Статті в журналах: "Pseudo-density operator"

1

XU, YE-JUN, JUN SONG, HONG-CHUN YUAN, HONG-YI FAN, and QIU-YU LIU. "QUANTIZATION SCHEME FOR FERMIONIC SYSTEM AND s-ORDERED OPERATOR EXPANSION FORMULA OF FERMIONIC DENSITY OPERATORS." Modern Physics Letters A 26, no. 11 (April 10, 2011): 833–42. http://dx.doi.org/10.1142/s0217732311035213.

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We introduce the generalized fermionic Wigner operator with an s parameter. Based on its remarkable properties, we establish one-to-one mapping between fermion operators and their s-parametrized pseudo-classical correspondence, which may involve fermionic Weyl pseudo-classical correspondence, P-representation and Q-representation in a unified way. Furthermore, starting with the projector of the fermionic coherent state, we obtain the s-ordered operator expansion formula of fermionic density operators, which includes normally ordered, antinormally ordered and Weyl ordered product of operators for different values of s. Applications in calculating some Fermi operators' s-ordered expansions are presented.

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2

Liu, Junfeng, and Litan Yan. "On a nonlinear stochastic pseudo-differential equation driven by fractional noise." Stochastics and Dynamics 18, no. 01 (November 6, 2017): 1850002. http://dx.doi.org/10.1142/s0219493718500028.

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In this paper, we study the existence, uniqueness and Hölder regularity of the solution to a class of nonlinear stochastic pseudo-differential equation of the following form [Formula: see text] where [Formula: see text] is a pseudo-differential operator with negative definite symbol of variable order which generates a stable-like process with transition density, the coefficient [Formula: see text] is a measurable function, and [Formula: see text] is a double-parameter fractional noise. In addition, the existence and Gaussian type estimates for the density of the mild solution are proved via Malliavin calculus.

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3

Hanyga, Andrzej, and Richard L. Magin. "A new anisotropic fractional model of diffusion suitable for applications of diffusion tensor imaging in biological tissues." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2170 (October 8, 2014): 20140319. http://dx.doi.org/10.1098/rspa.2014.0319.

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An anomalous anisotropic diffusion equation is constructed in which the order of the spatial pseudo-differential operator is generalized to be distributed with a directionally dependent distribution. A time fractional version of this equation is also considered. First, it is proved that the equation is positivity-preserving and properly normalized. Second, the existence of a smooth Green's function solution is proved. Finally, an expression for the diffusive flux density for this new fractional order process is calculated. This approach may find utility in modelling diffusion tensor imaging data in the white matter of the human brain where both the apparent diffusion coefficient and the order of the pseudo-differential operator are anisotropic.

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4

Atallah-Baraket, Amel, and Maryem Trabelsi. "Analysis of the energy decay of a viscoelasticity type equation." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 3 (November 1, 2016): 21–45. http://dx.doi.org/10.1515/auom-2016-0046.

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AbstractIn this paper, we study the evolution of the energy density of a sequence of solutions of a problem related to a viscoelasticity model where the viscosity term is a pseudo-differential operator of order 2α with α ∈ (0, 1). We calculate the weak limit of the energy density in terms of microlocal defect measures and under special assumption we prove that the viscosity term prevents propagation of concentration and oscillation effects contrary to what happens in the wave equation.

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5

Allen, Blake J., Edward R. Mansell, David C. Dowell, and Wiebke Deierling. "Assimilation of Pseudo-GLM Data Using the Ensemble Kalman Filter." Monthly Weather Review 144, no. 9 (September 2016): 3465–86. http://dx.doi.org/10.1175/mwr-d-16-0117.1.

