Infinite Radius Research Articles

Fundamental Investigation on the Polishing Aspheric Elements with Doughnut-Shaped MCF Slurry

Previous researches have confirmed that MCF (magnetic compound fluid) slurry shows outstanding performance in the nanoprecision polishing of flat surfaces and V-grooves. However, no investigations have been conducted on the polishing of aspheric surfaces using MCF slurry. In this work, a novel method employing a doughnut-shaped MCF polishing tool and a 6-DOF manipulator has been proposed for the aspheric surface polishing. The time consumption for forming stable polishing tool and its final appearance are investigated. Flat aluminum alloy workpieces that can be considered as a kind of aspheric elements with infinite curve radius were adopted in the investigation of the polished forces under variable parameters. As a typical experimental result, with MCF3 slurry, 2.5ml volume of supplied slurry and work gap 3.5 mm, the surface roughness Ra decreases from 125nm to almost 10nm after 90 min polishing, confirming that the proposed method has the potential to polish aspheric surfaces.

Comprehensive high-precision high-accuracy equation of state and coexistence properties for classical Lennard-Jones crystals and low-temperature fluid phases.

We report equilibrium molecular simulation data for the classical Lennard-Jones (LJ) model, covering all thermodynamic states where the crystal is stable, as well as fluid states near coexistence with the crystal; both fcc and hcp polymorphs are considered. These data are used to compute coexistence lines and triple points for equilibrium among the fcc, hcp, and fluid phases. All results are obtained with very high accuracy and precision such that coexistence conditions are obtained with one to two significant figures more than previously reported. All properties are computed in the limit of an infinite cutoff radius of the LJ potential and in the limit of an infinite number of atoms; furthermore, the effect of vacancy defects on the free energy of the crystals is included. Data are fit to a semi-empirical equation of state to within their estimated precision, and convenient formulas for the thermodynamic and coexistence properties are provided. Of particular interest is the liquid-vapor-fcc triple point temperature, which we compute to be 0.694 55 ± 0.000 02 (in LJ units).

Zilch vortical effect

We study the question if a helicity transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant "zilch" current. In order to avoid problems of causality, we quantize the system on a cylinder of a finite radius and then discuss the limit of infinite radius. We find that net helicity- and zilch currents are only generated in the case of the finite radius and are due to duality violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the well-known temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies.

ANALYSIS OF THE NETWORK WITH MULTIPLE CLASSES OF POSITIVE CUSTOMERS AND SIGNALS AT A NON-STATIONARY REGIME

The object of research is G-network with positive customers and signals of multiple classes. The present paper describes an analysis of this network at a non-stationary regime, also provided a description of method for finding non-stationary state probabilities.At the beginning of the article, a description of the network with positive customers and signals is given. A signal when entering the system destroys a positive customer of its type or moves the customer of its type to another system. Streams of positive customers and signals arriving to each of the network systems are independent. Selection of positive customers of all classes for service – randomly. For non-stationary state probabilities of the network, the system of Kolmogorov difference-differential equations (DDE) has been derived. It is solved by a modified method of successive approximations, combined with the method of series. The convergence of successive approximations with time has been proved to the stationary distribution of probabilities, the form of which is indicated in the article, and the sequence of approximations converges to the unique solution of the DDE system. Any successive approximation is representable in the form of a convergent power series with an infinite radius of convergence, the coefficients of which satisfy recurrence relations, which is convenient for computer calculations.The obtained results can be applied for modeling behavior of computer viruses and attack in computer systems and networks, for example, as model impact of some file viruses on server resources.

Analysis of axisymmetric boundary layers

Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on boundary layer parameters such as shape factor ($H$) and skin-friction coefficient ($C_{f}$), defined as$H=\unicode[STIX]{x1D6FF}^{\ast }/\unicode[STIX]{x1D703}$and$C_{f}=\unicode[STIX]{x1D70F}_{w}/(0.5\unicode[STIX]{x1D70C}U_{e}^{2})$respectively, where$\unicode[STIX]{x1D6FF}^{\ast }$is displacement thickness,$\unicode[STIX]{x1D703}$is momentum thickness,$\unicode[STIX]{x1D70F}_{w}$is the shear stress at the wall,$\unicode[STIX]{x1D70C}$is density and$U_{e}$is the streamwise velocity at the edge of the boundary layer. Relations are obtained relating the mean wall-normal velocity at the edge of the boundary layer ($V_{e}$) and$C_{f}$to the boundary layer and pressure gradient parameters. The analytical relations reduce to established results for planar boundary layers in the limit of infinite radius of curvature. The relations are used to obtain$C_{f}$which shows good agreement with the data reported in the literature. The analytical results are used to discuss different flow regimes of axisymmetric boundary layers in the presence of pressure gradients.

