The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.Comment: 9 pages,Revte

From Quantity to Quality: Massive Molecular Dynamics Simulation of Nanostructures under Plastic Deformation in Desktop and Service Grid Distributed Computing Infrastructure

The distributed computing infrastructure (DCI) on the basis of BOINC and EDGeS-bridge technologies for high-performance distributed computing is used for porting the sequential molecular dynamics (MD) application to its parallel version for DCI with Desktop Grids (DGs) and Service Grids (SGs). The actual metrics of the working DG-SG DCI were measured, and the normal distribution of host performances, and signs of log-normal distributions of other characteristics (CPUs, RAM, and HDD per host) were found. The practical feasibility and high efficiency of the MD simulations on the basis of DG-SG DCI were demonstrated during the experiment with the massive MD simulations for the large quantity of aluminum nanocrystals ($\sim10^2$-$10^3$). Statistical analysis (Kolmogorov-Smirnov test, moment analysis, and bootstrapping analysis) of the defect density distribution over the ensemble of nanocrystals had shown that change of plastic deformation mode is followed by the qualitative change of defect density distribution type over ensemble of nanocrystals. Some limitations (fluctuating performance, unpredictable availability of resources, etc.) of the typical DG-SG DCI were outlined, and some advantages (high efficiency, high speedup, and low cost) were demonstrated. Deploying on DG DCI allows to get new scientific $\it{quality}$ from the simulated $\it{quantity}$ of numerous configurations by harnessing sufficient computational power to undertake MD simulations in a wider range of physical parameters (configurations) in a much shorter timeframe.Comment: 13 pages, 11 pages (http://journals.agh.edu.pl/csci/article/view/106

Magnetostriction studies up to megagauss fields using fiber Bragg grating technique

We here report magnetostriction measurements under pulsed megagauss fields using a high-speed 100 MHz strain monitoring system devised using fiber Bragg grating (FBG) technique with optical filter method. The optical filter method is a detection scheme of the strain of FBG, where the changing Bragg wavelength of the FBG reflection is converted to the intensity of reflected light to enable the 100 MHz measurement. In order to show the usefulness and reliability of the method, we report the measurements for solid oxygen, spin-controlled crystal, and volborthite, a deformed Kagom\'{e} quantum spin lattice, using static magnetic fields up to 7 T and non-destructive millisecond pulse magnets up to 50 T. Then, we show the application of the method for the magnetostriction measurements of CaV$_{4}$O$_{9}$, a two-dimensional antiferromagnet with spin-halves, and LaCoO$_{3}$, an anomalous spin-crossover oxide, in the megagauss fields.Comment: 9pages, 6 figures, Conference proceedings for MegaGauss16 at Kashiwa, Japan in Sept. 201

Theory and Applications of X-ray Standing Waves in Real Crystals

Theoretical aspects of x-ray standing wave method for investigation of the real structure of crystals are considered in this review paper. Starting from the general approach of the secondary radiation yield from deformed crystals this theory is applied to different concreat cases. Various models of deformed crystals like: bicrystal model, multilayer model, crystals with extended deformation field are considered in detailes. Peculiarities of x-ray standing wave behavior in different scattering geometries (Bragg, Laue) are analysed in detailes. New possibilities to solve the phase problem with x-ray standing wave method are discussed in the review. General theoretical approaches are illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table

Cross-linking patterns and their images in swollen and deformed gels

Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image (both types of deformation yield affinely stretched images in $\theta$ solvents). We show that in ordinary solids with spatially inhomogeneous profile of the shear modulus, isotropic stretching leads to distorted density image of this profile under isotropic deformation. Using simple physical arguments we demonstrate that the different response to isotropic stretching stems from fundamental differences between the theory of elasticity of solids and that of gels. Possible tests of our predictions and some potential applications are discussed.Comment: 16 pages, 3 figure

Geometric auxetics

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures

Minimal Length, Measurability and Gravity

The present work is a continuation of the previous papers written by the author on the subject. In terms of the measurability (or measurable quantities) notion introduced in a minimal length theory, first the consideration is given to a quantum theory in the momentum representation. The same terms are used to consider the Markov gravity model that here illustrates the general approach to studies of gravity in terms of measurable quantities. This paper is dedicated to the 75th Anniversary of Professor Vladimir Grigor'evich Baryshevsky.Comment: 34 pages, Late