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Total lightning observations that will be available from the GOES-R Geostationary Lightning Mapper (GLM) have the potential to be useful in the initialization of convection-resolving numerical weather models, particularly in areas where other types of convective-scale observations are sparse or nonexistent. This study used the ensemble Kalman filter (EnKF) to assimilate real-data pseudo-GLM flash extent density (FED) observations at convection-resolving scale for a nonsevere multicell storm case (6 June 2000) and a tornadic supercell case (8 May 2003). For each case, pseudo-GLM FED observations were generated from ground-based lightning mapping array data with a spacing approximately equal to the nadir pixel width of the GLM, and tests were done to examine different FED observation operators and the utility of temporally averaging observations to smooth rapid variations in flash rates. The best results were obtained when assimilating 1-min temporal resolution data using any of three observation operators that utilized graupel mass or graupel volume. Each of these three observation operators performed well for both the weak, disorganized convection of the multicell case and the much more intense convection of the supercell case. An observation operator using the noninductive charging rate performed poorly compared to the graupel mass and graupel volume operators, a result that appears likely to be due to the inability of the noninductive charging rate to account for advection of space charge after charge separation occurs.

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6

Mamalyha, Kh V., and M. M. Osypchuk. "On single-layer potentials for a class of pseudo-differential equations related to linear transformations of a symmetric $\alpha$-stable stochastic process." Carpathian Mathematical Publications 11, no. 2 (December 31, 2019): 350–60. http://dx.doi.org/10.15330/cmp.11.2.350-360.

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In this article an arbitrary invertible linear transformations of a symmetric $\alpha$-stable stochastic process in $d$-dimensional Euclidean space $\mathbb{R}^d$ are investigated. The result of such transformation is a Markov process in $\mathbb{R}^d$ whose generator is the pseudo-differential operator defined by its symbol $(-(Q\xi,\xi)^{\alpha/2})_{\xi\in\mathbb{R}^d}$ with some symmetric positive definite $d\times d$-matrix $Q$ and fixed exponent $\alpha\in(1,2)$. The transition probability density of this process is the fundamental solution of some parabolic pseudo-differential equation. The notion of a single-layer potential for that equation is introduced and its properties are investigated. In particular, an operator is constructed whose role in our consideration is analogous to that the gradient in the classical theory. An analogy to the classical theorem on the jump of the co-normal derivative of the single-layer potential is proved. This result can be applied for solving some boundary-value problems for the parabolic pseudo-differential equations under consideration. For $\alpha=2$, the process under consideration is a linear transformation of Brownian motion, and all the investigated properties of the single-layer potential are well known.

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7

Mamalyha, Kh V., and M. M. Osypchuk. "Properties of single layer potentials for a pseudo- differential equation related to a linear transformation of a rotationally invariant stable stochastic process." Matematychni Studii 55, no. 1 (March 4, 2021): 94–106. http://dx.doi.org/10.30970/ms.55.1.94-106.

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This article is aimed at determining existence conditions of single layer potentials for pseudo-differential equations related to some linear transformations of a rotationally invariant stable stochastic process in a multidimensional Euclidean space and investigating their properties as well. The carrier surface of the potential is smooth enough. In this article, we consider two main cases: the first, when this surface is bounded and closed; the second, when it is unbounded, but could be presented by an explicit equation in some coordinate system. The density of this potential is a continuous function. It is bounded with respect to the spatial variable and, probably, has an integrable singularity with respect to the time variable at zero. Classic properties of this potential, including a jump theorem of the action result of some operator (an analog of the co-normal differential) at its surface points, considered. A rotationally invariant $\alpha$-stable stochastic process in $\mathbb{R}^d$ is a L\'{e}vy process with the characte\-ristic function of its value in the moment of time $t>0$ defined by the expression $\exp\{-tc|\xi|^\alpha\}$, $\xi\in\mathbb{R}^d$, where $\alpha\in(0,2]$, $c>0$ are some constants. If $\alpha=2$ and $c=1/2$, we get Brownian motion and classic theory of potential. There are many different results in this case. The situation of $\alpha\in(1,2)$ is considered in this paper. We study constant and invertible linear transformations of the rotationally invariant $\alpha$-stable stochastic process. The related pseudo-differential equation is the parabolic equation of the order $\alpha$ of the ``heat'' type in which the operator with respect to the spatial variable is the process generator. The single layer potential is constructed in the same way as the single layer potential for the heat equation in the classical theory of potentials. That is, we use the fundamental solution of the equation, which is the transition probability density of the related process. In our theory, the role of the gradient operator is performed by some vector pseudo-differential operator of the order $\alpha-1$. We have already studied the following main properties of the single layer potentials: the single layer potential is a solution of the relating equation outside of the carrier surface and the jump theorem is held. These properties can be useful to solving initial boundary value problems for the considered equations.

