Optimal with respect to accuracy methods for evaluating hypersingular integrals

In this paper we constructed optimal with respect to order quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M), Ω¯ur,γ(Ω,M), Ω=[−1,1]l, l=1,2,…,M=Const, and γ is a real positive number. The functions that belong to classes Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M) have bounded derivatives up to the rth order in domain Ω and derivatives up to the sth order (s=r+⌈γ⌉) in domain Ω∖Γ, Γ=∂Ω. Moduli of derivatives of the vth order (r<v≤s) are power functions of d(x,Γ)−1(1+|lnd(x,Γ)|), where d(x,Γ) is a distance between point x and Γ. The interest in these classes of functions is due to the fact that solutions of singular and hypersingular integral equations are their members. Moreover various physical fields, in particular gravitational and electromagnetic fields belong to these classes as well. We give definitions of optimal with respect to accuracy methods for solving hypersingular integrals. We constructed optimal with respect to order of accuracy quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M).

Dynamical Field Inference and Supersymmetry

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.

Gauge Symmetries in Physical Fields (Review)

Gauge invariance is one of the fundamental symmetries in theoretical physics. In this paper, the gauge symmetry is reviewed to see how it is working in fundamental physical fields: Electromagnetism, Quantum Electro Dynamics and Geometric Theory of Gravity. In the 19th century, the gauge invariance was recognized as a mathematical non-uniqueness of the electromagnetic potentials. Real recognition of the gauge symmetry and its physical significance required two new fields developed in the 20th century: the relativity theory for physics of the world structure of linked 4d-spacetime and the quantum mechanics for the new dimension of a phase factor in complex representation of wave function. Finally the gauge theory was formulated on the basis of the gauge principle which played a role of guiding principle in the study of physicalfields such as Quantum Electrodynamics, Particle Physics and Theory of Gravitation. Fluid mechanics of a perfect fluid can join in this circles, which is another motivation of the present review. There is a hint of fluid gauge theory in the general representation of rotational flows of an ideal compressible fluid satisfying the Euler’s equation, found in 2013 by the author. In fact, law of mass conservation can be deduced from the gauge symmetry equipped in the new system of fluid-flow field combined with a gauge field, rather than given a priori.

Irregular layout of fiber-optical lines for tomographic monitoring of nautical structures

В статье рассматривается решение волоконно-оптической томографической задачи для мониторинга морских конструкций на основе новой, впервые публично представляемой, схемы укладки волоконно-оптических измерительных линий распределенной сети. В предлагаемой схеме укладки устраняется сдерживающий фактор линейности линий малоракурсной томографии и впервые анализируются возможности неравномерной схемы укладки. Сравнение предложенной схемы укладки с классическими схемами показало преимущество в точности определения места воздействия при уменьшении числа измерительных линий. Численное сравнение полученных результатов вычислительных экспериментов с ранее полученными результатами по другим схемам сканирования показали перспективность предлагаемого способа. Использование неравномерных схем укладок волоконно-оптических линий, наряду с применением систем искусственного интеллекта к информации на выходе этих линий, позволяет их изгибать теоретически на любых поверхностях морских конструкций, огибая углы балок, шпангоутов, неровных уплотнений и других подобных выпуклых поверхностей, для проектирования на их основе систем мониторинга состояния медленных физических полей на поверхностях со сложным произвольным профилем. The article discusses the solution of fiber-optical tomographic problem for monitoring nautical structures based on new layout of fiber-optic measuring lines. In the proposed scheme, the limiting factor of linearity of low-angle tomography lines is eliminated. The possibilities of Irregular layouts are analyzed. Comparison of the proposed layout with classical options showed gain in the accuracy of determining the location of the impact while reducing the number of measuring lines. A numerical comparison of the obtained results of computational experiments with previously obtained results for other scanning schemes showed the promise of the proposed method. Artificial intelligence systems are applied to the output data of these lines. This allows, in theory, to use uneven fiber-optic lines on any surfaces of nautical structures. At the same time, they will be able to bend around the corners of girders, ribs, uneven seals and other similar convex surfaces. All this will make it possible to design on their basis monitoring systems for slow physical fields on random profile surfaces.

Study on Micro Recoil Mechanism of the Weapon with a Nozzle and Two Chambers Separated by a Partition

In order to improve the recoil reduction ability of the weapon without reducing the projectile velocity, the weapon with a nozzle and two chambers separated by a partition is proposed. Taking the 35 mm caliber grenade launcher as the research object, the physical model of its launching process is proposed, and the one-dimensional two-phase flow interior ballistic model is established. MacCormack difference scheme is used to calculate the coupling of multiple physical fields formed by front and rear chambers and nozzles. Compared with the calculation results obtained by using the classical interior ballistic model, the correctness of the two-phase flow interior ballistic model is verified. The effects of the charge amount in the rear chamber and the size of the air guide hole in the barrel on the internal ballistic performance of the weapon with a nozzle and two chambers separated by a partition. The calculation results show that compared with conventional weapons, the recoil impulse can be reduced with maintaining muzzle velocity, and the recoil reduction efficiency can reach 72.27%, which is of great significance for improving weapon performance.

