design, generalizing a number of previously known
results of the same flavor. The method is based on a mathematical optimization
model that can incorporate various criteria of optimality and can be solved
efficiently by well established numerical optimization methods. In contrast to
previous optimization-based methods proposed for similar design problems, it
also has theoretical guarantee of its algorithmic efficiency; in fact, the
running times of all numerical examples considered in the paper are negligible.
The stability of the method is demonstrated in an example involving high degree
polynomials. After discussing linear models, applications for finding locally
optimal designs for nonlinear regression models involving rational functions
are presented, then extensions to robust regression designs, and trigonometric
regression are shown. As a corollary, an upper bound on the size of the support
set of the minimally-supported optimal designs is also found. The method is of
considerable practical importance, with the potential for instance to impact
design software development. Further study of the optimality conditions of the
main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory
and additional example
Annealed lower tails for the energy of a polymer
We consider the energy of a randomly charged polymer. We assume that only
charges on the same site interact pairwise. We study the lower tails of the
energy, when averaged over both randomness, in dimension three or more. As a
corollary, we obtain the correct temperature-scale for the Gibbs measure.Comment: 27 page
Nuclear Activity of MLA Immune Receptors Links Isolate-Specific and Basal Disease-Resistance Responses
General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions
We present a general, rigorous theory of Lee-Yang zeros for models with
first-order phase transitions that admit convergent contour expansions. We
derive formulas for the positions and the density of the zeros. In particular,
we show that for models without symmetry, the curves on which the zeros lie are
generically not circles, and can have topologically nontrivial features, such
as bifurcation. Our results are illustrated in three models in a complex field:
the low-temperature Ising and Blume-Capel models, and the -state Potts model
for large enough.Comment: 4 pgs, 2 figs, to appear in Phys. Rev. Let
Yang-Lee Zeros of the Two- and Three-State Potts Model Defined on Feynman Diagrams
We present both analytic and numerical results on the position of the
partition function zeros on the complex magnetic field plane of the
(Ising) and states Potts model defined on Feynman diagrams
(thin random graphs). Our analytic results are based on the ideas of
destructive interference of coexisting phases and low temperature expansions.
For the case of the Ising model an argument based on a symmetry of the saddle
point equations leads us to a nonperturbative proof that the Yang-Lee zeros are
located on the unit circle, although no circle theorem is known in this case of
random graphs. For the states Potts model our perturbative results
indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic
results are confirmed by finite lattice numerical calculations.Comment: 16 pages, 2 figures. Third version: the title was slightly changed.
To be published in Physical Review
Random-cluster representation of the Blume-Capel model
The so-called diluted-random-cluster model may be viewed as a random-cluster
representation of the Blume--Capel model. It has three parameters, a vertex
parameter , an edge parameter , and a cluster weighting factor .
Stochastic comparisons of measures are developed for the `vertex marginal' when
, and the `edge marginal' when q\in[1,\oo). Taken in conjunction
with arguments used earlier for the random-cluster model, these permit a
rigorous study of part of the phase diagram of the Blume--Capel model
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