Gauge-Invariant Differential Renormalization: Abelian Case

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automatically preserved to all orders in Abelian case. Since differential renormalization is a strictly four-dimensional renormalization scheme it looks preferable for application in each situation when dimensional renormalization meets difficulties, especially, in theories with chiral and super symmetries. The calculation of the ABJ triangle anomaly is given as an example to demonstrate simplicity of calculations within the presented version of differential renormalization.Comment: 15 pages, late

MODEL OF DECOMPRESSION MELTING MECHANISM IN CONVECTIVE-UNSTABLE THERMAL LITHOSPHERE (FIRST APPROXIMATION)

We propose a model of decompression melting, separation, migration and freezing of the melt in the upper mantle during the convective instability process. The model takes into account differences between phase diagrams of the melt and the matrix and the resultant features of the melt’s behavior, without calculating reaction rates in a multicomponent medium. It is constructed under an explicit concept of the local thermodynamic equilibrium of the existing phases. Therefore, we further develop the first approximation of the descriptions of convection in the upper mantle and the formation of large epicontinental sedimentary basins, which have been presented in earlier publications. Our computational experiments show that primary melting of the upper mantle’s fertile material occurs intensively in a narrow frontal part of the ascending hot material flow. Then, the depleted and partially melted material rises farther upward from the front of primary melting. Melting of the depleted material continues at lower pressures in a rather wide range of depths (120–77 km). Further, the migrating melt is supplied by two sources, i.e. a deep-seated one, wherein the fertile material melts, and the medium-depth one, wherein melting of the depleted material takes place. Once the temperature and pressure rates of the melt reach the values corresponding to those of its solidus, a narrow freezing front is formed. Its width is almost similar to the primary melting front. As the ascending convective flow develops, the freezing front shifts upward. As a result, a quite thick (around 40–50 km) basalt-saturated layer occurs above the freezing front. An important observation in our modeling experiments is that, despite a considerably large total volume of the melted material, a one-time melt content in the mantle does not exceed tenths of one percent, when we consider averaging to volumes with a linear size of about 1.0 km. The basalt melt extraction depletes iron in the mantle and significantly reduces the mantle density. Considering the calculated basalt-depletion values for the matrix at 0.1–0.2, the density deficit doubles in comparison to the thermal expansion of the material. Logically, both the Rayleigh number and the intensity of convection also double (and this is confirmed by the calculations), which means that convection is enhanced after the melting start.Testing of the model shows that it gives a reasonable picture that is consistent with the available geological and geophysical data on the structure of the lithosphere underneath the currently developing epicontinental sedimentary basins. Furthermore, within the limits of its detail, this model is consistent with the results of modeling experiments focused on melting and melting dynamics, which are based on calculations of reactions between components of the mantle material

Effect of hydrogen on plastic strain localization and fracture of steels

The effect of interstitial hydrogen atoms on the mechanical properties and plastic strain localization patterns in tensile tested specimens of low-carbon steels have been studied using a double exposure speckle photography technique. It is found that the mechanical properties of low-carbon steels are affected adversely by hydrogen embrittlement. The deformation diagrams were examined for the deformed samples of low-carbon steels. These are found to show all the plastic flow stages: the linear, parabolic and pre-failure stages would occur for the respective values of the exponent n from the Ludwik-Holomon equation

Influence of hydrogen embrittlement on the localization of plastic strain in Al-Cu-Mg alloy

The influence of hydrogen embrittlement of the aluminum Al–4%Cu–0.2%Mg alloy on the parameters of localized plastic strain is studied. Digital speckle photography is used to visualize the localized strain patterns in the D1 alloy. The velocity of localized deformation bands as a function of the yield strength for nonhydrogenated and hydrogenated samples is found

Autowave process of the localized plastic deformation of high-chromium steel saturated with hydrogen

The deformation behavior of high-chromium stainless steel of sorbitic structure upon high-temperature tempering and of electrically saturated with hydrogen in the electrochemical cell during 12 hours is investigated. The stress-strain curves for each state were obtained. From the stress-strain curves, one can conclude that hydrogen markedly reduces the elongation to the fracture of specimen. Using double-exposed speckle photography method it was found that the plastic flow of the material is of a localized character. The pattern distribution of localized plastic flow domains at the linear hardening stage was investigated. Comparative study of autowave parameters was carried out for the tempered steel as well as the electrically saturated with hydrogen steel

Модель первого приближения формирования эпиконтинентальных осадочных бассейнов вследствие конвективной неустойчивости термической литосферы

