Conjugate Pairs Research Articles

Pro-Inflammatory Cytokines are Dysregulated in Depression and Correlated With Measures of Psychopathology

This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain and finite deformation for thermoviscoelastic plates/shells based on the conservation and balance laws of the classical continuum mechanics (CCM) in R3 (see Surana and Mathi, (2020) for linear theory). The conservation and balance laws in Lagrangian description with finite strain measure and the conjugate stress measure in R3 are considered. The conjugate pairs in the second law of thermodynamics (SLT), the consideration of additional physics and the principle of equipresence are utilized to determine the constitutive variables and their argument tensors. The constitutive theory for the contravariant second Piola–Kirchhoff stress tensor is derived using Green’s strain tensor and its convected time derivatives of up to order n as its argument tensors using representation theorem with complete basis (i.e. using integrity). The convected time derivatives of the Green’s strain tensor up to order n provide ordered rate constitutive theory for the dissipation mechanism that is naturally non-linear due to Green’s strain measure. The constitutive theory for heat vector derived using representation theorem and integrity is also a non-linear constitutive theory. Simplified linear forms of these constitutive theories are also presented. The solution methods for the mathematical model for the BVPs as well as the IVPs using p-version hierarchical higher degree and higher order finite element method are presented. Due to dissipation, the energy equation is integral part of the mathematical model that accounts for rate of mechanical work resulting in rate of entropy production, hence heat.The plate/shell geometry (flat or curved) is described by its middle surface containing the nodal vectors (at each of the nine nodes), the ends of which define bottom and top surfaces of the plate/shell (Surana and Mathi, 2020). The geometry is mapped into ξηζ natural coordinate space in a two unit cube. The p-version hierarchical local approximations in ξηζ are constructed to describe the deformation of the plate/shell middle surface as well as its faces that is controlled by p-levels in ξ,η and ζ directions (element local approximation). The formulation presented here is accurate for very thin as well as very thick plate/shells and for small as well as finite deformation and finite strains. Non-linear constitutive theories based on integrity allow more complex constitutive behavior in term of strains as well as strain rates, hence dissipation mechanism. Dissipation mechanism is described by an ordered rate theory based on SLT and additional physics. The formulation presented here always ensures thermodynamic equilibrium during the evolution as it is derived using the conservation and balance laws of CCM in R3. The formulation always preserves three dimensional nature of the deformation physics regardless of the plate/shell thickness and is free of locking problems and shear correction factors that plague most of the currently used plate/shell formulations.

Generation of off-critical zeros for hypercubic Epstein zeta functions

We study the Epstein zeta-function formulated on the d-dimensional hypercubic lattice ζ(d)(s)=12∑′n1,…,nd(n12+…+nd2)−s/2 where the real part ℜ(s)>d and the summation runs over all integers except of the origin (0,0,…,0). An analytical continuation of the Epstein zeta-function to the whole complex s-plane is constructed for the spatial dimension d being a continuous variable ranging from 0 to ∞. Zeros of the Epstein zeta-function ρ=ρx+iρy are defined by ζ(d)(ρ)=0. The nontrivial zeros split into the “critical” zeros (on the critical line) with ρx=d2 and the “off-critical” zeros (off the critical line) with ρx≠d2. Numerical calculations reveal that the critical zeros form closed or semi-open curves ρy(d) which enclose disjunctive regions of the plane (ρx=d2,ρy). Each curve involves a number of left/right edge points ρ*=(d*2,ρy*), defined by a divergent tangent dρy/dd|ρ*. Every edge point gives rise to two conjugate tails of off-critical zeros with continuously varying dimension d which exhibit a singular expansion around the edge point, in analogy with critical phenomena for second-order phase transitions. For each dimension d>9.24555… there exists a conjugate pair of real off-critical zeros which tend to the boundaries 0 and d of the critical strip in the limit d→∞. As a by-product of the formalism, we derive an exact formula for limd→0ζ(d)(s)/d. An equidistant distribution of critical zeros along the imaginary axis is obtained for large d, with spacing between the nearest-neighbour zeros vanishing as 2π/lnd in the limit d→∞.

Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals

The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with ${C}_{6v}$ symmetry and the PC-air-PC interface are studied based on first-principle calculation. To illustrate the importance of parity-time (PT) symmetry, three systems are considered, namely the PT-symmetric, PT-asymmetric, and lossy systems. We find that the system with gain and loss distributed in a PT symmetric manner exhibits a phase transition from a PT exact phase to a PT broken phase as the strength of the gain and loss increases, while for the PT-asymmetric and lossy systems, no such phase transition occurs. Furthermore, based on the Wilson loop calculation, the topology of the PT-symmetric system in the PT exact phase is demonstrated to keep unchanged as the Hermitian system. At last, different kinds of edge states in Hermitian systems under the influences of gain and loss are studied and we find that while the eigenfrequencies of nontrivial edge states become complex conjugate pairs, they keep real for the trivial defect states.

Cylindrical bending of transversely isotropic composite panels with finite strains

sThe article is devoted to solving the problem of cylindrical bending of a flat panel made of a transversely isotropic incompressible composite material with finite deformations. The focus of the article is that in this problem the so-called universal model of constitutive relations is considered, which allows one to obtain solutions to problems simultaneously for several classes of models related to different conjugate pairs of stress-strain tensors. This method was proposed earlier in the works of Yu.I. Dimitrienko. Using this method, the difference in the calculation results, which are obtained using various models of composites with finite strains, is shown.

A case study based on ground observations of the conjugate ionospheric response to interplanetary shock in polar regions

Data acquired by imaging relative ionospheric opacity meters (riometers), ionospheric total electron content (TEC) monitors, and three-wavelength auroral imagers at the conjugate Zhongshan station (ZHS) in Antarctica and Yellow River station (YRS) in the Arctic were analyzed to investigate the response of the polar ionosphere to an interplanetary shock event induced by solar flare activity on July 12, 2012. After the arrival of the interplanetary shock wave at the magnetosphere at approximately 18:10 UT, significantly enhanced auroral activity was observed by the auroral imagers at the ZHS. Additionally, the polar conjugate observation stations in both hemispheres recorded notable evolution in the two-dimensional movement of cosmic noise absorption. Comparison of the ionospheric TEC data acquired by the conjugate pair showed that the TEC at both sites increased considerably after the interplanetary shock wave arrived, although the two stations featured different sunlight conditions (polar night in July in the Antarctic region and polar day in the Arctic region). However, the high-frequency (HF) coherent radar data demonstrated that different sources might be responsible for the electron density enhancement in the ionosphere. During the Arctic polar day period in July, the increased electron density over YRS might have been caused by anti-sunward convection of the plasma irregularity, whereas in Antarctica during the polar night, the increased electron density over ZHS might have been caused by energetic particle precipitation from the magnetotail. These different physical processes might be responsible for the different responses of the ionosphere at the two conjugate stations in response to the same interplanetary shock event. Citation : He F, Hu Z J, Hu H Q, et al. A case study based on ground observations of the conjugate ionospheric response to interplanetary shock in polar regions. Adv Polar Sci, 2021, 32(2): 139-158, doi: 10.13679/j.advps.2021.0012

Phase diagrams with the driving force and extent of reaction as axis variables

A method where a conjugate pair of the driving force (affinity, D) and extent of reaction (EOR, ξ) are used as axis variables to present non-equilibrium conditions of multiphase systems as Calphadian phase diagrams is introduced. Three examples for various thermochemical systems include a solid state reaction, steel melt solidification and an aqueous sorption-precipitation system. Both equilibrium and non-equilibrium diagrams were produced to study the thermodynamic validity of the suggested technique. The use of D,ξ variables can be applied in typical Gibbs energy minimizing programs and provides additional degrees of freedom in the diagrammatic analysis of various multiphase problems.

Diagonalization of the Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode decomposition

We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.

Binary de Bruijn Sequences via Zech’s Logarithms

The focus of this work is to show how to combine Zech’s logarithms and each of the cycle joining and cross-join pairing methods to construct binary de Bruijn sequences. Basic implementations are supplied as proofs of concept. The cycles, in the cycle joining method, are typically generated by a linear feedback shift register. We prove a crucial characterization that determining Zech’s logarithms is equivalent to identifying conjugate pairs shared by any two distinct cycles. This speeds up the task of building a connected adjacency subgraph that contains all vertices of the complete adjacency graph. Distinct spanning trees in either graph correspond to cyclically inequivalent de Bruijn sequences. As the cycles are being joined, guided by the conjugate pairs, we track the changes in the feedback function. We show how to produce certificates of existence for spanning trees of certain types to conveniently handle large order cases. The characterization of conjugate pairs via Zech’s logarithms, as positional markings, is then adapted to identify cross-join pairs. A modified m-sequence is initially used, for ease of generation. The process can be repeated on each of the resulting de Bruijn sequences. Most prior constructions in the literature measure the complexity of the corresponding bit-by-bit algorithms. Our approach is different. We aim first to build a connected adjacency subgraph that is certified to contain all of the cycles as vertices. The ingredients are computed just once and concisely stored. Simple strategies are offered to keep the complexities low as the order grows.

