Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis

Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied.Comment: 9 pages, 13 figure

Event-Driven Monte Carlo: exact dynamics at all time-scales for discrete-variable models

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real time dynamics of a large class of classical markovian chains, and particularly to short-time situations where the exact evolution is relevant

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-\alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $\alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $\alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $\alpha \geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($\alpha=1$) and dipolar magnetic films ($\alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.Comment: 5 pages, 2 figures. Supplemental Material include

The nematic phase in stripe forming systems within the self consistent screening approximation

We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of two-point correlation function characteristic of a nematic phase.Comment: 8 pages, 4 figure

Cognitive Engagement in Virtual Collaboration: The Role of Social Presence, Sociability and Immersion

国際基督教大学2018年

Considerations for Discrete Element Modeling of Rock Cutting

This study attempts to build a framework within the Discrete Element Method (DEM) to produce a reliable predictive tool in rock cutting applications, such that the cutting forces and fragmentation process are reasonably estimated. The study is limited to shallow depth cutting, often the mode of cutting involved in drilling operations. Rock cutting requires the consideration of tool-rock interaction and the damage or fracture of rocks. With respect to modeling, rock cutting becomes a sequence of difficult problems: A contact problem first arises as a cutter advances and interacts with a target rock. This is followed by the problem of determining the location and nature of the rock failure. In the event of rock failure, a modeler must then consider modeling the initiation of the fragmentation process. The adopted approach utilizes the intrinsic capability of DEM to adequately consider contacts and model fractures. The commercial DEM codes PFC2D and PFC3D from Itasca were used. This modeling effort focuses on the rock cutting that occurs during rock scratching tests. Two primary reasons provide the impetus of this investigation: first, a rock scratching test possesses all essential characteristics of a general rock cutting problem; second, available test data, particularly data obtained by Richard [1], provide a basis for validation. Modeling the scratch test also served another purpose for understanding the mechanics of drilling into rock because the cutting action is very similar to that of a single polycrystalline diamond compact (PDC) bit. The validation of the present modeling effort utilizes an observation made by Richard and Dagrain [2] during shallow cuts that the specific energy obtained in a scratch test is approximately equal to the uniaxial strength of the rock. Rocks were represented as bonded particles [3]. This study first explores the sensitivity of the essential parameters that affect rock behavior and parameter selection necessary to realistically represent a rock. Extensive two-dimensional analyses were first completed and followed by three-dimensional analyses, all of which were conducted under an ambient pressure environment. This study also addressed an important question regarding rock porosity. The current practice often implicitly considers porosity. Essentially, a porosity that is computationally simple and advantageous but ultimately unrealistic is used and other DEM parameters are consequently adjusted until the desired modulus and strength are produced. This sample is then considered mechanically equivalent. The ability to substitute rock materials of low porosities with higher values is extremely beneficial for computational efficiency. Samples with small porosity values were generated by solving the Apollonius’ problem to fill voids with particles, and therefore, the influence of initial sample microstructure could be studied. The Unconfined Compressive Strength (UCS) for most rocks is generally about ten times greater than that of the tensile strength [4]. This ratio, considered to be realistic rock behavior, has been historically difficult to obtain in similar models. In order to achieve this strength ratio, microdefects were also introduced into the sample. This study was able to implicitly model porosity by introducing optimal microdefects percentages in order to create equivalent rock samples with varying porosity values. Moreover, a connection between two-dimensional and three-dimensional samples was also established by finding an appropriate porosity to match the two models. This study presented a validated and simplified framework for modeling rock cutting, and should be useful for general applications for a wide variety of fields. Preliminary work on cutting under high pressure was also initiated and yielded results that would be useful for subsequent studies

MODELING ROCK CUTTING USING DEM WITH CRUSHABLE PARTICLES

A numerical model for the rock scratching test using a sharp cutter is proposed in which the rock is represented by a bonded-particle model and its mechanical behavior is simulated by the Distinct-Element Method using the discrete element program PFC2D. The rocks that are simulated represent sandstones and their mechanical laboratory parameters are characterized by the ones obtained in laboratory test simulations using the same numerical approach and program named above. The environment of the rock scratching test is distinguished by the particle size and crushability, which are highly important parameters that affect the failure mode and the cutting force pattern. The implementation of a crushing criterion and strength is introduced to the particles based on micromechanics and laboratory results, respectively. The depth of cutting is considerably shallow and the cutting force results are processed under the physical concept of mechanical work. The proportion of the cutting force to the depth of cutting is possible in any type of sandstone-like simulated material, which has been demonstrated by laboratory results. The correlation of the cutting force and the unconfined compressive strength of different rock scratching tests show that the simulations provide effective results. The failure characteristics of micro-cracks and macro-cracks under the cutting tool, represented by broken bonds, simulates the damage occurring in real scratching tests, taking the model to a realistic plane

Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension

In general C*-algebras, elements with minimal norm in some equivalence class are introduced and characterized. We study the set of minimal hermitian matrices, in the case where the C*-algebra consists of 3 × 3 complex matrices, and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matrices particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For the flag manifold of 'four mutually orthogonal complex lines' in C4, it is shown that there are infinitely many minimal curves joining arbitrarily close points. In the case of the flag manifold of 'three mutually orthogonal complex lines' in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does not occur.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Mata Lorenzo, Luis E.. Universidad Simón Bolivar; VenezuelaFil: Mendoza, Alberto. Universidad Simón Bolivar; VenezuelaFil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simón Bolivar; VenezuelaFil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentin