Longitudinal vector form factors in weak decays of nuclei

The longitudinal form factors of the weak vector current of particles with spin $J = 1/2$ and isospin $I = 1/2$ are determined by the mass difference and the charge radii of members of the isotopic doublets. The most promising reactions to measure these form factors are the reactions with large momentum transfers involving the spin-1/2 isotopic doublets with a maximum mass splitting. Numerical estimates of longitudinal form factors are given for nucleons and eight nuclear spin-1/2 isotopic doublets.Comment: 6 pages. Talk given at the 10th MEDEX'15 meeting Matrix Elements for the Double-beta-decay Experiments, Prague, June 9-12, 201

Method for calculation of drilling-and-blasting operations parameters for emulsion explosives

Purpose. Development of a new method for calculation of drilling-and-blasting operations parameters during underground mining with application of emulsion explosives taking into account their energy characteristics as well as physical and mechanical properties of rocks. Methods. The integrated methodological approach including analytical transformations of the received formulas for calculation of drilling-and-blasting operations parameters, their improvement and also computer modeling on the basis of a finite element method were used for the establishment of compression zones and formations of cracks in the massif around shots taking into account such energy characteristics of emulsion explosive as detonation velocity, explosion heat, density of the explosives, etc. Findings. The relative force coefficient was determined for the emulsion explosive of “Ukrainit” type taking into account the extent of detonation velocity realization, which allowed to calculate the necessary amount of explosives. On the basis of experimental data, consistent patterns of detonation velocity change depending on the charge density and diameter yielding to power law are determined for the emulsion explosive of “Ukrainit” type. Improvements have been made to the analytical expression determining the sizes of compression and fracturing zones around blast holes taking into account energy characteristics of the emulsion explosive of “Ukrainit” type as well as physical and mechanical properties of the blasted rocks. This allowed to develop a new algorithm of calculating parameters for drawing up the passport of drilling-and-blasting operations during underground mining. Originality. The method for calculating drilling-and-blasting operations parameters is based on the regularities of emulsion explosives energy characteristics change, the extent of detonation velocity realization as well as physical and mechanical properties of rocks. Practical implications. A new method has been developed for calculation of drilling-and-blasting operations parameters during mining with emulsion explosives application, which results in minimization of energy consumption for the mass breakage.Мета. Розробка нової методики розрахунку параметрів буропідривних робіт (БПР) при проведенні підземних гірничих виробок із використанням емульсійних вибухових речовин (ЕВР) з урахуванням їх енергетичних характеристик і фізико-механічних властивостей порід. Методика. У роботі використано комплексний методичний підхід, що включає аналітичні перетворення раніше отриманих формул розрахунку параметрів БПР та їх удосконалення, а також комп’ютерне моделювання на основі методу скінчених елементів зі встановлення зон зминання та утворення тріщин в масиві навколо шпурів з урахуванням енергетичних характеристик емульсійної вибухівки: швидкість детонації, теплота вибуху, щільність вибухових речовин (ВР) та ін. Результати. Визначено коефіцієнт відносної працездатності емульсійної вибухівки типу “Україніт” з урахуванням ступеня реалізації швидкості детонації, що дозволило визначити необхідну кількість ВР. На основі експериментальних даних встановлено закономірності зміни швидкості детонації від щільності та діаметру заряду для ЕВР типу “Україніт”, які змінюються за ступеневим законом. Удосконалено аналітичний вираз, що визначає розміри зон зминання та тріщин, які утворюються навколо шпурів з урахуванням енерге- тичних характеристик ЕВР “Україніт” і фізико-механічних властивостей порід, на чому ґрунтується подальший вдосконалений алгоритм розрахунку параметрів для складання паспорта БПР при проведенні підземних гірничих виробок. Наукова новизна. Полягає у використанні закономірностей зміни енергетичних властивостей ЕВР, ступеня реалізації швидкості детонації та фізико-механічних властивостей гірських порід при розробці методики розрахунку параметрів БПР. Практична значимість. Розроблено нову методику розрахунку параметрів БПР при проведенні гірничих виробок на основі використання ЕВР, що забезпечує мінімізацію енергетичних витрат на руйнування масиву.Цель. Разработка новой методики расчета параметров буровзрывных работ (БВР) при проведении подземных горных выработок с использованием эмульсионных взрывчатых веществ (ЭВВ) с учетом их энергетических характеристик и физико-механических свойств пород. Методика. В работе использован комплексный методический подход, включающий аналитические преобразования ранее полученных формул расчета параметров БВР и их усовершенствование, а также компьютерное моделирование на основе метода конечных элементов по установлению зон смятия и образования трещин в массиве вокруг шпуров с учетом энергетических характеристик ЭВВ: скорость детонации, теплота взрыва, плотность взрывчатых веществ (ВВ) и др. Результаты. Определен коэффициент относительной работоспособности ЭВВ типа “Украинит” с учетом степени реализации скорости детонации, что позволило определить необходимое количество ВВ. На основе экспериментальных данных установлены закономерности изменения скорости детонации от плотности и диаметра заряда для ЭВВ типа “Украинит”, которые изменяются по степенному закону. Усовершенствовано аналитическое выражение, определяющее размеры зон смятия и трещинообразования, образуемых вокруг шпуров с учетом энергетических характеристик ЭВВ “Украинит” и физико-механических свойств взрываемых пород, на чем основывается дальнейший усовершенствованный алгоритм расчета параметров для составления паспорта БВР при проведении подземных горных выработок. Научная новизна. Состоит в использовании закономерностей изменения энергетических характеристик ЭВВ, степени реализации скорости детонации и физико-механических свойств горных пород при разработке методики расчета параметров БВР. Практическая значимость. Разработана новая методика расчета параметров БВР при проведении горных выработок на основе использования ЭВВ, обеспечивающая минимизацию энергетических затрат на разрушение массива.The authors express their deepest gratitude to V.P. Kuprin, Doctor of Philosophy in Chemistry, Professor, State Prize Laureate of Ukraine in Science and Technology for providing research base and organizational support during industrial experiments

Wavelength limits on isobaricity of perturbations in a thermally unstable radiatively cooling medium

Nonlinear evolution of one-dimensional planar perturbations in an optically thin radiatively cooling medium in the long-wavelength limit is studied numerically. The accepted cooling function generates in thermal equilibrium a bistable equation of state $P(\rho)$. The unperturbed state is taken close to the upper (low-density) unstable state with infinite compressibility ($dP/d\rho= 0$). The evolution is shown to proceed in three different stages. At first stage, pressure and density set in the equilibrium equation of state, and velocity profile steepens gradually as in case of pressure-free flows. At second stage, those regions of the flow where anomalous pressure (i.e. with negative compressibility) holds, create velocity profile more sharp than in pressure-free case, which in turn results in formation of a very narrow (short-wavelength) region where gas separates the equilibrium equation of state and pressure equilibrium sets in rapidly. On this stage, variation in pressure between narrow dense region and extended environment does not exceed more than 0.01 of the unperturbed value. On third stage, gas in the short-wavelength region reaches the second (high-density) stable state, and pressure balance establishes through the flow with pressure equal to the one in the unperturbed state. In external (long-wavelength) regions, gas forms slow isobaric inflow toward the short-wavelength layer. The duration of these stages decreases when the ratio of the acoustic time to the radiative cooling time increases. Limits in which nonlinear evolution of thermally unstable long-wavelength perturbations develops in isobaric regime are obtained.Comment: 21 pages with 7 figures, Revtex, accepted in Physics of Plasma

THE MACROKINETICS PARAMETERS OF THE HYDROCARBONS COMBUSTION IN THE NUMERICAL CALCULATION OF ACCIDENTAL EXPLOSIONS IN MINES

Purpose. Obtaining effective parameters of the macrokinetics of combustion of hydrocarbons in the deflagration and detonation regime for the numerical calculation of emergency explosions in mine workings. Methodology. Mathematical modeling, numerical experiment, kinetics analysis of explosive combustion reaction, analysis and synthesis. Findings. The paper analyzes the parameters of the kinetic equation against experimental data. Obtaining such data in a physical experiment for explosive chemical reactions meets serious difficulties. This is due to the size of the reaction zone not exceeding fractions of a millimeter, the lack of time resolution of experimental techniques and other factors leading to errors in direct measurements and the emergence of multiple solutions. This possibility contributes to obtaining a simultaneous numerical solution of the equations of gas dynamics and chemical kinetics. In the numerical experiment, a direct relationship between the macrokinetic characteristics of the chemical reaction and the parameters of the discontinuous flow of the reacting gas stream is established: velocity, pressure in the front and behind the front of the detonation and deflagration wave. Based on this, Arrhenius characteristics of the reaction – preexponential and effective activation energy for the hydrocarbons under consideration are obtained. Originality. Macrokinetic parameters are established for simulating one-stage ignition and burning of the most probable hydrocarbons of the mine atmosphere in the deflagration and detonation regime. Modeling of explosive combustion of premixed hydrocarbons in stoichiometric concentrations is performed. It is shown that the values of the effective activation energy in explosive combustion reactions are of less importance in contrast to steady-state combustion reactions because of the effect of the gas-dynamical effects of the shock wave on the reaction rate. The Arrhenius characteristics of the reaction – the pre-exponential and the effective activation energy – have been agreed upon, according to the gas dynamic and kinetic parameters of the course of the explosive combustion reaction. Practical value. The obtained parameters of the macrokinetics of the explosive combustion reaction make it possible to apply simple kinetic mechanisms in practical calculations of the processes of deflagration and detonation combustion, and to predict the parameters of emergency explosions in conditions of mine workings with sufficient accuracy. This also makes it possible to solve the problem of accounting for the presence of heavy hydrocarbons in themine atmosphere as products of coal pyrolysis in underground fires as factors of increasing the risk of emergency explosions

Analysis of the Efficiency PETSc and PETIGA Libraries in Solving the Problem of Crystal Growth

We present an analysis of high performance computational method for solving the problem of crystal grows. The method uses PETSc and PETIGA C-language based libraries and supports parallel computing. The evolution of calculation process was studied in series of special computations are obtained on innovative mobile cluster platform, which provides exclusive system tuning abilities. The results of research confirm the high efficiency of the proposed algorithm on multi-core computer systems and allow us to recommend the use of PETSc and PETIGA for solving high order differential equations