Ising-like transitions in the O(nn) loop model on the square lattice

We explore the phase diagram of the O($n$) loop model on the square lattice in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For $n>>2$ we find Ising-like phase transitions associated with the onset of a checkerboard-like ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of $n$ represents a softening of its particle-particle potentials. We also determine critical points in the range $-2\leq n\leq 2$. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the $n>2$ transition may continue into the dense phase of the $n \leq 2$ loop model, or continue as a line of $n \leq 2$ O($n$) multicritical points

Special transitions in an O(nn) loop model with an Ising-like constraint

We investigate the O($n$) nonintersecting loop model on the square lattice under the constraint that the loops consist of ninety-degree bends only. The model is governed by the loop weight $n$, a weight $x$ for each vertex of the lattice visited once by a loop, and a weight $z$ for each vertex visited twice by a loop. We explore the $(x,z)$ phase diagram for some values of $n$. For $0<n<1$, the diagram has the same topology as the generic O($n$) phase diagram with $n<2$, with a first-order line when $z$ starts to dominate, and an O($n$)-like transition when $x$ starts to dominate. Both lines meet in an exactly solved higher critical point. For $n>1$, the O($n$)-like transition line appears to be absent. Thus, for $z=0$, the $(n,x)$ phase diagram displays a line of phase transitions for $n\le 1$. The line ends at $n=1$ in an infinite-order transition. We determine the conformal anomaly and the critical exponents along this line. These results agree accurately with a recent proposal for the universal classification of this type of model, at least in most of the range $-1 \leq n \leq 1$. We also determine the exponent describing crossover to the generic O($n$) universality class, by introducing topological defects associated with the introduction of `straight' vertices violating the ninety-degree-bend rule. These results are obtained by means of transfer-matrix calculations and finite-size scaling.Comment: 19 pages, 11 figure

Influence of absorbed water on the dielectric properties and glass-transition temperature of silica-filled epoxy nanocomposites

Work on dielectric spectroscopy of epoxy resin filled with nano-SiO2 at different relative humidities and temperatures is reported. Above the glass-transition temperature (Tg), dc-like imperfect charge transport (QDC or LFD) dominates the low frequency dielectric spectrum. Another mid-frequency relaxation process was found in the non-dried composites. Water also induces glass-transition temperature decreases, which can be measured both by dielectric spectroscopy and DSC. Both theory and experiment demonstrated that a higher water content could exist in nanocomposites than unfilled epoxy suggesting a bigger free volume when nanostructured. In our system, the hydrophilic surface of silica is likely to cause water to surround and lead to delamination of the epoxy from SiO2. This is a potential mechanical and dielectric weakness in the nanocomposites, which may lead to an ageing phenomenon. Hydrophobic surface group may reduce the water adsorption in nanocomposites

Método acuoso avanzado para recuperar aceites de pepitas de calabaza y harina desengrasada: optimización y comparación con otros métodos

The optimal process conditions of the advanced aqueous method for recovering oil and de-oiled meal from pumpkin seed kernels were: baking the kernels at 110 °C for 1 min, grinding them to pass through a sieve of 150 μm pore size, adding 1.60 ml brine to 10.00 g ground kernels, stirring for 30 min at 30 °C, centrifuging at 4000 r/min for 30 min and cold-pressing the residue from centrifugation. This method recovered &gt; 94% oil. Its oil recovery rate was comparable to that of solvent extraction and higher than that of enzyme-assisted aqueous method or hot-pressing. It recovered edible oil with higher quality and level of coenzyme Q10, tocopherols, carotenoids, total phytosterols and squalene as compared to solvent extraction or hot-pressing and requirements of China’s national standard. It is superior to enzyme-assisted aqueous method or hot-pressing for recovering de-oiled meal which is suitable for making texturized protein.Las condiciones óptimas del proceso del nuevo método acuoso para la recuperación de aceite y harina desengrasada de las pepitas de calabaza fueron: horneado a 110 °C durante 1 min, molienda para que pasen por un tamiz con un tamaño de poro de 150 μm, adición de 1,60 ml de salmuera a 10,00 g de pepita molida, agitando durante 30 min a 30 °C, centrifugación a 4000 r/min durante 30 min y presión en frío del residuo de la centrifugación. Este método recuperó &gt; 94% de aceites. Esta tasa de recuperación de aceite fue comparable a la de la extracción con solvente y más alta que la del método acuoso asistido por enzimas o prensado en caliente. Se recuperó aceite comestible con mayor calidad y nivel de coenzima Q10, tocoferoles, carotenoides, fitoesteroles totales y escualeno en comparación con la extracción con solvente o prensado en caliente cumpliendo los requisitos de la norma nacional de China. La extracción es superior a la obtenida mediante el método acuoso asistido por enzimas o al prensado en caliente por lo que se recupera una harina desengrasada adecuada para hacer proteínas texturizadas

A system for learning statistical motion patterns

Analysis of motion patterns is an effective approach for anomaly detection and behavior prediction. Current approaches for the analysis of motion patterns depend on known scenes, where objects move in predefined ways. It is highly desirable to automatically construct object motion patterns which reflect the knowledge of the scene. In this paper, we present a system for automatically learning motion patterns for anomaly detection and behavior prediction based on a proposed algorithm for robustly tracking multiple objects. In the tracking algorithm, foreground pixels are clustered using a fast accurate fuzzy k-means algorithm. Growing and prediction of the cluster centroids of foreground pixels ensure that each cluster centroid is associated with a moving object in the scene. In the algorithm for learning motion patterns, trajectories are clustered hierarchically using spatial and temporal information and then each motion pattern is represented with a chain of Gaussian distributions. Based on the learned statistical motion patterns, statistical methods are used to detect anomalies and predict behaviors. Our system is tested using image sequences acquired, respectively, from a crowded real traffic scene and a model traffic scene. Experimental results show the robustness of the tracking algorithm, the efficiency of the algorithm for learning motion patterns, and the encouraging performance of algorithms for anomaly detection and behavior prediction

A system for learning statistical motion patterns

Analysis of motion patterns is an effective approach for anomaly detection and behavior prediction. Current approaches for the analysis of motion patterns depend on known scenes, where objects move in predefined ways. It is highly desirable to automatically construct object motion patterns which reflect the knowledge of the scene. In this paper, we present a system for automatically learning motion patterns for anomaly detection and behavior prediction based on a proposed algorithm for robustly tracking multiple objects. In the tracking algorithm, foreground pixels are clustered using a fast accurate fuzzy k-means algorithm. Growing and prediction of the cluster centroids of foreground pixels ensure that each cluster centroid is associated with a moving object in the scene. In the algorithm for learning motion patterns, trajectories are clustered hierarchically using spatial and temporal information and then each motion pattern is represented with a chain of Gaussian distributions. Based on the learned statistical motion patterns, statistical methods are used to detect anomalies and predict behaviors. Our system is tested using image sequences acquired, respectively, from a crowded real traffic scene and a model traffic scene. Experimental results show the robustness of the tracking algorithm, the efficiency of the algorithm for learning motion patterns, and the encouraging performance of algorithms for anomaly detection and behavior prediction

On the Dichotomy between the Nodal and Antinodal Excitations in High-temperature Superconductors

Angle-resolved photoemission data on optimally- and under-doped high temperature superconductors reveal a dichotomy between the nodal and antinodal electronic excitations. In this paper we propose an explanation of this unusual phenomenon by employing the coupling between the quasiparticle and the commensurate/incommensurate magnetic excitations.Comment: 11 pages, 9 figure