REGULARITY RADIUS: PROPERTIES, APPROXIMATION AND A NOT A PRIORI EXPONENTIAL ALGORITHM

The radius of regularity, sometimes spelled as the radius of nonsingularity, is a measure providing the distance of a given matrix to the nearest singular one. Despite its possible application strength this measure is still far from being handled in an efficient way also due to findings of Poljak and Rohn providing proof that checking this property is NP-hard for a general matrix. There are basically two approaches to handle this situation. Firstly, approximation algorithms are applied and secondly, tighter bounds for radius of regularity are considered. Improvements of both approaches have been recently shown by Hartman and Hlad\'{i}k (doi:10.1007/978-3-319-31769-4\_9) utilizing relaxation of the radius computation to semidefinite programming. An estimation of the regularity radius using any of the above mentioned approaches is usually applied to general matrices considering none or just weak assumptions about the original matrix. Surprisingly less explored area is represented by utilization of properties of special classes of matrices as well as utilization of classical algorithms extended to be used to compute the considered radius. This work explores a process of regularity radius analysis and identifies useful properties enabling easier estimation of the corresponding radius values. At first, checking finiteness of this characteristic is shown to be a polynomial problem along with determining a sharp upper bound on the number of nonzero elements of the matrix to obtain infinite radius. Further, relationship between maximum (Chebyshev) norm and spectral norm is used to construct new bounds for the radius of regularity. Considering situations where the known bounds are not tight enough, a new method based on Jansson-Rohn algorithm for testing regularity of an interval matrix is presented which is not a priory exponential along with numerical experiments. For a situation where an input matrix has a special form, several corresponding results are provided such as exact formulas for several special classes of matrices, e.g., for totally positive and inverse non-negative, or approximation algorithms, e.g., rank-one radius matrices. For tridiagonal matrices, an algorithm by Bar-On, Codenotti and Leoncini is utilized to design a polynomial algorithm to compute the radius of regularity.

ANALYSIS OF THE NETWORK WITH MULTIPLE CLASSES OF POSITIVE AND NEGATIVE CUSTOMERS AT A TRANSIENT REGIME

This paper is devoted to the investigation of the G-network with multiple classes of positive and negative customers. The purpose of the investigation is to analyze such a network at a transient regime, to find the state probabilities of the network that depend on time. In the first part, a description of the functioning of G-networks with positive and negative customers is provided, when a negative customer when arriving to the system destroys a positive customer of its class. Streams of positive and negative customers arriving at each of the network systems are independent. Services of positive customers of all types occur in accordance with a random selection of them for service. For nonstationary probabilities of network states, a system of Kolmogorov's difference-differential equations (DDE) has been derived. A method for their finding is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. It is proved that successive approximations converge with time to a stationary probability distribution, the form of which is indicated in this paper, and the sequence of approximations converges to the unique solution of the DDE system. Any successive approximation is representable in the form of a convergent power series with an infinite radius of convergence, the coefficients of which satisfy recurrence relations, which is convenient for computer calculations. A model example illustrating the determination of the time-dependent probabilities of network states using this technique has been calculated. The obtained results can be applied in modeling the behavior of computer viruses and attacks in information and telecommunication systems and networks, for example, as a model of the impact of some file viruses on server resources. variable.

Laser induced wavefront distortion in thick-disk material: An analytical description

Laser induced wavefront distortion is critical for designing and evaluation of optical components for high-power laser and can affect performance and stability of optical systems. The analysis of this effect involves a complex thermoelastic problem only solved in simplified conditions such as the plane-stress or plane-strain configurations. For more realistic descriptions, numerical solutions are required, although recent advances allowed for a unified model to describe the optical path change, regardless of the sample thickness, assuming a sample of infinite radius. In this work, we extend this result for the case of a thick-disk sample by solving the set of differential equations governing the thermoelastic response for the finite radius configuration. These results could represent a significant contribution for designing and characterization of laser systems with potential application in many photothermal methods for material characterization.

Model for how an accretion disk drives astrophysical jets and sheds angular momentum

Clumps of ions and neutrals in the weakly ionized plasma in an accretion disk are shown to follow trajectories analogous to those of fictitious ‘metaparticles’ having a charge to mass ratio reduced from that of an ion by the ionization fraction. A certain class of meta-particles have zero-canonical angular momentum and so spiral in towards the star. Accumulation of these meta-particles establishes a radial electric field that drives the electric current that flows in bidirectional astrophysical jets lying along the disk axis and provides forces that drive the jets. The entire process converts gravitational potential energy into jet energy while absorbing angular momentum from accreting material and shedding this angular momentum at near infinite radius.