Duality of fractional systems

In this paper we reveal a common property of generalized fractional equations used for the description of many physical systems related to non-exponential relaxation and anomalous diffusion. It follows from conjugate pairs of Bernstein functions being Laplace exponents of random processes that participate at subordination of simple processes such as ordinary exponential relaxation or Brownian motion. The reciprocals of such pair after the inverse Laplace transform obey the Sonine equation in which the Sonine pair consists of two interconnected memory functions being kernels of two generalized fractional equations. Their solutions are transformed into each other. This property is considered as duality in which each generalized fractional system has a partner.

An improved seismic data completion algorithm using low-rank tensor optimization: Cost reduction and optimal data orientation

Seismic data are often incomplete due to equipment malfunction, limited source and receiver placement at near and far offsets, and missing crossline data. Seismic data contain redundancies because they are repeatedly recorded over the same or adjacent subsurface regions, causing the data to have a low-rank structure. To recover missing data, one can organize the data into a multidimensional array or tensor and apply a tensor completion method. We can increase the effectiveness and efficiency of low-rank data reconstruction based on tensor singular value decomposition (tSVD) by analyzing the effect of tensor orientation and exploiting the conjugate symmetry of the multidimensional Fourier transform. In fact, these results can be generalized to any order tensor. Relating the singular values of the tSVD to those of a matrix leads to a simplified analysis, revealing that the most square orientation gives the best data structure for low-rank reconstruction. After the first step of the tSVD, a multidimensional Fourier transform, frontal slices of the tensor form conjugate pairs. For each pair, a singular value decomposition can be replaced with a much cheaper conjugate calculation, allowing for faster computation of the tSVD. Using conjugate symmetry in our improved tSVD algorithm reduces the runtime of the inner loop by 35%–50%. We consider synthetic and real seismic data sets from the Viking Graben Region and the Northwest Shelf of Australia arranged as high-dimensional tensors. We compare the tSVD-based reconstruction with traditional methods, projection onto convex sets and multichannel singular spectrum analysis, and we see that the tSVD-based method gives similar or better accuracy and is more efficient, converging with runtimes that are an order of magnitude faster than the traditional methods. In addition, we verify that the most square orientation improves recovery for these examples by 10%–20% compared with the other orientations.

An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms

The versatile and exactly solvable Scarf II potential has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector, it has gone underutilised. Here, we present the most simple analytic forms for the scattering coefficients \((T(k),R(k),|\det S(k)|)\). On the one hand, these forms demonstrate earlier effects and confirm the recent ones. On the other hand, they make new predictions – all simple and analytical. We show the possibilities of both self-dual and non-self-dual spectral singularities (NSDSS) in two non-PT sectors (potentials). The former one is not accompanied by time-reversed coherent perfect absorption (CPA) and gives rise to the parametrically controlled splitting of spectral singularity (SS) into a finite number of complex conjugate pairs of eigenvalues (CCPEs). NSDSS behave just oppositely: CPA but no splitting of SS. We demonstrate a one-sided reflectionlessness without invisibility. Most importantly, we bring out a surprising coexistence of both real discrete spectrum and a single SS in a fixed potential. Nevertheless, so far, the complex Scarf II potential is not known to be pseudo-Hermitian (\(\eta ^{-1} H\eta =H^\dagger \)) under a metric of the type \(\eta (x)\).

Two- and three-dimensional size-dependent couple stress response using a displacement-based variational method

Based upon the principle of minimum total potential energy for consistent couple stress theory, a Ritz variational approach is developed using tensor product B-splines for both two- and three-dimensional elastostatic analysis. The underlying theory is size-dependent due to incorporation of the energy conjugate skew-symmetric couple-stress and mean curvature tensors, in addition to the force-stress and strain conjugate pair of classical theory. The use of B-splines as the basis functions can assure the required C1 continuity of the displacement field, while also permitting higher order representations. Both displacements and rotations are essential boundary conditions in this theory. Displacements can be enforced in the usual way, but rotations require special treatment to maintain symmetry and positive definiteness of the stiffness matrix for well-posed elastostatic problems. Several computational examples are considered to validate the formulation, illustrate convergence characteristics, and investigate mechanical behavior under consistent couple stress theory. All previous numerical analysis of consistent couple stress theory has been limited to plane strain problems. Thus, the extension here to three-dimensions is of great importance, especially because the behavior in several cases shows significant deviation from the plane strain solutions. Consequently, the variational formulations and computational methodology presented in this paper can play a critical role in assessing the predictive capability of consistent couple stress theory and in understanding size-dependent elastic response.

