Linear Charges Research Articles

Linear Newman-Penrose charges as subleading BMS and dual BMS charges

In this paper, we further develop previous work on asymptotically flat spacetimes and extend subleading BMS and dual BMS charges in a large r expansion to all orders in r −1. This forms a complete account of this prescription in relation to the previously discovered Newman-Penrose charges. We provide an explanation for the origin of the infinite tower of linear Newman-Penrose charges with regards to asymptotic symmetries and justify why these charges fail to be conserved at the non-linear level as well as failing to exhibit full supertranslation invariance even at the linear level.

Carroll Expansion of General Relativity

We study the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry. This is an expansion around the ultra-local Carroll limit, in which light cones close up. To this end, we first rewrite the Einstein--Hilbert action in pre-ultra-local variables, which is closely related to the 3+1 decomposition of general relativity. At leading order in the expansion, these pre-ultra-local variables yield Carroll geometry and the resulting action describes the electric Carroll limit of general relativity. We also obtain the next-to-leading order action in terms of Carroll geometry and next-to-leading order geometric fields. The leading order theory yields constraint and evolution equations, and we can solve the evolution analytically. We furthermore construct a Carroll version of Bowen--York initial data, which has associated conserved boundary linear and angular momentum charges. The notion of mass is not present at leading order and only enters at next-to-leading order. This is illustrated by considering a particular truncation of the next-to-leading order action, corresponding to the magnetic Carroll limit, where we find a solution that describes the Carroll limit of a Schwarzschild black hole. Finally, we comment on how a cosmological constant can be incorporated in our analysis.

Scalar vortex beam produced through faithful reconstruction of polarization holography

Vortex beams have been widely analyzed and applied in various fields owing to their unique phase and intensity distribution, along with their orbital angular momentum; they can be produced through various methods. This study proposes a method based on polarization holography, contrary to the traditional method of producing vortex beams. This method is significant in that the signal wave in the recording stage is not the generated vortex beam; the reconstructed wave is the vortex beam obtained in the reconstruction stage, which varies from the vortex beams produced by holography, where the signal wave is already a vortex beam. Faithful reconstruction of polarization holography is applied in the experiment, where phenanthrenequinone-doped polymethyl methacrylate (PQ/PMMA) photopolymers are used as the recording material. Scalar vortex beams with arbitrary linear polarization and topological charges can be produced by changing the experimental parameters. The experimental results are satisfactory. Additionally, this work demonstrates the application of polarization holography in light field manipulation. This proposed method has potential applications in optical micro-manipulation and optical tweezers.

Physical and numerical assessments of the penetration behavior of coplanar linear shape charges

In this study, we aimed to demolish irregular constructions that are usually composed of convex, concave, and straight structures based on the shaped charge jet. Accordingly, the penetration behaviour of convergent, divergent, and straight linear shaped charges (LSCs) have been detected with numerical and physical methods. For comparison purposes, numerical models for all three types of LSCs with identical cross-sections have been established to investigate the impacts of structural features. It is found that the shaped charge structure not only determines the kinematic consumption during the penetration process but also influences the initial value of the jet velocity. Additionally, because of the interactions between the previous and subsequent jets, the jet velocity of the convergent LSC shows an obvious undulation during the penetration process. Furthermore, quantitative analyses of the kinematic consumption and initial velocity differences for three types of LSCs are conducted with physical models. A kinematic consumption difference is revealed, and the mass of the charge that determines the initial jet velocity as a function of the geometric parameters in three types of LSCs is deduced. Finally, we combined the numerical and physical models and conducted integral analyses to assess the penetration behaviours of the three LSC types.

Study of combustion wave propagation in linear charges from mechanically activated thermite mixtures

The combustion wave propagation in Al–CuO and Al–Bi2O3 termite mixtures was experimentally investigated. Waveforms of electric current through the reaction area between electrodes with a given potential difference, chronograms of piezo- and photodiode response, the data of pyrometric measurements, as well as photos of the glowing area were obtained and analyzed. There were revealed the advance filtration of the gas component through pores of mixture, the generation of charges providing considerable electrical conductivity of chemical reaction products, the connection of electrical conductivity dynamics with the optical radiation of the chemical conversion region.