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8

Wang, Yuwei, Liangguo Dong, Yuzhu Liu, and Jizhong Yang. "2D frequency-domain elastic full-waveform inversion using the block-diagonal pseudo-Hessian approximation." GEOPHYSICS 81, no. 5 (September 2016): R247—R259. http://dx.doi.org/10.1190/geo2015-0678.1.

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Elastic full-waveform inversion (EFWI) of multicomponent seismic data is a powerful tool for estimating the subsurface elastic parameters with high accuracy. However, the trade-offs between multiple parameters increase the nonlinearity of EFWI. Although the conventional diagonal-approximate Hessian matrix describes the illumination and limited bandwidth effects, it ignores the trade-off effects and decreases the convergence rate of EFWI. We have developed a block-diagonal pseudo-Hessian operator for 2D frequency-domain EFWI to take into account the approximate trade-offs among the P-wave (compressional-wave) velocity, S-wave (shear-wave) velocity, and density without extra computational costs on forward simulations. The Hessian matrix tends toward a block-diagonal matrix as the frequency grows to infinity; thus, the proposed block-diagonal pseudo-Hessian matrix is more accurate at higher frequencies. The inverse of the block-diagonal pseudo-Hessian matrix is used as a preconditioner for the nonlinear conjugate-gradient method to simultaneously reconstruct P- and S-wave velocities and density. This approach effectively mitigates the crosstalk artifacts by correcting the gradients from the trade-off effects and produces more rapid inversion convergence, which becomes more significant at higher frequencies. Synthetic experiments on an inclusion model and the elastic Marmousi2 model demonstrate its feasibility and validity in EFWI.

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9

Murguía-Romero, Gabriela, Angel Sánchez, and Ricardo Zavaleta-Madrid. "Electromagnetic Properties in Multilayer Graphene within the Ritus Formalism: Transverse Electrical Conductivity." Advances in Science and Technology 98 (October 2016): 125–30. http://dx.doi.org/10.4028/www.scientific.net/ast.98.125.

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Within the framework of the Quantum Field Theory, we discuss how to study electromagnetic properties of a multilayer graphene sample in the presence of electric and magnetic fields, both perpendicular to the graphene planes. We deal with the multilayer system by taking into account the quantum mechanical supersymmetric property of the monolayer Hamiltonian. We solve the Dirac equation for the graphene charge carriers by using the Ritus formalism. This formalism consists in the diagonalization of the operator with and the Dirac gamma matrices which contain information about the pseudo-spin. We calculate the charge carrier propagator for the monolayer case, and we obtain the photon polarization operator, the leading quantum correction to the classical Lagrangian density that encodes the electromagnetic properties of the system through the constitutive equations. With the quantum supersymmetrical properties of both, the monolayer and the multilayer graphene Hamiltonians, it is possible to extend our results to obtain the charge carrier propagator for the multilayer case.

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10

Lee, Hyun Geun. "Numerical Simulation of Pattern Formation on Surfaces Using an Efficient Linear Second-Order Method." Symmetry 11, no. 8 (August 5, 2019): 1010. http://dx.doi.org/10.3390/sym11081010.