FINDING EXPECTED REVENUES IN G-NETWORK WITH SIGNALS AND CUSTOMERS BATCH REMOVAL

The paper provides an analysis of G-network with positive customers and signals when signals arriving to the system move customer to another system or destroy in it a group of customers, reducing their number to a random value that is given by a probability distribution. The signal arriving to the system, in which there are no positive customers, does not exert any influence on the queueing network and immediately disappears from it. Streams of positive customers and signals arriving to each of the network systems are independent. Customer in the transition from one system to another brings the latest some revenue, and the revenue of the first system is reduced by this amount. A method of finding the expected revenues of the systems of such a network has been proposed. The case when the revenues from transitions between network states are deterministic functions depending on its states has been considered. A description of the network is given, all possible transitions between network states, transition probabilities, and revenues from state transitions are indicated. A system of difference-differential equations for the expected revenues of network systems has been obtained. To solve it, we propose a method of successive approximations, combined with the method of series. It is proved that successive approximations converge to the stationary solution of such a system of equations, and the sequence of approximations converges to a unique solution of the system. Each approximation can be represented as a convergent power series with an infinite radius of convergence, the coefficients of which are related by recurrence relations. Therefore, it is convenient to use them for calculations on a PC. The obtained results can be applied in forecasting losses in information and telecommunication systems and networks from the penetration of computer viruses into it and conducting computer attacks.

On indirect noise in multicomponent nozzle flows

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multicomponent gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an accelerating flow is a source of sound induced by inhomogeneities in the mixture (i) chemical potentials and (ii) specific heat capacities. Second, it is shown that the acoustic, entropy and compositional linear perturbations evolve independently from each other and they become coupled through mean-flow gradients and/or at the boundaries. Third, the equations are cast in invariant formulation and a mathematical solution is found by asymptotic expansion of path-ordered integrals with an infinite radius of convergence. Finally, the transfer functions are calculated for a supersonic nozzle with finite spatial extent perturbed by a methane–air compositional inhomogeneity. The proposed framework will help identify and quantify the sources of sound in nozzles with relevance, for example, to aeronautical gas turbines.

On indirect noise in multicomponent nozzle flows

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multi-component gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an accelerating flow is a source of sound induced by inhomogeneities in the mixture (i) chemical potentials and (ii) specific heat capacities. Second, it is shown that the acoustic, entropy and compositional linear perturbations evolve independently from each other and they become coupled through mean-flow gradients and/or at the boundaries. Third, the equations are cast in invariant formulation and a mathematical solution is found by asymptotic expansion of path-ordered integrals with an infinite radius of convergence. Finally, the transfer functions are calculated for a supersonic nozzle with finite spatial extent perturbed by a methane-air compositional inhomogeneity. The proposed framework will help identify and quantify the sources of sound in nozzles with relevance, for example, to aeronautical gas turbines.

Effects of the circularly polarized beam of linearized gravitational waves

Solutions of the linearized Einstein equations are found that describe a transversely confined beam of circularly polarized gravitational waves on a Minkowski backdrop. By evaluating the cycle-averaged stress-energy-momentum pseudotensor of Landau & Lifshitz it is found that the angular momentum density is concentrated in the ‘skin’ at the edge of the beam where the intensity falls, and that the ratio of angular momentum to energy per unit length of the beam is , where ω is the wave frequency, as expected for a beam of spin-2 gravitons. For sharply-defined, uniform, axisymmetric beams, the induced background metric is shown to produce the gravitomagnetic field and frame-dragging effects of a gravitational solenoid, whilst the angular momentum current helically twists the space at infinite radius along the beam axis.

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter e(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value e and rms fluctuation Δe of the coupling parameter between waves from the homogeneous case (e ≠ 0, Δe = 0) to the extremely randomized case (e = 0, Δe ≠ 0) at various correlation wavenumbers of inhomogeneities k c. For the limiting case of infinite correlation radius (k c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k c values), because it describes both the shape and width of peaks much better than the standard approximation.