A NEW TECHNOLOGY FOR REGULATING ACTIONS OF ENERGY OF MASS EXPLOSION AT THE OPEN PITS

The efficiency of blasting operations in open pits is characterized by the output of oversized material, the study of the foot of the ledge, the parameter of the collapse of the exploded rock mass and the size of the structural violation of the legit part of the mountain range. During the production of mass explosions in an open pit, the natural structure of the rock mass is always violated behind the contour of the exploding block, which is the source of the oversized output, negatively affects the stability of the ledge slopes, and also makes it difficult to regulate the parameters of the collapse of the exploded mass. The work is devoted to the development of effective methods for conducting blasting operations to limit the zones of fracturing and zones of rock mass breakaway behind the contour of the exploding block. A new complex method of ledge breaking has been developed by using large-diameter borehole charges and explosives with greater detonation, as well as exploding linear charges. The proposed method of rebounding allows to limit the radius of the crack formation and the breakaway zones, therefore, to ensure the stability of the slope of the ledge, as well as to obtain a smooth surface of the ledge, which eliminates the exit of oversized rock and makes it possible to obtain the collapse of the rock mass of the specified parameters.

Fields of a relativistic beam of charged particles between parallel planes: Exact two-dimensional solutions obtained by the method of images

We calculate exact two-dimensional analytic expressions for the electric and magnetic fields and their potentials generated by a linear beam of relativistic charged particles between infinite ideally conducting planes and ferromagnetic poles. We use the method of summing an infinite sequence of fields of linear image charges and image currents to obtain solutions and also calculate the density distribution of the electric charge on the conductor surface induced by the charged particle beam. We obtain new formulas for the linear approximation of the fields near the beam and discuss the mathematical features of the exact solutions and the applicability constraints for the linear approximations.

Topological Bands and Triply Degenerate Points in Non-Hermitian Hyperbolic Metamaterials.

Hyperbolic metamaterials (HMMs), an unusual class of electromagnetic metamaterials, have found important applications in various fields due to their distinctive properties. A surprising feature of HMMs is that even continuous HMMs can possess topological edge modes. However, previous studies based on equal-frequency surface (analogy of Fermi surface) may not correctly capture the topology of entire bands. Here we develop a topological band description for continuous HMMs that can be described by a non-Hermitian Hamiltonian formulated from Maxwell's equations. We find two types of three-dimensional non-Hermitian triply degenerate points with complex linear dispersions and topological charges ±2 and 0 induced by chiral and gyromagnetic effects. Because of the photonic nature, the vacuum band plays an important role for topological edge states and bulk-edge correspondence in HMMs. The topological band results are numerically confirmed by direct simulation of Maxwell's equations. Our work presents a general non-Hermitian topological band treatment of continuous HMMs, paving the way for exploring interesting topological phases in photonic continua and device implementations of topological HMMs.

New Approach to Definition of Potential of the Electric Field Created by Set Distribution in Space of Electric Charges

Abstract We study the dependence of the rate of convergence of the relaxation process on the value of ω. We compare the rate of convergence of methods for the upper and lower relaxation. We calculate the dependence of the potentials difference on the distance between two linear charges. The obtained numerical results are compared with the recognized analytical solution of this problem. The dependence of the rate of convergence of the relaxation techniques and the accuracy of the numerical solution on the step of grid is investigated here. Algorithms, allowing visualization of the distribution process of the electric field strength have been created. The obtained results can be used in stand-alone complex measuring devices for automatic quality control system and measurement of electric field parameters in microwave transmission lines.

Elaboration of the Charge Constructions of Explosives for the Structure of Facing Stone

Increased demand for high-strength facing material caused the enhancement of the volume of explosives use in modern technologies of blocks production. The volume of broken rocks and crushing quality depends on the rock characteristics and on the properties of the explosive, in particular on its brisance and serviceability. Therefore, the correct selection of the explosive for the specific massif is of a considerable practical importance. For efficient mining of facing materials by explosion method the solving of such problems as determination of the method of blasthole drilling as well as of the regime and charge values, selection of the explosive, blastholes distribution in the face and their order is necessary. This paper focuses on technical solutions for conservation of rock natural structure in the blocks of facing material, mined by the use of the explosives. It has been established that the efficient solving of mentioned problem is attained by reducing of shock pulse duration. In such conditions the rigidity of crystalline lattice increases in high pressure area. As a result, the hazard if crack formation in structural unites and the increases of natural cracks are excluded. Short-time action of explosion pulse is possible only by linear charges of the explosives, characterized by high detonation velocity which detonate by the velocity of 7-7.5 km/sec and are characterized by very small critical diameter.