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We present an efficient linear second-order method for a Swift–Hohenberg (SH) type of a partial differential equation having quadratic-cubic nonlinearity on surfaces to simulate pattern formation on surfaces numerically. The equation is symmetric under a change of sign of the density field if there is no quadratic nonlinearity. We introduce a narrow band neighborhood of a surface and extend the equation on the surface to the narrow band domain. By applying a pseudo-Neumann boundary condition through the closest point, the Laplace–Beltrami operator can be replaced by the standard Laplacian operator. The equation on the narrow band domain is split into one linear and two nonlinear subequations, where the nonlinear subequations are independent of spatial derivatives and thus are ordinary differential equations and have closed-form solutions. Therefore, we only solve the linear subequation on the narrow band domain using the Crank–Nicolson method. Numerical experiments on various surfaces are given verifying the accuracy and efficiency of the proposed method.

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11

Lang, Lucas, Enrico Ravera, Giacomo Parigi, Claudio Luchinat, and Frank Neese. "Theoretical analysis of the long-distance limit of NMR chemical shieldings." Journal of Chemical Physics 156, no. 15 (April 21, 2022): 154115. http://dx.doi.org/10.1063/5.0088162.

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After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland–McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel–Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree–Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin–orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland–McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

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12

Balakin, Alexander, and Alexei Ilin. "Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem." Symmetry 10, no. 9 (September 18, 2018): 411. http://dx.doi.org/10.3390/sym10090411.

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We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explicitly; the scale factor is found in quadratures. Asymptotic analysis of the exact solutions has shown that the Big Rip, Little Rip, Pseudo Rip regimes can be realized with the specific choice of guiding parameters of the model. We show that the Coincidence problem can be solved if we consider the memory effect associated with the interactions in the Dark Sector of the universe.

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13

Mitra, Ayan, Pritam Chattopadhyay, Goutam Paul, and Vasilios Zarikas. "Binary Black Hole Information Loss Paradox and Future Prospects." Entropy 22, no. 12 (December 8, 2020): 1387. http://dx.doi.org/10.3390/e22121387.

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Various techniques to tackle the black hole information paradox have been proposed. A new way out to tackle the paradox is via the use of a pseudo-density operator. This approach has successfully dealt with the problem with a two-qubit entangle system for a single black hole. In this paper, we present the interaction with a binary black hole system by using an arrangement of the three-qubit system of Greenberger–Horne–Zeilinger (GHZ) state. We show that our results are in excellent agreement with the theoretical value. We have also studied the interaction between the two black holes by considering the correlation between the qubits in the binary black hole system. The results depict a complete agreement with the proposed model. In addition to the verification, we also propose how modern detection of gravitational waves can be used on our optical setup as an input source, thus bridging the gap with the gravitational wave’s observational resources in terms of studying black hole properties with respect to quantum information and entanglement.

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14

Boyarsky, Abraham, and Pawel Góra. "The Pseudo-Orbit Shadowing Property for Markov Operators in the Space of Probability Density Functions." Canadian Journal of Mathematics 42, no. 6 (December 1, 1990): 1000–1017. http://dx.doi.org/10.4153/cjm-1990-053-2.

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AbstractLet X be a space with two metrics d1 and d2. Let S :(X, d1) → (X, d2) be continuous. We say S has the generalized pseudoorbit shadowing property with respect to the metrics d1 and d2 if for every every δ-pseudo-orbit in d1 can be ∊-shadowed by a true orbit in d2, i.e., if {x0, x1,…} satisfies for all i ≧ 0, then for all i ≧ 0. The main result of this note shows that certain Markov operators P : L1→ L1 have the generalized shadowing property on weakly compact subsets of the space of probability density functions, where d1 is the metric of norm convergence and d2 is the metric of weak convergence. An important class of such operators are the Frobenius-Perron operators induced by certain expanding and nonexpanding maps on the interval. When there is exponential convergence of the iterates to the density, we can express δ in terms of ∊. We also show that, unlike the situation in the space X itself, the generalized shadowing property is valid for all parameters in families of maps and that there is stability of the shadowing property.

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15

Yan, Jia, and Paul Sava. "Elastic wave-mode separation for VTI media." GEOPHYSICS 74, no. 5 (September 2009): WB19—WB32. http://dx.doi.org/10.1190/1.3184014.

