Center of mass integral in canonical general relativity

For a two-surface B tending to an infinite--radius round sphere at spatial infinity, we consider the Brown--York boundary integral H_B belonging to the energy sector of the gravitational Hamiltonian. Assuming that the lapse function behaves as N \sim 1 in the limit, we find agreement between H_B and the total Arnowitt--Deser--Misner energy, an agreement first noted by Braden, Brown, Whiting, and York. However, we argue that the Arnowitt--Deser--Misner mass--aspect differs from a gauge invariant mass--aspect by a pure divergence on the unit sphere. We also examine the boundary integral H_B corresponding to the Hamiltonian generator of an asymptotic boost, in which case the lapse N \sim x^k grows like one of the asymptotically Cartesian coordinate functions. Such an integral defines the kth component of the center of mass for a Cauchy surface \Sigma bounded by B. In the large--radius limit, we find agreement between H_B and an integral introduced by Beig and O'Murchadha. Although both H_B and the Beig--O'Murchadha integral are naively divergent, they are in fact finite modulo the Hamiltonian constraint. Furthermore, we examine the relationship between H_B and a certain two--surface integral linear in the spacetime Riemann curvature tensor. Similar integrals featuring the curvature appear in works by Ashtekar and Hansen, Penrose, Goldberg, and Hayward. Within the canonical 3+1 formalism, we define gravitational energy and center--of--mass as certain moments of Riemann curvature.Comment: 52 pages, revtex4, uses amsmath and amssym

Two-parameter models of brittle materials behavior under uniaxial compression

Numerical and analytical models are widely presented in the literature. In this report, analytical models of only one class are considered, the first of which is the Furamura model. Models of this class do not require a large amount of input data; in addition, their mathematical description does not contain complex equations. The researchers initially used these models to analyze the behavior of concrete at high temperatures. The current scope of these models covers applied analysis of the behavior of rocks, frozen soils, and other materials, including their behavior on the downward branch under controlled deformation. The purpose of this report is to discuss not only the positive characteristics of the models of the class under consideration, but also to draw the readers' attention to the limitations in the use of the models, which will contribute to their improvement and effective application for sustainable development

On Dual Formulation of Gravity

In this paper we consider a possibility to construct dual formulation of gravity where the main dynamical field is the Lorentz connection \omega_\mu^{ab} and not that of tetrad e_\mu^a or metric g_\mu\nu. Our approach is based on the usual dualization procedure which uses first order parent Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It turns out that in d=3 dimensions such dual formulation is related with the so called exotic parity-violating interactions for massless spin-2 particles.Comment: 7 pages, plain LaTe

Context Free Evolution of Words

Projet MEVALRandom grammars were introduced in computer science, but the study of their thermodynamic and long time behaviour started only recently. In this paper we undertake more detailed study of context free grammars in the supercritical case, that is when the word grows exponentially fast. We study and calculate the statistics of factors for large t, prove the existence of various limiting measures and study relations between them

Phase Transitions in Higher Derivative Gravity

This paper deals with black holes, bubbles and orbifolds in Gauss-Bonnet theory in five dimensional anti de Sitter space. In particular, we study stable, unstable and metastable phases of black holes from thermodynamical perspective. By comparing bubble and orbifold geometries, we analyse associated instabilities. Assuming AdS/CFT correspondence, we discuss the effects of this higher derivative bulk coupling on a specific matrix model near the critical points of the boundary gauge theory at finite temperature. Finally, we propose another phenomenological model on the boundary which mimics various phases of the bulk space-time.Comment: 33 pages, 12 figures, LaTeX, typos corrected, clarifications in sections 5 and 6, references adde

Theoretical consideration of pits recording and etching processes in chalcogenide vitreous semiconductors

We propose theoretical consideration and computer modeling of information pit recording and etching processes in chalcogenide vitreous semiconductors. We demonstrate how to record and develop information pits with the necessary shape and sizes in chalcogenide photoresists using gaussian laser beam and selective etching. It has been shown that phototransformed region cross-section could be almost trapezoidal or parabolic depending on the photoresist material optical absorption, recording beam power, exposure, etchant selectivity and etching time. After illumination, the spatial distribution of photo-transformed material fraction was calculated using the Kolmogorov-Awrami equation. Analyzing obtained results, we derived a rather simple approximate analytical expression for the dependence of the photo-transformed region width and depth on the recording gaussian beam power, radius and exposure time. Then the selective etching process was simulated numerically. The obtained results quantitatively describes the characteristics of pits recorded by the gaussian laser beam in thin layers of As40S60 chalcogenide semiconductor.Comment: 14 pages, 1 scheme, 9 figure