Formation of Bottom Conjugate Pair Grooves by Femtosecond Laser Grooving on Transparent Substrate

Ultrashort pulsed laser is a promising tool for processing transparent materials. We report on a new approach that simultaneously creates a pair of conjugate grooves on the bottom surface of a thin glass substrate at the duration of plowing a V-shaped microgroove on the top surface using the technique of direct laser ablation. We propose a hypothesis to explain the accompanying grooves’ formation mechanism and simulate Maxwell’s equations to verify its applicability. Measurements showed the surface roughness of the groove’s sidewalls was 0.14 $\mu \text{m}$ . This method requires no mask, can be directly performed in the atmosphere, and can simultaneously produce microgrooves on both sides of the substrate that render it an effective approach for producing high quality V-shaped microgrooves on both sides of the substrate.

Solitons in Kerr media with two-dimensional non-parity-time-symmetric complex potentials

Our results indicate that continuous soliton families can exist and be stable in Kerr media with two-dimensional (2D) non-parity-time (PT)-symmetric complex potentials. There are several discrete eigenvalues in the linear spectra of these complex potentials. Fundamental solitons bifurcate from the largest discrete eigenvalue while the dipole solitons bifurcate from the second- or third- largest discrete eigenvalue. We further find that eigenvalues of the soliton linear-stability spectra emerge as complex conjugate pairs. The effect of different parameters of the complex potentials on soliton stability is discussed in detail. Moreover, we study the transverse energy flow vector of the solitons in these complex potentials.

Magnetic Conjugacy of Pc1 Waves and Isolated Proton Precipitation at Subauroral Latitudes: Importance of Ionosphere as Intensity Modulation Region

AbstractPc1 geomagnetic pulsations, equivalent to electromagnetic ion cyclotron waves in the magnetosphere, display a specific amplitude modulation, though the region of the modulation remains an open issue. To classify whether the amplitude modulation has a magnetospheric or ionospheric origin, an isolated proton aurora (IPA), which is a proxy of Pc1 wave‐particle interactions, is compared with the associated Pc1 waves for a geomagnetic conjugate pair, Halley Research Base in Antarctica and Nain in Canada. The temporal variation of an IPA shows a higher correlation coefficient (0.88) with Pc1 waves in the same hemisphere than that in the opposite hemisphere. This conjugate observation reveals that the classic cyclotron resonance is insufficient to determine the amplitude modulation. We suggest that direct wave radiation from the ionospheric current by IPA should also contribute to the amplitude modulation.

Long-Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions in the Presence of a Discrete Spectrum

The long-time asymptotic behavior of solutions to the focusing nonlinear Schrödinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the presence of discrete spectrum. The results of the analysis provide the first rigorous characterization of the nonlinear interactions between solitons and the coherent oscillating structures produced by localized perturbations in a modulationally unstable medium. The study makes crucial use of the inverse scattering transform for the focusing NLS equation with nonzero boundary conditions, as well as of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–Hilbert problems. Previously, it was shown that in the absence of discrete spectrum the xt-plane decomposes asymptotically in time into two types of regions: a left far-field region and a right far-field region, where to leading order the solution equals the condition at infinity up to a phase shift, and a central region where the asymptotic behavior is described by slowly modulated periodic oscillations. Here, it is shown that in the presence of a conjugate pair of discrete eigenvalues in the spectrum a similar coherent oscillatory structure emerges but, in addition, three different interaction outcomes can arise depending on the precise location of the eigenvalues: (i) soliton transmission, (ii) soliton trapping, and (iii) a mixed regime in which the soliton transmission or trapping is accompanied by the formation of an additional, nondispersive localized structure akin to a soliton-generated wake. The soliton-induced position and phase shifts of the oscillatory structure are computed, and the analytical results are validated by a set of accurate numerical simulations.