Shell-crossing in quasi-one-dimensional flow

Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid. At this instant, the velocity becomes multi-valued and the density singular. Shell-crossing is well understood in one dimension (1D), but not in higher dimensions. This paper is about quasi-one-dimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shell-crossing using the Euler--Poisson equations written in Lagrangian coordinates. The signature of shell-crossing is then just the vanishing of the Jacobian of the Lagrangian map, a regular perturbation problem. In essence the problem of the first shell-crossing, which is highly singular in Eulerian coordinates, has been desingularized by switching to Lagrangian coordinates, and can then be handled by perturbation theory. Here, all-order recursion relations are obtained for the time-Taylor coefficients of the displacement field, and it is shown that the Taylor series has an infinite radius of convergence. This allows the determination of the time and location of the first shell-crossing, which is generically shown to be taking place earlier than for the unperturbed 1D flow. The time variable used for these statements is not the cosmic time $t$ but the linear growth time $\tau \sim t^{2/3}$. For simplicity, calculations are restricted to an Einstein--de Sitter universe in the Newtonian approximation, and tailored initial data are used. However it is straightforward to relax these limitations, if needed.

FINDING NON-STATIONARY STATE PROBABILITIES OF G-NETWORK WITH SIGNALS AND CUSTOMERS BATCH REMOVAL

This paper is devoted to the research of an open Markov queueing network with positive customers and signals, and positive customers batch removal. A way of finding in a non-stationary regime time-dependent state probabilities has been proposed. The Kolmogorov system of difference-differential equations for state probabilities of such network was derived. The technique of its building, based on the use of the modified method of successive approximations combined with a series method, has been proposed. It is proved that the successive approximations converge over time to the stationary state probabilities, and the sequence of approximations converges to the unique solution of the Kolmogorov equations. Any successive approximation can be represented as a convergent power series with infinite radius of convergence, the coefficients of which satisfy the recurrence relations; that is useful for estimations. Model example illustrating the finding of time-dependent state probabilities of the network has been provided.

A continuum model to study interphase effects on elastic properties of CNT/GS-nanocomposite

In the present study, initially a continuum level model of interphase region in a carbon nanotube (CNT)/graphene sheet (GS) based nanocomposite is established. Cohesive zone model through Lennard Jones (i.e. LJ) potential is utilized to model the interphase zone in terms of its thickness and elastic modulus, for different matrix materials containing CNTs of various radii (including graphene—a CNT of infinite radius). Thereafter, a finite element based study is conducted to characterize and compare the CNT- and GS-reinforced nanocomposites with and without interphase, using the method of representative volume element (RVE). Based on the study, it is concluded that the thickness as well as elastic modulus of the interphase zone is significantly affected by the matrix material of nanocomposite which is in contrast to the general assumption, made in the literature, of constant thickness of interphase zone for different matrix materials. In the case of nanocomposite with small radius CNTs, slightly higher, noticeable only at narrow scale, elastic modulus of interphase zone is obtained than the nanocomposite with large radius CNTs, irrespective of matrix materials. For metal nanocomposites, interphase zone results in loss of all stiffness properties of the resulting CNT/GS nanocomposite, and this loss is more prevalent in GS nanocomposite for its out-of-plane stiffness properties. But, on the contrary, in the case of polyethylene (i.e. PE) nanocomposite, the elastic modulus of interphase causes enhanced stiffness properties of the resulting nanocomposite, as compared to the perfectly bonded nanocomposite, for CNT and GS reinforcements.

The Arithmetic Geometry of Resonant Rossby Wave Triads

Linear wave solutions to the Charney--Hasegawa--Mima equation with periodic boundary conditions have two physical interpretations: Rossby (atmospheric) waves, and drift (plasma) waves in a tokamak. These waves display resonance in triads. In the case of infinite Rossby deformation radius, the set of resonant triads may be described as the set of integer solutions to a particular homogeneous Diophantine equation, or as the set of rational points on a projective surface $X$. The set of all resonant triads was found by Bustamante and Hayat (2013) via mapping to quadratic forms. Our work independently finds all resonant triads via a rational parametrization of $X$. We provide a fiberwise description of $X$ as a rational singular elliptic surface, yielding many new results about the set of wavevectors belonging to resonant triads. In particular, we show there is an infinite number of resonant triads (with relatively prime wavevectors) containing a wavevector $(a,b)$ with $a/b=r$, where $r$ is any given rationa...

The analytic structure of non-global logarithms: convergence of the dressed gluon expansion

Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon expansion was introduced that enables an expansion of the NGL series in terms of a "dressed gluon" building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-$N_c$ master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluon expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of $\alpha_s$log. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. This allows us to calculate the NGL distribution for all values of $\alpha_s$log from the coefficients of the fixed order expansion.

Convergent perturbation theory for lattice models with fermions

The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.