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Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because P- and S-modes are both propagated using elastic wave equations, there is a need to separate P- and S-modes to efficiently apply single-mode processing tools. In isotropic media, wave modes are usually separated using Helmholtz decomposition. However, Helmholtz decomposition using conventional divergence and curl operators in anisotropic media does not give satisfactory results and leaves the different wave modes only partially separated. The separation of anisotropic wavefields requires more sophisticated operators that depend on local material parameters. Anisotropic wavefield-separation operators are constructed using the polarization vectors evaluated at each point of the medium by solving the Christoffel equation for local medium parameters. These polarization vectors can be represented in the space domain as localized filtering operators, which resemble conventional derivative operators. The spatially variable pseudo-derivative operators perform well in heterogeneous VTI media even at places of rapid velocity/density variation. Synthetic results indicate that the operators can be used to separate wavefields for VTI media with an arbitrary degree of anisotropy.

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16

Varghese, Prathibha, and Dr G. Arockia Selva Saroja. "A Novel Hexagonal Psuedo framework for Edge Detection Operators on Hexagonal Framework." International Journal of Electrical and Electronics Research 10, no. 4 (December 30, 2022): 1036–42. http://dx.doi.org/10.37391/ijeer.100446.

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Edge detection using a gradient-based detector is a gold-standard method for identifying and analyzing different edge points in an image. A hexagonal grid structure is a powerful architecture dominant for intelligent human-computer vision. This structure provides the best angle resolution, good packing density, high sampling efficiency, equidistant pixels, and consistent connectivity. Edge detection application on hexagonal framework provides more accurate and efficient computations. All the real-time hardware devices available capture and display images in rectangular-shaped pixels. So, an alternative approach to mimic hexagonal pixels using software approaches is modeled in this paper. In this research work, an innovative method to create a pseudo hexagonal lattice has been simulated and the performance is compared with various edge detection operators on the hexagonal framework by comparing the quantitative and qualitative metrics of the grayscale image in both square and hexagonal lattice. The quantitative performance of the edge detection on the hexagonal framework is compared based on the experimental facts. The pseudo-hexagonal lattice structure assures to be aligned toward the human vision.

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17

Morozov, Sergey, Leonid Parnovski, and Roman Shterenberg. "Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators." Annales Henri Poincaré 15, no. 2 (April 5, 2013): 263–312. http://dx.doi.org/10.1007/s00023-013-0246-8.

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18

Eparu, Cristian Nicolae, Sorin Neacsu, and Adrian Neacsa. "Correlation of Gas Quality with Hydrodynamic Parameters in Transmission Networks." MATEC Web of Conferences 290 (2019): 10001. http://dx.doi.org/10.1051/matecconf/201929010001.

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Natural gases are a mixture of hydrocarbons. Their composition determines the basic variables that need to be taken into account in the calculation of transport or gathering systems. In the daily operation of gas gathering and transport networks, the available composition measured by online systems is reduced. In the usual composition a pseudo-component called C6+ (or C7+) is used. If this component is defined from the complete chromatograph analysis of gas, the properties are established through a lumping procedure. Online chromatographic analysis is done on a small group of basic components, usually for heavy components by introducing a pseudo-component, in this paper called C6+. In this paper we will show how to determine the properties of the pseudo-component according to the measured density of the mixture and its dynamics through the network. Generally, transport networks operators are interested in operating them so as to maximize the benefit and reduce any penalties. For this they have SCADA systems, which provide information on transport parameters and gas quality at the monitored points. The overall picture of the network and its short and medium-term evolution is achieved with a powerful simulator. Managing the gas quality from the entry points to the exit points must be made dynamically by the simulator. In this paper we will present results obtained with the ADMODUNET simulator produced by NetGas R&D based on the company’s agreement.

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19

Redchyts, D. O., and S. V. Moiseienko. "Numerical simulation of unsteady flows of cold plasma during plasma actuator operation." Kosmìčna nauka ì tehnologìâ 27, no. 1 (2021): 85–96. http://dx.doi.org/10.15407/knit2021.01.085.

