Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure

Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

Quantum walks can unitarily match random walks on finite graphs

Quantum and random walks were proven to be equivalent on finite graphs by demonstrating how to construct a time-dependent random walk sharing the exact same evolution of vertex probability of any given discrete-time coined quantum walk. Such equivalence stipulated a deep connection between the processes that is far stronger than simply considering quantum walks as quantum analogues of random walks. This article expands on the connection between quantum and random walks by demonstrating a procedure that constructs a time-dependent quantum walk matching the evolution of vertex probability of any given random walk in a unitary way. It is a trivial fact that a quantum walk measured at all time steps of its evolution degrades to a random walk. More interestingly, the method presented describes a quantum walk that matches a random walk without measurement operations, such that the unitary evolution of the quantum walk captures the probability evolution of the random walk. The construction procedure is general, covering both homogeneous and non-homogeneous random walks. For the homogeneous random walk case, the properties of unitary evolution imply that the quantum walk described is time-dependent since homogeneous quantum walks do not converge for arbitrary initial conditionsComment: 9 pages, 1 figur

Influência do uso da terra no Nordeste Paraense sobre indicadores físico-químicos de qualidade da água do escoamento superficial no solo.

RESUMO: O presente trabalho teve como objetivo caracterizar a hidrogeoquímica do escoamento superficial em solos de diferentes ecossistemas, na mesobacia dos igarapés contíguos Timboteua e Buiuna (afluentes do rio Marapanim) no nordeste paraense, monitorando-se duas variáveis físicoquímicas da água (condutividade elétrica e pH). Foram alocadas três parcelas experimentais (1m2) em seis ecossistemas, sob mesmas condições biofísicas de solo e clima, totalizando 18 parcelas de tratamento. Instalaram-se também na mesma bacia três coletores de água de chuva e dois pluviômetros. No período de janeiro a junho de 2010, foram coletadas 234 amostras água de chuva e de escoamento superficial. O pH apresentou-se mais ácido nas amostras de água da chuva, seguido pela Capoeira e Sistema Agroflorestal (com preparo por derruba-e-queima), que pode estar relacionado à concentração de material orgânico em decomposição. Os agroecossistemas Roça (derruba-e-queima), Sistema Agroflorestal (com preparo por corte-e-trituração) e Pastagem se destacaram apresentando os maiores valores de condutividade elétrica (CE). O manejo do solo parece influenciar a CE e o pH. Abstract: The objective of this study was to characterize the hydrogeochemistry of the overland flow, in the watershed of the Timboteua and Buiuna streams (tributaries of the Marapanim River), Northeast of Pará, through measurements of two physico-chemical variables of water (electrical conductivity and pH). It was placed three experimental plots (1m2) in each six ecosystems, under the same biophysical conditions of soil and climate, summing up 18 treatment plots. It was also installed three rainwater collectors and two rain gauges in the same watershed. In the period January to June/ 2010, it was collected 234 rainwater and overland flow samples. The pH was more acidic in rainwater samples, followed by Capoeira and agroforestry system (prepared by slash-and-burn) overland flow samples, what may be related to the soil organic matter decomposition. Agroecosystems (slash-and-burn), Agroforestry system (chop-and-mulch) and Pasture overland flow were distinguished by higher electrical conductivity (EC). Soil management seems to influence both EC and pH