Development of a system of plane radial cracks during explosion of linear blasthole and borehole charges

Numerical algorithms have been developed to determine the shape and dimensions of radial cracks formed during confined explosions of linear charges in a monolithic rock massif at a great depth and near its surface. The influence of the charge length on the dimensions of radial cracks in a confined explosion has been studied. The burial depth of a borehole or blast charge for which the area of radial cracks is maximal is determined.

A review of the fundamentals of the Fundamental Review of the Trading Book: standard foreign exchange rules are highly asymmetric with respect to reporting currencies

We examine the mathematical formalism underlying the Basel Committee on Banking Supervision’s “Revised standardized approach of the Fundamental Review of the Trading Book”. One of its goals is to provide a simple, uniform methodology for market risk that applies to all banks independently of their internal models. The formalism exhibits subtle nonlinearities that can have deep implications and deserve careful analysis. We demonstrate that the capital charge for the linear part of the foreign exchange book can differ substantially, depending on the reporting currency. Indeed, we prove that the linear charge is the same for any reporting currency if and only if the correlation between risk-weighted positions in the currencies is 50%, and the intra-bucket correlation is 100%. We show that the capital charge for the nonlinear part of the book fails to be invariant regardless of the correlation values. We demonstrate (in the most recent version of the rules) up to 58% and 300% anomalies for the linear and nonlinear charges, respectively, depending on the book. We also show the rather surprising result that, for a given reporting currency, the capital charges are only functionally dependent on the original underlying rates of the portfolio and are not necessarily dependent on the rates referencing the reporting currency. The anomaly is therefore due to the noninvariance of the aggregation mechanism under a change of reporting currency. We solve the problem by offering a proposal that carefully restores the invariance, using the same regulatory framework and without changing the underlying conservatism. Our analysis also has the practical application of facilitating the transformations of the computations in any reporting currency, possibly circumventing the need for system changes in some cases.

Analysis of fuel thrift of fulldrive truck depending on the terms of motion

In the article the analysis of charges of fuel is conducted by fulldrive trucks depending on the terms of motion. By the method of the multivariable planning of experiment and use of polinomial models the matrix of researches was created, on the basis of which the real terms of motion were formed. Regressive equalization of nonlinear description of the probed processes allowed to build fuel-velocity description of permanent motion of car and carry out the comparative estimation of range of linear charges of fuel of car of KAMAZ–4310 on different types dear.

Notes on toric Sasaki-Einstein seven-manifolds and AdS4/CFT3

We study the geometry and topology of two infinite families Y^{p,k} of Sasaki-Einstein seven-manifolds, that are expected to be AdS_4/CFT_3 dual to families of N=2 superconformal field theories in three dimensions. These manifolds, labelled by two positive integers p and k, are Lens space bundles S^3/Z_p over CP^2 and CP^1 x CP^1, respectively. The corresponding Calabi-Yau cones are toric. We present their toric diagrams and gauged linear sigma model charges in terms of p and k, and find that the Y^{p,k} manifolds interpolate between certain orbifolds of the homogeneous spaces S^7, M^{3,2} and Q^{1,1,1}.

On size and boundary effects in scaled model blasts—fractures and fragmentation patterns

This contribution is the third part of a paper addressing size and boundary effects on explosively induced wave propagation, fracturing and fracture pattern development in small scale laboratory specimens, which are frequently used for model blast tests. Small cylindrical and block type specimens fabricated from concrete, sandstone and amphibolite are centre-line loaded by linear explosive charges and supersonically detonated. Using shock wave theory, elastic wave propagation theory, and fracture mechanics it is shown that the type of boundary conditions prescribed at the outer boundary of the cylinder controls the extension of stem cracking and the development of the fragmentation pattern within the body of the cylinder and the cube specimens. In the case of a composite specimen, where a cylindrical core of different material is embedded in a cylinder or in a cube, the level of fracturing and fragmentation is controlled by the conditions and possible de-lamination of the interface which, in turn, depends...