ПІДВИЩЕННЯ НАДІЙНОСТІ СУДНОВИХ ЕНЕРГЕТИЧНИХ УСТАНОВОК ШЛЯХОМ УСУНЕННЯ НЕГАТИВНОГО ВПЛИВУ РОЗЦЕНТРОВОК ОСЕЙ З'ЄДНУВАЛЬНИХ ВАЛІВ

The influence of skew axes of the connecting shafts of marine aggregates on the efficiency and reliability of ship power plants is investigated. The reasons for the occurrence of centerings of axes of connecting shafts of marine aggregates are considered and their classification is offered. Failures of ship power plants are classified according to their impact on the efficiency of the installation (according to the consequences), according to the methods of their elimination, and by their nature and are divided into the groups according to the classes. It is shown that during operation, in the conditions of axial skew, traditional designs of the toothed clutch are characterized by non-uniform distribution of forces between pair of gears, which leads to their overload and, as a consequence, reduced load capacity, increased contact stresses, deterioration of lubrication surfaces of gears, increase in power consumption for friction, reduction of efficiency and deterioration of vibroacoustic characteristics due to shock load of gear. Ways to increase the efficiency of ship power plants by providing parameters of reliability of the main power plants by eliminating the negative impact of the centering axes of the connecting shafts of marine aggregates through the use of compensating devices are considered. It is proposed to use as compensating devices, the design of high-efficiency clutch, which in the conditions of axial skew, are characterized by a more uniform distribution of forces between pair of gears than existing ones, ie work almost as a perfect hinge. Regarding the proposed toothed couplings, a previously unknown objectively existing property of the toothed clutch operating at the skew of the axes of the connecting shafts is established, which is that under a certain nonlinear law changes in the generating side surfaces of the outer teeth evenly between all conjugate pairs of teeth. The use of a high-efficiency clutch in the ship power plants is considered and the basic and functional (structural) scheme of the main marine aggregate with a series connection of elements is made to assess the impact on reliability parameters.

Self-dualities and renormalization dependence of the phase diagram in 3d O(N) vector models

In the classically unbroken phase, 3d O(N) symmetric ϕ4 vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by κ) and for any N. It is shown that for κ = κ∗ the two fixed points merge and then, for κ < κ∗, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the N = 1 ϕ4 theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d O(N) models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large N in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.

{101̄2} twinning in single-crystal titanium under shock loading

ABSTRACT We employ molecular dynamics simulations to investigate the evolution dynamics of twinning in single-crystal Ti under shock loading. The shock compression applied perpendicular to the c-axis leads to the activation of twins in single-crystal Ti. We find the twin variant activation for each case of the applied loading conditions follows Schmid criterion. However, the time for the activation of twin variants is not the same even with equal Schmid factor. The evolution and dominance of twin variants in each case of the applied loading conditions do not depend on the Schmid factor. High nucleation events and low overall twin volume fraction occur for the case where two conjugate pairs of twin variants activate while low nucleation events and high overall twin volume fraction occur for the case where only one conjugate pair of twin variants activate. Twin nucleation takes place throughout the simulation time for each case of the applied loading conditions. High twin growth occurs for the case where only one conjugate pair of twin variants activate in comparison to the case where two conjugate pairs of twin variants activate. This indicates that the number of activated twin variants affects the growth rate of the twins.

A Depth-First Iterative Algorithm for the Conjugate Pair Fast Fourier Transform

The Split-Radix Fast Fourier Transform has the same low arithmetic complexity as the related Conjugate Pair Fast Fourier Transform. Both transforms have an irregular datapath structure which is straightforwardly expressed only in recursive forms. Furthermore, the conjugate pair variant has a complicated input indexing pattern which requires existing iterative implementations to rely on precomputed tables. It however allows optimization of the memory bandwidth as it requires a single twiddle factor load per radix-4 butterfly. In existing algorithms, this comes at the cost of using additional precomputed tables or performing recursive function calls. In this paper we present two novel approaches that handle both the butterfly scheduling and the input index generation of the Conjugate Pair Fast Fourier Transform. The proposed algorithm is cache-friendly because it is depth-first, non-recursive and does not rely on precomputed index tables. In order to achieve this, we relate the butterfly execution pattern of the Split-Radix and Conjugate Pair FFTs to the binary carry sequence. Based on this finding, we describe how common integer arithmetic and bitwise operations can be used to perform input reordering and depth-first traversal of the transform datapath with O(1) space complexity.