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The numerical simulation of unsteady flows of cold plasma is considered in this article. A low-temperature non-equilibrium ideal plasma is formed when the plasma actuator interacts with the air. The mathematical model has been developed to describe the behavior of low-temperature plasma. It is based on non-stationary equations describing the dynamics of charged particles and plasma electrodynamics equations. The 14 types of particles: metastable and excited nitrogen and oxygen atoms, positive and negative ions, electrons and atomic oxygen are considered. Volumetric and surface chemical reactions describing processes in a barrier discharge that occur above the dielectric surface are considered. For non-stationary equations of plasma dynamics, an implicit numerical algorithm with pseudo-time iteration has been developed, which is based on a finite-volume approach. The equation for the electrostatic potential with sources was solved using the generalized minimal residual method with incomplete LU preconditioning. In non-stationary equations for the density of plasma particles, the drift derivatives were approximated using the TVD scheme with the MinMod limiter function. The derivatives in the equation for the electric potential were calculated using finite-volume relations taking into account the upwind approximation of the concentration of charged plasma particles. The numerical results of the generation, propagation and destruction of a streamer during a dielectric barrier discharge are obtained. The unsteady plasma characteristics in the region above the dielectric surface are analyzed, including the distribution of the particles density, electric potential and the Lorentz force components. The results of numerical simulation of unsteady flows of low-temperature plasma are in good agreement with the available experimental data.

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20

Gorbunov, Michael E., Estel Cardellach, and Kent B. Lauritsen. "Reflected ray retrieval from radio occultation data using radio holographic filtering of wave fields in ray space." Atmospheric Measurement Techniques 11, no. 2 (March 1, 2018): 1181–91. http://dx.doi.org/10.5194/amt-11-1181-2018.

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Abstract. Linear and non-linear representations of wave fields constitute the basis of modern algorithms for analysis of radio occultation (RO) data. Linear representations are implemented by Fourier Integral Operators, which allow for high-resolution retrieval of bending angles. Non-linear representations include Wigner Distribution Function (WDF), which equals the pseudo-density of energy in the ray space. Representations allow for filtering wave fields by suppressing some areas of the ray space and mapping the field back from the transformed space to the initial one. We apply this technique to the retrieval of reflected rays from RO observations. The use of reflected rays may increase the accuracy of the retrieval of the atmospheric refractivity. Reflected rays can be identified by the visual inspection of WDF or spectrogram plots. Numerous examples from COSMIC data indicate that reflections are mostly observed over oceans or snow, in particular over Antarctica. We introduce the reflection index that characterizes the relative intensity of the reflected ray with respect to the direct ray. The index allows for the automatic identification of events with reflections. We use the radio holographic estimate of the errors of the retrieved bending angle profiles of reflected rays. A comparison of indices evaluated for a large base of events including the visual identification of reflections indicated a good agreement with our definition of reflection index.

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21

ten Kroode, Fons. "An omnidirectional seismic image extension." Inverse Problems, January 12, 2023. http://dx.doi.org/10.1088/1361-6420/acb285.

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Abstract This paper introduces an operator, which extends the Born operator for the linearized variable density acoustic wave equation. Inspired by angle dependent scattering, I will define it as an operator acting on distributions depending on space and angle coordinates. I will show that it can be written as a weighted integral of space-shift extended operators associated to arbitrary directions, after a suitable coordinate transform. I will also formulate conditions under which its normal operator is a pseudo-differential operator. These will be seen to be less restrictive than the ones imposed on horizontal space-shift extended operators in the sense that they allow diving wave paths.

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22

Chergui, Djamila, Ahcene Merad, and Sandra Pinelas. "Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions." Analysis, October 26, 2022. http://dx.doi.org/10.1515/anly-2021-0016.

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Abstract In this paper, we prove the existence and uniqueness of Caputo time fractional pseudo-hyperbolic equations of higher order with purely nonlocal conditions of integral type. We use an a priori estimate method; the so-called energy inequalities method, based on some functional analysis tools, is developed for a Caputo time fractional of 2 ⁢ m {2m} -th and ( 2 ⁢ m + 1 ) {(2m+1)} -th order and the density of the range of the operator generated by the considered problem. Using the Laplace transform and homotopy perturbation, we find a semi-analytical solution. Finally, we give some examples for illustration.