Analysis of the engineering mathematical model of the physical properties of a three-layer hydroacoustic screen with anisotropic components

A numerical-analytical technique for analyzing the physical effects of the formation of fields of hydroacoustic waves in the area in front of a flat three-layer hydroacoustic screen and in the space behind the screen at normal incidence of a stationary hydroacoustic wave on it is presented. The engineering model of the screen uses the assumption that its components are made of anisotropic functional-gradient materials with exponential inhomogeneity in thickness, and thin, absolutely flexible, inextensible coatings can be applied to the outer and contact surfaces of the layers. The technique is based on the analytical integration of the equations of wave deformation of the screen components and obtaining complex amplitude characteristics for the reflected and generated hydroacoustic waves behind the screen when solving a system of algebraic equations with a functional matrix, which follows from the boundary conditions for the investigated problem. Parametric descriptions for the characteristics of the investigated physical fields are obtained and examples of numerical analysis of the considered engineering model are presented.

On a pseudotensor generalization of the Hugoniot-Hadamard linking boundary conditions

В представляемой работе исследуются особенности связывающих двусторонних граничных условий на поверхностях разрывов, распространяющихся в сплошных средах (в частности, в микрополярных континуумах). Теория Югонио-Адамара, существенно развитая Г.И. Быковцевым, распространения поверхностей разрывов физических полей обобщена на случай псевдотензорного полевого описания. Вводятся понятия фундаментального ориентирующего псевдоскаляра и псевдоскалярного времени. Исследуется геометрия поверхностей уровня псевдоскалярного поля, представляющих интерес для механики наращиваемых тел. Вводится понятие псевдонормали к поверхности. Обсуждаются вопросы дифференцирования по псевдоскалярному времени и его преобразования при зеркальных отражениях и инверсиях пространства. Получены геометрические и кинематические условия совместности первого порядка в терминах псевдотензоров. Выведены условия совместности для слабых разрывов перемещений и микровращений в микрополярном континууме. The present work deals with the linking boundary conditions formulated on the both sides of a propagating wave surface (in particular, in micropolar continua). The Hugoniot-Hadamard theory of physical fields wave surfaces propagation, essentially developed by G.I. Bykovtsev, is generalized to the case of a pseudotensor field description. The concepts of fundamental orienting pseudoscalar and pseudoscalar time are introduced and discussed. The geometry of level surfaces of a given pseudoscalar field is studied. The concept of a pseudovector normal to a surface is introduced. The pseudoscalar time derivative is proposed and discussed. Geometric and kinematic first order compatibility conditions are obtained in terms of pseudotensors. The compatibility conditions are derived for weak discontinuities of displacements and microrotations due to defromations of the micropolar solid.

Can Environmental Conditions at North Atlantic Deep-Sea Habitats Be Predicted Several Years Ahead? ——Taking Sponge Habitats as an Example

Predicting the ambient environmental conditions in the coming several years to one decade is of key relevance for elucidating how deep-sea habitats, like for example sponge habitats, in the North Atlantic will evolve under near-future climate change. However, it is still not well known to what extent the deep-sea environmental properties can be predicted in advance. A regional downscaling prediction system is developed to assess the potential predictability of the North Atlantic deep-sea environmental factors. The large-scale climate variability predicted with the coupled Max Planck Institute Earth System Model with low-resolution configuration (MPI-ESM-LR) is dynamically downscaled to the North Atlantic by providing surface and lateral boundary conditions to the regional coupled physical-ecosystem model HYCOM-ECOSMO. Model results of two physical fields (temperature and salinity) and two biogeochemical fields (concentrations of silicate and oxygen) over 21 sponge habitats are taken as an example to assess the ability of the downscaling system to predict the interannual to decadal variations of the environmental properties based on ensembles of retrospective predictions over the period from 1985 to 2014. The ensemble simulations reveal skillful predictions of the environmental conditions several years in advance with distinct regional differences. In areas closely tied to large-scale climate variability and ice dynamics, both the physical and biogeochemical fields can be skillfully predicted more than 4 years ahead, while in areas under strong influence of upper oceans or open boundaries, the predictive skill for both fields is limited to a maximum of 2 years. The simulations suggest higher predictability for the biogeochemical fields than for the physical fields, which can be partly attributed to the longer persistence of the former fields. Predictability is improved by initialization in areas away from the influence of Mediterranean outflow and areas with weak coupling between the upper and deep oceans. Our study highlights the ability of the downscaling regional system to predict the environmental variations at deep-sea benthic habitats on time scales of management relevance. The downscaling system therefore will be an important part of an integrated approach towards the preservation and sustainable exploitation of the North Atlantic benthic habitats.

Coupling effects between elastic and electromagnetic fields from the perspective of conservation of energy

Coupling effects among different physical fields reflect the conversion of energies from one field into another substantially. For simple physical processes, their governing or constitutive equations all satisfy the law of conservation of energy (LCE). Then, an analysis is extended to the coupling effects. First, for the linear direct and converse piezoelectric and piezomagnetic effects, their constitutive equations guarantee that the total energy is conserved during the process of energy conversion between the elastic and electromagnetic fields. However, the energies are converted via the work terms, (βijkEi),kvj and (γijkHi),kvj, rather than via the energy terms, βijkEiejk and γijkHiejk. Second, for the generalized Villari effects, the electromagnetic energy can be treated as an extra contribution to the generalized elastic energy. Third, for electrostriction and magnetostriction, both effects are induced by the Maxwell stress. Moreover, their energies are purely electromagnetic and thus both have no converse effects. During these processes, the energies can be converted in three different ways, i.e., via the non-potential forces, via the cross-dependence of the energy terms, and directly via the electromagnetic interactions of ions and electrons. In the end, the general coupling processes which involve elastic, electromagnetic fields and diffusion are also analyzed. The advantages of using this energy formulation are that it facilitates discussion of the conversion of energies and provides better physical insights into the mechanisms of these coupling effects.