2,183 research outputs found
Potts Model On Random Trees
We study the Potts model on locally tree-like random graphs of arbitrary
degree distribution. Using a population dynamics algorithm we numerically solve
the problem exactly. We confirm our results with simulations. Comparisons with
a previous approach are made, showing where its assumption of uniform local
fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure
Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons
We consider the problem of reflectionless propagation of PT-symmetric
solitons described by the nonlocal nonlinear Schroedinger equation on a line in
the framework of the concept of transparent boundary conditions for evolution
equations. Transparent boundary conditions for the nonlocal nonlinear
Schroedinger equation are derived. The absence of backscattering at the
artificial boundaries is confirmed by the numerical implementation of the
transparent boundary conditions
BKT-like transition in the Potts model on an inhomogeneous annealed network
We solve the ferromagnetic q-state Potts model on an inhomogeneous annealed
network which mimics a random recursive graph. We find that this system has the
inverted Berezinskii--Kosterlitz--Thouless (BKT) phase transition for any , including the values , where the Potts model normally shows
a first order phase transition. We obtain the temperature dependences of the
order parameter, specific heat, and susceptibility demonstrating features
typical for the BKT transition. We show that in the entire normal phase, both
the distribution of a linear response to an applied local field and the
distribution of spin-spin correlations have a critical, i.e. power-law, form.Comment: 7 pages, 3 figure
Half the entanglement in critical systems is distillable from a single specimen
We establish that the leading critical scaling of the single-copy
entanglement is exactly one half of the entropy of entanglement of a block in
critical infinite spin chains in a general setting, using methods of conformal
field theory. Conformal symmetry imposes that the single-copy entanglement for
critical many-body systems scales as E_1(\rho_L)=(c/6) \log L- (c/6)
(\pi^2/\log L) + O(1/L), where L is the number of constituents in a block of an
infinite chain and c corresponds to the central charge. This proves that from a
single specimen of a critical chain, already half the entanglement can be
distilled compared to the rate that is asymptotically available. The result is
substantiated by a quantitative analysis for all translationally invariant
quantum spin chains corresponding to general isotropic quasi-free fermionic
models. An analytic example of the XY model shows that away from criticality
the above simple relation is only maintained near the quantum phase transition
point.Comment: 4 pages RevTeX, 1 figure, final versio
Phenomenological Models of Socio-Economic Network Dynamics
We study a general set of models of social network evolution and dynamics.
The models consist of both a dynamics on the network and evolution of the
network. Links are formed preferentially between 'similar' nodes, where the
similarity is defined by the particular process taking place on the network.
The interplay between the two processes produces phase transitions and
hysteresis, as seen using numerical simulations for three specific processes.
We obtain analytic results using mean field approximations, and for a
particular case we derive an exact solution for the network. In common with
real-world social networks, we find coexistence of high and low connectivity
phases and history dependence.Comment: 11 pages, 8 figure
Correlations in interacting systems with a network topology
We study pair correlations in cooperative systems placed on complex networks.
We show that usually in these systems, the correlations between two interacting
objects (e.g., spins), separated by a distance , decay, on average,
faster than . Here is the mean number of the
-th nearest neighbors of a vertex in a network. This behavior, in
particular, leads to a dramatic weakening of correlations between second and
more distant neighbors on networks with fat-tailed degree distributions, which
have a divergent number in the infinite network limit. In this case, only
the pair correlations between the nearest neighbors are observable. We obtain
the pair correlation function of the Ising model on a complex network and also
derive our results in the framework of a phenomenological approach.Comment: 5 page
The Lovastatin-Treated Rodent: A New Model of Barrier Disruption and Epidermal Hyperplasia
Recent studies have linked epidermal cholesterol synthesis with maintenance of the permeability barrier. To assess directly the importance of cholesterol synthesis, we applied lovastatin, a potent inhibitor of cholesterol synthesis, to hairless mouse skin. Transepidermal water loss (TEWL) began to increase after four to six daily applications. Co-application of cholesterol blocked the expected increase in TEWL, demonstrating the importance of cholesterol for development of the lesion. The histology of lovastatin-treated skin revealed epidermal hyperplasia, accompanied by accelerated DNA synthesis. Whereas cholesterol synthesis initially was reduced in lovastatin-treated epidermis, with further treatment cholesterol synthesis normalized, while fatty acid synthesis accelerated greatly. Although the total free sterol content of lovastatin-treated epidermis remained normal, the fatty acid content increased coincident with barrier disruption. Finally, morphologic abnormalities of both lamellar body structure and their deposited, intercellular contents occurred coincident with the emerging biochemical abnormalities. Thus, the abnormal barrier function in this model can be ascribed to an initial inhibition of epidermal sterol synthesis followed by an alteration in cholesterol and fatty acid synthesis, leading to an imbalance in stratum corneum lipid composition and abnormal membrane bilayer structure
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