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23

Pali, Nefton. "The Soliton-Ricci Flow with variable volume forms." Complex Manifolds 3, no. 1 (January 17, 2016). http://dx.doi.org/10.1515/coma-2016-0003.

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AbstractWe introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation. This gauge is generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times. It represents the gradient flow of Perelman’s W functional with respect to a pseudo-Riemannian structure over the space of metrics and normalized positive volume forms. We obtain an expression of the Hessian of the W functional with respect to such structure. Our expression shows the elliptic nature of this operator in the orthogonal directions to the orbits obtained by the action of the group of diffeomorphism. In the case that initial data is Kähler, the Soliton-Ricci flow over a Fano manifold preserves the Kähler condition and the symplectic form. Over a Fano manifold, the space of tamed complex structures embeds naturally, via the Chern-Ricci map, into the space of metrics and normalized positive volume forms. Over such space the pseudo-Riemannian structure restricts to a Riemannian one. We perform a study of the sign of the restriction of the Hessian of the W functional over such space. This allows us to obtain a finite dimensional reduction of the stability problem for Kähler-Ricci solitons. This reduction represents the solution of this well known problem. A less precise and less geometric version of this result has been obtained recently by the author in [28].

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Wang, Yueya, Xiaoming Shi, Lili Lei, and Jimmy Chi-Hung Fung. "Deep Learning Augmented Data Assimilation: Reconstructing Missing Information With Convolutional Autoencoders." Monthly Weather Review, April 26, 2022. http://dx.doi.org/10.1175/mwr-d-21-0288.1.

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Abstract Remote sensing data play a critical role in improving numerical weather prediction (NWP). However, the physical principles of radiation dictate that data voids frequently exist in physical space (e.g., sub-cloud area for satellite infrared radiance or no-precipitation region for radar reflectivity). Such data gaps impair the accuracy of initial conditions derived from data assimilation (DA), which has a negative impact on NWP. We use the barotropic vorticity equation to demonstrate the potential of deep learning augmented data assimilation (DDA), which involves reconstructing spatially complete pseudo-observation fields from incomplete observations and using them for DA. By training a convolutional autoencoder (CAE) with a long simulation at a coarse “forecast” resolution (T63), we obtained a deep-learning approximation of the “reconstruction operator,” which maps spatially incomplete observations to a model state with full spatial coverage and resolution. The CAE was applied to an incomplete stream function observation (∼30% missing) from a high-resolution benchmark simulation and demonstrated satisfactory reconstruction performance, even when only very sparse (1/16 of T63 grid density) observations were used as input. When only spatially incomplete observations are used, the analysis fields obtained from Ensemble Square Root Filter (EnSRF) assimilation exhibit significant error. However, in DDA, when EnSRF takes in the combined data from the incomplete observations and CAE reconstruction, analysis error reduces significantly. Such gains are more pronounced with sparse observation and small ensemble size because the DDA analysis is much less sensitive to observation density and ensemble size than the conventional DA analysis, which is based solely on incomplete observations.

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25

Wang, Yueya, Xiaoming Shi, Lili Lei, and Jimmy Chi-Hung Fung. "Deep Learning Augmented Data Assimilation: Reconstructing Missing Information With Convolutional Autoencoders." Monthly Weather Review, April 26, 2022. http://dx.doi.org/10.1175/mwr-d-21-0288.1.

