Action at a distance in classical uniaxial ferromagnetic arrays

We examine in detail the theoretical foundations of striking long-range couplings emerging in arrays of fluid cells connected by narrow channels by using a lattice gas (Ising model) description of a system. We present a reexamination of the well known exact determination of the two-point correlation function along the edge of a channel using the transfer matrix technique and a new interpretation is provided. The explicit form of the correlation length is found to grow exponentially with the cross section of the channels at the bulk two-phase coexistence. The aforementioned result is recaptured by a refined version of the Fisher-Privman theory of first order phase transitions in which the Boltzmann factor for a domain wall is decorated with a contribution stemming from the point tension originated at its endpoints. The Boltzmann factor for a domain wall together with the point tension is then identified exactly thanks to two independent analytical techniques, providing a critical test of the Fisher-Privman theory. We then illustrate how to build up the network model from its elementary constituents, the cells and the channels. Moreover, we are able to extract the strength of the coupling between cells and express them in terms of the length and width and coarse grained quantities such as surface and point tensions. We then support our theoretical investigation with a series of corroborating results based on Monte Carlo simulations. We illustrate how the long range ordering occurs and how the latter is signaled by the thermodynamic quantities corresponding to both planar and three-dimensional Ising arrays.Comment: 36 pages, 19 figure

Derivation of the Casimir contribution to the binding potential for 3D wetting

The renormalisation group theory of critical and tri-critical wetting transitions in three-dimensional systems with short-ranged forces, based on analysis of an effective Hamiltonian with an interfacial binding potential w(ℓ), predicts very strong non-universal critical singularities. These, however, have famously not been observed in extensive Monte Carlo simulations of the transitions in the simple cubic Ising model. Here, we show that previous treatments have missed an entropic, or low-temperature Casimir, contribution to the binding potential, arising from the many different microscopic configurations which correspond to a given interfacial one. We derive the full binding potential, including the Casimir correction term, starting from a microscopic Landau–Ginzburg–Wilson Hamiltonian, using a continuum transfer-matrix (path-integral) method. This is illustrated first in one dimension before generalising to arbitrary dimension. The Casimir contribution is qualitatively different for first-order, critical and tri-critical wetting transitions and substantially alters previous predictions for critical singularities bringing them much closer to the simulation results

Passive advection of fractional Brownian motion by random layered flows

Studiamo le proprietà statistiche del processo Y(t) di un'avvezione passiva da flussi stratificati casuali estinti in situazioni in cui il trasferimento tra gli strati è governato da un moto browniano frazionario X(t) con l'indice di Hurst H ∈ (0,1). Mostriamo che lo spostamento medio-quadrato mediato dal disordine dell'avvezione passiva cresce nel limite del grande tempo t in proporzione a t2-H, che definisce una famiglia di super-diffusioni anomale. Valutiamo lo spettro di Wigner-Ville mediato dal disordine del processo di avvezione Y(t) e dimostriamo che ha una forma piuttosto insolita di legge di potenza con un esponente caratteristico che supera il valore 2. I nostri risultati suggeriscono anche che le fluttuazioni da campione a campione dello spettro possono essere molto importanti.We study statistical properties of the process Y(t) of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion X(t) with the Hurst index H ∈ (0,1). We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time t limit in proportion to t2-H, which defines a family of anomalous super-diffusions. We evaluate the disorder-averaged Wigner-Ville spectrum of the advection process Y(t) and demonstrate that it has a rather unusual power-law form with a characteristic exponent which exceed the value 2. Our results also suggest that sample-to-sample fluctuations of the spectrum can be very important

Interface in presence of a wall. Results from field theory

We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge, we show how the problem can be studied analytically from first principles, starting from the degrees of freedom (particle modes) of the bulk field theory. After deriving the passage probability of the interface and the order parameter profile in the regime in which the interface is not bound to the wall, we show how the theory accounts at the fundamental level also for the binding transition and its key parameter

Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

We discuss the statistical properties of a single-trajectory power spectral density S ( ω , T ) of an arbitrary one-dimensional real-valued centered Gaussian process X(t), where ω is the angular frequency and T the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of S ( ω , T ) . Our findings imply that the fluctuations of S ( ω , T ) exceed its average value μ ( ω , T ) . This implies that using μ ( ω , T ) to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of S ( ω , T ) and find that it deviates markedly from the average μ ( ω , T ) in most cases

Spectral content of a single non-Brownian trajectory

Time-dependent processes are often analysed using the power spectral density (PSD), calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble-average. Frequently, the available experimental data sets are too small for such ensemble averages, and hence it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from $S(f,T)$, the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable, parametrized by frequency $f$ and observation-time $T$, for a broad family of anomalous diffusions---fractional Brownian motion (fBm) with Hurst-index $H$---and derive exactly its probability density function. We show that $S(f,T)$ is proportional---up to a random numerical factor whose universal distribution we determine---to the ensemble-averaged PSD. For subdiffusion ($H<1/2$) we find that $S(f,T)\sim A/f^{2H+1}$ with random-amplitude $A$. In sharp contrast, for superdiffusion $(H>1/2)$ $S(f,T)\sim BT^{2H-1}/f^2$ with random amplitude $B$. Remarkably, for $H>1/2$ the PSD exhibits the same frequency-dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for $H>1/2$ the PSD is ageing and is dependent on $T$. Our predictions for both sub- and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels, and by extensive simulations.Comment: 13 pages, 5 figures, Supplemental Material can be found at https://journals.aps.org/prx/supplemental/10.1103/PhysRevX.9.011019/prx_SM_final.pd

Sleep patterns over 15-day period in rats with spinal cord injury

Study design: Experimental, controlled trial.Objectives: the purpose of this study was to evaluate over a 15-day period alterations in sleep pattern of rats after spinal cord injury (SCI).Setting: Federal University of São Paulo, Department of Psychobiology.Methods: in total, 20 male Wistar rats were used. the rats were divided in two groups: SHAM and SCI. the rats were submitted to the following procedures: electrode insertion surgery, 24 h duration baseline sleep recording, SCI (level T9) and subsequent sleep recording for 15 consecutive days.Results: the results showed a reduction in sleep efficiency in the light period for Days 1-3, 5, 10 and 12 after SCI in relation to the SHAM group, with alterations in total waking time and sleep stages. Limb movements were observed 4 days after SCI.Conclusion: the present findings suggest that SCI may be heavily involved in altering sleep pattern in SCI subjects and that the inactivity caused by SCI may be exacerbating this altered sleep pattern.Universidade Federal de São Paulo, Dept Psychobiol, BR-04020060 São Paulo, BrazilUniversidade Federal de São Paulo, Ctr Psychobiol & Exercise Res, BR-04020060 São Paulo, BrazilSanta Casa, Dept Pathol, São Paulo, BrazilUniversidade Federal de São Paulo, Dept Psychobiol, BR-04020060 São Paulo, BrazilUniversidade Federal de São Paulo, Ctr Psychobiol & Exercise Res, BR-04020060 São Paulo, BrazilWeb of Scienc

Casimir contribution to the interfacial Hamiltonian for 3D wetting

Previous treatments of three-dimensional (3D) short-ranged wetting transitions have missed an entropic or low-temperature Casimir contribution to the binding potential describing the interaction between the unbinding interface and wall. This we determine by exactly deriving the interfacial model for 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. The Casimir term changes the interpretation of fluctuation effects occurring at wetting transitions so that, for example, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. While the Casimir contribution does not alter the surface phase diagram, it significantly increases the adsorption near a first-order wetting transition and changes completely the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. Using the numerical renormalization group, we show that, for critical wetting, the asymptotic regime is extremely narrow with the growth of the parallel correlation length characterized by an effective exponent in quantitative agreement with Ising model simulations, resolving a long-standing controversy