Comment on "Canonical formalism for Lagrangians with nonlocality of finite extent"

The paper by Woodward [Phys. Rev. A 62, 052105 (2000)] claimed to have proved that Lagrangian theories with a nonlocality of finite extent are necessarily unstable. In this Comment we propose that this conclusion is false.

Intramolecular coupling as a mechanism for a liquid-liquid phase transition

We study a model for water with a tunable intramolecular interaction Js, using mean-field theory and off-lattice Monte Carlo simulations. For all Js>~0, the model displays a temperature of maximum density. For a finite intramolecular interaction Js>0, our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely preempted by inevitable freezing. For J=0, the liquid-liquid critical point disappears at T=0.

Finite-size effects in nonequilibrium correlation functions

We have shown that finite-size effects in the correlation functions away from equilibrium may be introduced through dimensionless numbers: the Nusselt numbers, accounting for both the nature of the boundaries and the size of the system. From an analysis based on fluctuating hydrodynamics, we conclude that the mean-square fluctuations satisfy scaling laws, since they depend only on the dimensionless numbers in addition to reduced variables. We focus on the case of diffusion modes and describe some physical situations in which finite-size effects may be relevant.

Liquid-liquid phase transition for soft-core attractive potential

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential¿s parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Comment on: Deuterium nuclear fusion at room temperature: A pertinent inequality on barrier penetration

In a recent letter, Rosen claims to justify ...

High-Temperature magnetic ordering in a new organic magnet

Magnetization, heat capacity, and neutron diffraction experiments on the beta-phase of the dithiadiazolyl radical, p-NC.C6F4.CNSSN., provide conclusive evidence that this system exhibits noncollinear antiferromagnetism at 35.5 K, an unprecedented temperature for an organic radical. On the basis of magnetization and powder neutron diffraction results, coupled with theoretical calculations of the spin distribution within the molecule, a magnetic structure for this compound is proposed in which the interactions propagate through S . . .N contacts.

A multilevel multiscale finite volume method

The Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.

Juxtaposition of melt impregnation and high-temperature shear zones in the upper mantle; field and petrological constraints from the Lanzo peridotite (Northern Italy)

Results of a field and microstructural study between the northern and the central bodies of the Lanzo plagioclase peridotite massif (NW Italy) indicate that the spatial distribution of deformation is asymmetric across kilometre-scale mantle shear zones. The southwestern part of the shear zone (footwall) shows a gradually increasing degree of deformation from porphyroclastic peridotites to mylonite, whereas the northeastern part (hanging wall) quickly grades into weakly deformed peridotites. Discordant gabbroic and basaltic dykes are asymmetrically distributed and far more abundant in the footwall of the shear zone. The porphyroclastic peridotite displays porphyroclastic zones and domains of igneous crystallization whereas mylonites are characterized by elongated porphyroclasts, embedded between fine-grained, polycrystalline bands of olivine, plagioclase, clinopyroxene, orthopyroxene, spinel, rare titanian pargasite, and domains of recrystallized olivine. Two types of melt impregnation textures have been found: (1) clinopyroxene porphyroclasts incongruently reacted with migrating melt to form orthopyroxene plagioclase; (2) olivine porphyroclasts are partially replaced by interstitial orthopyroxene. The meltrock reaction textures tend to disappear in the mylonites, indicating that deformation in the mylonite continued under subsolidus conditions. The pyroxene chemistry is correlated with grain size. High-Al pyroxene cores indicate high temperatures (11001030C), whereas low-Al neoblasts display lower final equilibration temperatures (860C). The spinel Cr-number [molar Cr/(Cr Al)] and TiO2 concentrations show extreme variability covering almost the entire range known from abyssal peridotites. The spinel compositions of porphyroclastic peridotites from the central body are more variable than spinel from mylonite, mylonite with ultra-mylonite bands, and porphyroclastic rocks of the northern body. The spinel compositions probably indicate disequilibrium and would favour rapid cooling, and a faster exhumation of the central peridotite body, relative to the northern one. Our results indicate that melt migration and high-temperature deformation are juxtaposed both in time and space. Meltrock reaction may have caused grain-size reduction, which in turn led to localization of deformation. It is likely that melt-lubricated, actively deforming peridotites acted as melt focusing zones, with permeabilities higher than the surrounding, less deformed peridotites. Later, under subsolidus conditions, pinning in polycrystalline bands in the mylonites inhibited substantial grain growth and led to permanent weak zones in the upper mantle peridotite, with a permeability that is lower than in the weakly deformed peridotites. Such an inversion in permeability might explain why actively deforming, fine-grained peridotite mylonite acted as a permeability barrier and why ascending mafic melts might terminate and crystallize as gabbros along actively deforming shear zones. Melt-lubricated mantle shear zones provide a mechanism for explaining the discontinuous distribution of gabbros in oceancontinent transition zones, oceanic core complexes and ultraslow-spreading ridges.