On size and boundary effects in scaled model blasts spatial problems

This paper addresses size and boundary effects on wave propagation, fracture pattern development and fragmentation in small scale laboratory-size specimens for model blasting. Small block type specimens are centre-line loaded by linear explosive charges and supersonically detonated. Using elastic wave propagation theory and fracture mechanics it is shown that the type of boundary conditions which prevail at the outer boundary of the cylinder control the extension of bore-hole cracking and fragmentation within the body of the cylinder. In the case of a composite block where a cylindrical core of different material is embedded, the level of fracturing and fragmentation is controlled by the separation of the interface which in turn depends on the relative dimensions of the core and the block. The most important parameter is the ratio between the length of the pulse (space-wise or time-wise) and the characteristic dimensions of the models, i.e. in this case the dimensions of the core and the mantel. Stress wa...

Induction of apoptosis by electrotransfer of positively charged proteins as Cytochrome C and Histone H1 into cells

Cytochrome C (Cyt. C) is a mitochondrial protein inducing apoptosis when it is accumulated in the cytosol by a currently unknown mechanism, but regulated by the bcl-2 family of proteins. The linker Histone H1 is another basic protein with highly conservative structure, composition, and equal molecular weight, not changed during the evolution. An attempt was made to understand better the apoptotic processes by electroloading of leukemic cells, such as K562, HL-60, and SKW3, and human lymphocytes with positively charged proteins, such as Cyt. C, Histone H1, and methylated BSA albumin (mBSA). The triggering apoptotic processes followed by MTT test, FACS analysis, and DNA fragmentation after the electrotransfer of these proteins into the cells were observed. Histone H1 and mBSA induce the release of Cyt. C from rat liver mitochondria. Cytochrome C release was higher when mitochondria were in "high-energy" state. It is supposed that release of Cyt. C from mitochondria is due to the mechanical rupture of the outer mitochondrial membrane, rich in negatively charged groups, predominately due to cardiolipin. The reason for the morphological rupture of the outer mitochondial membrane could be the rigidification and segregation of the membrane and the destroyed membrane asymmetries of both monolayers in the presence of positively charged proteins at higher linear charges such as Histone H1. We suggested that Histone H1, at a given moment of activated signaling for apoptosis, could be not transported to the nucleus and could lead to the release of Cyt. C from the mitochondria in the cytoplasm. It is temping to speculate that Histone H1 has other physiological extranuclear functions involved in apoptosis.

Shock-wave structure in the near zone upon explosion of spatial charges in air

Profiles and values of pressure in shock waves are determined for the case of spherical, linear, and spatial charges, such as a coil of a bulk spiral and plane annular coils and Archimedes’ spiral of various lenths, exploded in air. In the case of explosion of rings and spirals, a complex wave structure in the form of a sequence of several shock waves is registered near the charges along the spiral axes; a weaker attenuation of shock waves with distance and pressure amplitudes two to three times higher than in the case of a spherical charge of the same mass are observed. It was found that an increase in the length of a plane spiral does not lead to an increase in the maximum pressure in the shock wave at distances of the order of several pitches of the spiral from its plane. With distance from spatial charges of different shape but identical mass, the pressure values in the shock-wave fronts coincide and tend asymptotically to the parameters of a spherical explosion with a significant increase in the duration of a wave packet generated by the spatial charge. Dependences for evaluation of shock-wave pressure amplitudes in the near zone of the explosion are presented.

Ratio of the cavity volumes in confined explosions of concentrated and linear charges

Numerical calculations are performed to obtain a formula showing that confined cavities obtained from the explosions of linear charges are smaller in volume than those obtained from the explosions of concentrated charges containing the same mass of explosive. This phenomenon is explained by the fact that the energy similarity law governing the effect of explosions is satisfied approximately.

Calculation of the intensity of air shock waves in the near range of the explosion

The results of the studies dealing with the air shock-wave parameters are analyzed and the parameters obtained in the authors’ studies are reported. Generalized empirical dependences are obtained to calculate the wave intensity in the near range of the explosion of open concentrated and linear charges of large extent which consist of various shell-free explosives in a broad range of initial densities. The explosion fields of a full torus-like charge and linear and partially torus-like charges of finite length are considered theoretically. Formulas are derived to calculate the intensity of air shock waves of these charges, which agree with experiment.