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Abstract Remote sensing data play a critical role in improving numerical weather prediction (NWP). However, the physical principles of radiation dictate that data voids frequently exist in physical space (e.g., sub-cloud area for satellite infrared radiance or no-precipitation region for radar reflectivity). Such data gaps impair the accuracy of initial conditions derived from data assimilation (DA), which has a negative impact on NWP. We use the barotropic vorticity equation to demonstrate the potential of deep learning augmented data assimilation (DDA), which involves reconstructing spatially complete pseudo-observation fields from incomplete observations and using them for DA. By training a convolutional autoencoder (CAE) with a long simulation at a coarse “forecast” resolution (T63), we obtained a deep-learning approximation of the “reconstruction operator,” which maps spatially incomplete observations to a model state with full spatial coverage and resolution. The CAE was applied to an incomplete stream function observation (∼30% missing) from a high-resolution benchmark simulation and demonstrated satisfactory reconstruction performance, even when only very sparse (1/16 of T63 grid density) observations were used as input. When only spatially incomplete observations are used, the analysis fields obtained from Ensemble Square Root Filter (EnSRF) assimilation exhibit significant error. However, in DDA, when EnSRF takes in the combined data from the incomplete observations and CAE reconstruction, analysis error reduces significantly. Such gains are more pronounced with sparse observation and small ensemble size because the DDA analysis is much less sensitive to observation density and ensemble size than the conventional DA analysis, which is based solely on incomplete observations.

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26

Marletto, Chiara, Vlatko Vedral, Salvatore Virzì, Alessio Avella, Fabrizio Piacentini, Marco Gramegna, Ivo Pietro Degiovanni, and Marco Genovese. "Temporal teleportation with pseudo-density operators: How dynamics emerges from temporal entanglement." Science Advances 7, no. 38 (September 17, 2021). http://dx.doi.org/10.1126/sciadv.abe4742.

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27

Amoretti, Andrea, Daniel Areán, Daniel K. Brattan, and Nicodemo Magnoli. "Hydrodynamic magneto-transport in charge density wave states." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)027.

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Abstract In this paper we study the dynamical properties of charged systems immersed in an external magnetic field and perturbed by a set of scalar operators breaking translations either spontaneously or pseudo-spontaneously. By combining hydrodynamic and quantum field theory arguments we provide analytic expressions for all the hydrodynamic transport coefficients relevant for the diffusive regime in terms of thermodynamic quantities and DC thermo-electric conductivities. This includes the momentum dissipation rate. We shed light on the role of the momentum dissipation rate in the transition between the pseudo-spontaneous and the purely explicit regimes in this class of systems. Finally, we clarify several relations between the hydrodynamic transport coefficients which have been observed in the holographic literature of charge density wave models.

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28

Sobolev, Alexander. "Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one." Revista Matemática Iberoamericana, 2006, 55–92. http://dx.doi.org/10.4171/rmi/449.

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29

Marletto, Chiara, Vlatko Vedral, Salvatore Virzì, Enrico Rebufello, Alessio Avella, Fabrizio Piacentini, Marco Gramegna, Ivo Pietro Degiovanni, and Marco Genovese. "Theoretical description and experimental simulation of quantum entanglement near open time-like curves via pseudo-density operators." Nature Communications 10, no. 1 (January 14, 2019). http://dx.doi.org/10.1038/s41467-018-08100-1.

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30

Gutiérrez-García, Ismael, and Anselmo Torresblanca-Badillo. "Probability density functions and the dynamics of complex systems associated to some classes of non-archimedean pseudo-differential operators." Journal of Pseudo-Differential Operators and Applications 12, no. 1 (February 11, 2021). http://dx.doi.org/10.1007/s11868-021-00381-3.

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31

Camilo, Giancarlo, Thiago Fleury, Máté Lencsés, Stefano Negro, and Alexander Zamolodchikov. "On factorizable S-matrices, generalized TTbar, and the Hagedorn transition." Journal of High Energy Physics 2021, no. 10 (October 2021). http://dx.doi.org/10.1007/jhep10(2021)062.

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Abstract We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S-matrix of an integrable QFT deformed by CDD factors. Such S-matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E(R) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R. We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S-matrix by CDD factors with two elementary poles and regular high energy asymptotics — the “2CDD model”. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R*, which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the “turning point” R* (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E(R) is qualitatively the same as the one for standard TTbar deformations of local QFT.

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