Modern computational technologies make it possible to simulate practically any concept developed by geologists to investigate the processes of formation of the structures under study, including diametrically opposed ones. Today’s trend is to create complex ‘realistic’ models. Such models are based on a large number of parameters with properly set values and simulate the settings that can be viewed similar to the real situations. However, the adequacy of both the models themselves and the concepts used as the basis for simulation remains the issue of debate. Apparently, it is required to specify a general approach to theoretical constructions in geodynamics, which should ensure that the scope of applicability of the models can be correctly evaluated. Such an approach can be implemented by successive approximations based on the fundamental results of the theory of simple liquids with damping memory, the most general description of irreversible deformation of materials under non-isotropic stress. It is critical to correctly formulate a model in the first approximation. It should be fairly simple and based on reliably established experimental facts, give adequate and clearly interpretable non-trivial results and allow further logical refinement of the details, i.e. the next approximations. This article presents an attempt to strictly follow the requirements and consistently construct a model that can show the occurrence of large epicontinental sedimentary basins, the origin of which has been in the focus of geological studies for many years. Our model is based on the following reliably established facts: (1) at the surface of the planet, in continental areas there is an approximately 300-km-thick thermal boundary layer (TBL), wherein the temperature drop amounts to ~1300–1500 °C; (2) the material of the lithosphere, including the crust, is irreversibly deformed during slow geological processes; (3) the continental crust is the thick layer that is less dense than the material of the mantle. The numerical experiments demonstrate free convection in the upper mantle, which induces countercurrents in the light crust and leads to the occurrence of sedimentary basins above the ascending flows and uplifts above the descending flows, which form platform shields during the transition to the quasi-stationary mode. The parameters of the typical structures formed in the lithosphere and the crust and the sedimentary basins proper are estimated. Revealed are the stages of their evolution, which correlate with the available geological and geophysical data, except for the effects caused, in our opinion, by the higher temperature of the mantle and the dynamics of the resultant melt. (Our next publications will describe modeling with account of decompression melting of the mantle material and separation, migration and freezing of the resultant melt.) The proposed first-approximation model can be used to describe a wide variety of geodynamic processes of similar scales.Современные вычислительные возможности позволяют реализовать в виде расчетных моделей практически любые представления геологов о процессах формирования изучаемых структур, в том числе и диаметрально противоположные. При этом существует стремление использовать сложные, так называемые «реалистические» модели. Большое число параметров в таких моделях, путем надлежащего подбора значений, позволяет для разных постановок получить в результате расчета картину, сходную с реальной. Таким образом, вопрос об адекватности как самих моделей, так и лежащих в их основе представлений остается открытым. По-видимому, требуется некий общий подход к теоретическим построениям в геодинамике, который позволит определять область пригодности разрабатываемых моделей. Такой подход может быть реализован путем последовательных приближений на основе фундаментальных результатов «Теории простых жидкостей с затухающей памятью» – наиболее общего описания необратимого деформирования материала под действием неизотропных напряжений. При этом важно правильно сформулировать модель первого приближения. Она должна быть достаточно проста, основана на надежно установленных экспериментальных фактах, давать в рамках своей детальности адекватные, понятным образом интерпретируемые, нетривиальные результаты и естественным образом позволять дальнейшее уточнение – развитие следующих приближений. В настоящей работе мы попытались строго и последовательно построить такую модель для описания процесса формирования крупных эпиконтинентальных осадочных бассейнов, вопрос о генезисе которых в течение многих лет находится в центре внимания геологов. Модель основана на нескольких надежно установленных фактах: 1) у поверхности планеты в континентальных областях существует тепловой погранслой толщиной  с перепадом температуры ~1300–1500 °С; 2) вещество литосферы, включая кору, необратимо деформируется в исследуемых медленных геологических процессах; 3) континентальная кора является довольно мощным слоем, с малой, по сравнению с мантией, плотностью. Проведенные численные эксперименты показали развитие в верхней мантии свободной конвекции, индуцирующей в легкой коре противотечение, вызывающее формирование над восходящими потоками осадочных бассейнов, а над нисходящими – поднятий, образующих при переходе к квазистационарному режиму платформенные щиты. Расчеты воспроизводят характерные структуры литосферы, коры и собственно осадочных бассейнов и этапы их эволюции, соответствующие имеющимся геолого-геофизическим данным, за исключением эффектов, обусловленных, как мы полагаем, более высокой температурой мантии и динамикой возникающего при этом расплава. (Включение в модель описания декомпрессионного плавления мантийного вещества, сепарации, миграции и замерзания образующегося расплава предполагается в наших следующих публикациях). Предложенная модель первого приближения пригодна для описания широкого класса геодинамических процессов подобного масштаба

МОДЕЛЬ МЕХАНИЗМА ДЕКОМПРЕССИОННОГО ПЛАВЛЕНИЯ В КОНВЕКТИВНО-НЕУСТОЙЧИВОЙ ТЕРМИЧЕСКОЙ ЛИТОСФЕРЕ (ПЕРВОЕ ПРИБЛИЖЕНИЕ)