TECHNOLOGICAL PROPERTIES OF MILK OF COWS WITH DIFFERENT GENOTYPES OF KAPPA-CASEIN AND BETA-LACTOGLOBULIN

The presence of the desirable alleles and genotypes of casein and whey protein genes in the genome of cows affects the milk protein content, quality and technological properties of their milk. Two important properties of milk its producibility is judged on are cheeseability and heat resistance. The present studies aimed at estimating the technological properties of milk of black-motley × Holstein and Kholmogorskaya breeds cows of the Tatarstan type with different kappa-casein (CSN3) and beta-lactoglobulin (BLG) genotypes. The study was carried out using a sampling of the first-calf cows of 5 cattle-breeding farms of the Republic of Tatarstan. In animals, the CSN3 and BLG genotypes have been determined by a PCR-RFLP analysis. The cheeseability, heat resistance and thermostability of milk have been estimated using standard methods. The studies have established that the CSN3 and BLG genotypes of cows affected the condition of a casein clot and duration of milk clotting time. The best cheese-making properties of milk were inherent in the animals with the BB and AB genotypes of the CSN3 and BLG genes. They were superior to the coevals with the AA genotype in terms of the highest yield of the desired dense casein clot and the shortest duration of milk clotting time. The first-calf cows, which are the carriers of an A allele of the CSN3 gene, were superior to the animals with the BB genotype of the CSN3 gene on the thermostability of milk including that on the proportion of animals with this milk characteristic. The BLG genotype of the studied animals did not significantly affect the thermostability of milk. Moreover, the highest thermostability of milk was characteristic of black-motley × Holstein cows with the AA genotype

Efficacy and Safety of Netakimab, A Novel Anti-IL-17 Monoclonal Antibody, in Patients with Moderate to Severe Plaque Psoriasis. Results of A 54-Week Randomized Double-Blind Placebo-Controlled PLANETA Clinical Trial

Altres ajuts: Sponsorship for this study and the Rapid Service Fee were funded by JSC BIOCAD, Ul. Italianskaya 17, St Petersburg, Russia, 191186Introduction: Netakimab (NTK), an original humanized anti-interleukin-17 monoclonal antibody, showed therapeutic efficacy in moderate-to-severe plaque psoriasis in a phase 2 clinical study. Herein we report the results of 54 weeks of a phase 3 PLANETA trial aimed to evaluate the efficacy and safety of two NTK regimens vs. placebo. Methods: Two hundred thirteen patients with moderate-to-severe plaque psoriasis were randomly assigned to receive NTK 120 mg once every 2 weeks (NTK Q2W), NTK 120 mg once every 4 weeks (NTK Q4W) or placebo. During the first 3 weeks, patients received subcutaneous injections of NTK or placebo (according to the allocation) once a week. Patients in the NTK Q2W group then received NTK at weeks 4, 6, 8 and 10. Subjects in the NTK Q4W group received NTK at weeks 6 and 10 and placebo at weeks 4 and 8. Patients in the placebo group received placebo injections at weeks 4, 6, 8 and 10. Treatment was unblinded at week 12. During the open-label phase, patients in both NTK groups continued to receive NTK Q4W. The primary efficacy endpoint was the proportion of patients in each group who achieved a ≥ 75% reduction from baseline in psoriasis area and severity index (PASI 75) at week 12. Results: A total of 77.7%, 83.3% and 0% of patients had a PASI 75 response at week 12 in the NTK Q2W, NTK Q4W and placebo groups, respectively (P < 0.0001, Fisher's exact test, ITT). The effect was maintained throughout the 1-year treatment. NTK showed a good safety profile and low immunogenicity. Conclusion: Treatment with NTK results in high rates of sustained clinical response in patients with moderate-to-severe plaque psoriasis. The study is ongoing; thus, long-term use efficacy and safety data are forthcoming. Clinical Trial Registration: The trial is registered at the US National Institutes of Health (ClinicalTrials.gov; NCT03390101)

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps

We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering amplitude for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single channel s-wave scattering of $^{23}$Na atoms in an isotropic harmonic trap, even when outside the Wigner threshold regime. Our model works also for multi-channel scattering, where the scattering length can be made large due to a magnetically tunable Feshbach resonance.Comment: 7 pages, 4 figures (PostScript), submitted to Physical Review