We propose a model of decompression melting, separation, migration and freezing of the melt in the upper mantle during the convective instability process. The model takes into account differences between phase diagrams of the melt and the matrix and the resultant features of the melt’s behavior, without calculating reaction rates in a multicomponent medium. It is constructed under an explicit concept of the local thermodynamic equilibrium of the existing phases. Therefore, we further develop the first approximation of the descriptions of convection in the upper mantle and the formation of large epicontinental sedimentary basins, which have been presented in earlier publications. Our computational experiments show that primary melting of the upper mantle’s fertile material occurs intensively in a narrow frontal part of the ascending hot material flow. Then, the depleted and partially melted material rises farther upward from the front of primary melting. Melting of the depleted material continues at lower pressures in a rather wide range of depths (120–77 km). Further, the migrating melt is supplied by two sources, i.e. a deep-seated one, wherein the fertile material melts, and the medium-depth one, wherein melting of the depleted material takes place. Once the temperature and pressure rates of the melt reach the values corresponding to those of its solidus, a narrow freezing front is formed. Its width is almost similar to the primary melting front. As the ascending convective flow develops, the freezing front shifts upward. As a result, a quite thick (around 40–50 km) basalt-saturated layer occurs above the freezing front. An important observation in our modeling experiments is that, despite a considerably large total volume of the melted material, a one-time melt content in the mantle does not exceed tenths of one percent, when we consider averaging to volumes with a linear size of about 1.0 km. The basalt melt extraction depletes iron in the mantle and significantly reduces the mantle density. Considering the calculated basalt-depletion values for the matrix at 0.1–0.2, the density deficit doubles in comparison to the thermal expansion of the material. Logically, both the Rayleigh number and the intensity of convection also double (and this is confirmed by the calculations), which means that convection is enhanced after the melting start.Testing of the model shows that it gives a reasonable picture that is consistent with the available geological and geophysical data on the structure of the lithosphere underneath the currently developing epicontinental sedimentary basins. Furthermore, within the limits of its detail, this model is consistent with the results of modeling experiments focused on melting and melting dynamics, which are based on calculations of reactions between components of the mantle material.Предложена модель декомпрессионного плавления, сепарации, миграции и замерзания расплава в процессе развития конвективной неустойчивости верхней мантии, позволяющая учесть различие фазовых диаграмм расплава и матрицы и вытекающие особенности поведения расплава, без расчета скорости реакций в многокомпонентной среде, в рамках явного представления о локальном термодинамическом равновесии существующих фаз. Таким образом, дополняется развиваемое нами первое приближение описания процесса конвекции в верхней мантии и формирования крупных эпиконтинентальных осадочных бассейнов, опубликованное ранее.Вычислительными экспериментами показано, что первичное плавление фертильного вещества верхней мантии происходит интенсивно в узком фронте поднимающегося в восходящем потоке горячего вещества. Далее, вверх от фронта первичного плавления, поднимается деплетированное и частично выплавленное вещество. Дальнейшее плавление деплетированного вещества происходит выше, при меньших давлениях в довольно широком диапазоне глубин (120–77 км). Далее мигрирует расплав уже от двух источников – глубинного, где плавится фертильное вещество, и промежуточного, где плавится вещество деплетированное. Достигнув уровня температур и давлений, соответствующих его солидусу, расплав образует фронт замерзания, примерно такой же узкий, как и фронт первичного плавления. По мере развития восходящего конвективного потока фронт замерзания смещается вверх. В результате под ним формируется довольно толстый (около 40–50 км) слой вещества, насыщенного «базальтовым» компонентом. Важным результатом моделирования является то, что, несмотря на значительные общие объемы выплавляющегося вещества, единовременное содержание расплава в мантии, при осреднении на объемы с линейным размером порядка 1 км, не превышает десятых долей процента. Экстракция базальтовой выплавки, в связи с обеднением мантийного вещества железом, существенно снижает его плотность. При рассчитанных значениях обеднения матрицы базальтовым компонентом 0.1–0.2 дефицит плотности удваивается, по сравнению тепловым расширением вещества. Стало быть, удваивается и число Рэлея, и интенсивность конвекции, что мы и видим в расчетах – после начала плавления конвекция усиливается.Проведенное опробование модели дает разумную картину, согласующуюся как с известной геолого-геофизической информацией о строении литосферы под развивающимися эпиконтинентальными осадочными бассейнами, так и, в рамках своей детальности, – с результатами моделирования плавления и динамики расплава, полученными путем расчета реакций между компонентами мантийного вещества

About the Poisson Structure for D4 Spinning String

The model of D4 open string with non-Grassmann spinning variables is considered. The non-linear gauge, which is invariant both Poincar\'e and scale transformations of the space-time, is used for subsequent studies. It is shown that the reduction of the canonical Poisson structure from the original phase space to the surface of constraints and gauge conditions gives the degenerated Poisson brackets. Moreover it is shown that such reduction is non-unique. The conseption of the adjunct phase space is introduced. The consequences for subsequent quantization are discussed. Deduced dependence of spin $J$ from the square of mass $\mu^2$ of the string generalizes the ''Regge spectrum`` for conventional theory.Comment: 23 page