Article
Quantum Science & Technology
Henrik Wilming
Summary: This short note discusses a property of quantum states and density matrices. It states that if a density matrix ρ has a smaller entropy than ρ0, then the tensor product of sufficiently many copies of ρ can approximate a quantum state that is very close to the tensor product of the corresponding number of copies of ρ0. Additionally, if the rank of ρ is smaller than the rank of ρ0, then the tensor product of n copies of ρ can dominate a state with identical single-body marginals as ρ0 but allowing for arbitrary correlations.
Article
Astronomy & Astrophysics
Yuri Makeenko
Summary: This article investigates the two-dimensional four-derivative conformal theory derived from the Nambu-Goto string by path-integration. By using the method of singular products, the author demonstrates that the one-loop approximation provides an exact solution. The solution can be conveniently described using minimal models, where the central charge c in the Kac spectrum depends on the parameters of the four-derivative action. This relation is nonlinear, allowing the mapping of the domain of physical parameters to c < 1, bypassing the KPZ barrier of the Liouville action.
Article
Multidisciplinary Sciences
Aurelien Grabsch, Alexis Poncet, Pierre Rizkallah, Pierre Illien, Olivier Benichou
Summary: Single-file transport is a fundamental model for tracer subdiffusion observed in narrow channels. Despite previous difficulties in solving the equations involved, we have successfully broken the hierarchy and obtained a closed exact equation for the bath-tracer correlations in the symmetric exclusion process. Furthermore, this equation has been proven to be a useful tool for interacting particle systems, demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.
Article
Physics, Multidisciplinary
Yuan Miao
Summary: The study presents an exact solution to the asymptotic Bethe equation of weakly anisotropic Heisenberg spin chain, describing low-energy excitations above the ferromagnetic ground state with a fixed magnetization and closely related to generalised Jacobi polynomial. It is equivalent to a generalised Stieltjes problem and in the continuous limit, becomes a Riemann-Hilbert problem closely related to the finite-gap solutions of the classical Landau-Lifshitz field theory.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Physics, Multidisciplinary
R. Saleem, Iqra Shahid, Mudassar Sabir
Summary: This paper studies warm inflation in a modified cosmological scenario within Rastall gravity. The standard Friedmann equations are modified using Tsallis and Barrow holographic dark energy entropies. The exact solutions including the inflaton field, potential required for inflation, and the scale factor are obtained under the slow-roll approximation. The theoretical predictions are compared with observational data, and the results are consistent and interesting.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Multidisciplinary Sciences
Long-Sheng Liu, Qing-Wen Wang, Jiang-Feng Chen, Yu-Zhu Xie
Summary: In this paper, the solvability conditions and the general solution formula for a Sylvester-like quaternion matrix equation are established. A sufficient and necessary conditions for a system of quaternion matrix equations to be consistent are also given, along with an expression of the general solution when the system is solvable. An algorithm and an example are presented to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.
Article
Thermodynamics
Eugenya V. Makoveeva, Dmitri V. Alexandrov
Summary: This study focuses on the concluding stage of a phase transformation and examines the particle coagulation and Ostwald ripening processes. An exact solution to the non-stationary integrodifferential kinetic equation is derived, providing relationships between the particle-volume distribution function, time, number of particles, volume of the condensed phase, average particle radius, and liquid supersaturation. The study also compares the particle-volume distribution function and average radius of particles in cases of constant and averaged collision-frequency functions for different coagulation mechanisms, such as shear coagulation and coagulation under gravity.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Mathematics
Jim Agler, John E. Mccarthy
Summary: Research shows that if the minimum entropy of a polynomial with roots on the unit circle is achieved by polynomials with equally spaced roots, and a generic hypothesis about extremum nature is satisfied, then the Krzyz conjecture on the maximum modulus of Taylor coefficients of a holomorphic function is true when mapping the disk to the punctured disk.
JOURNAL D ANALYSE MATHEMATIQUE
(2021)
Article
Quantum Science & Technology
Honghao Fu
Summary: This study demonstrates the use of correlations to self-test maximally entangled states, with the size of the correlation dependent on the smallest generator of the multiplicative group. The results indicate that constant-sized correlations are sufficient for self-testing maximally entangled states with unbounded local dimension.
Article
Astronomy & Astrophysics
Oliver H. E. Philcox, Jeremy Goodman, Zachary Slepian
Summary: Kepler's equation is a fundamental relation in celestial mechanics that links mean anomaly, eccentric anomaly, and eccentricity. Conventional methods cannot directly solve for eccentric anomaly, so approximate methods have been developed. In this study, an explicit integral solution is presented, which has been found to be highly accurate and efficient in numerical computations for arbitrary eccentricities. The C++ implementation of this method outperforms traditional root-finding and series approaches by more than two times.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2021)
Article
Economics
Matias Alvo, Gustavo Angulo, Mathias A. Klapp
Summary: The study focuses on efficiently planning a bus dispatch operation within a public transport terminal with a mixed fleet and limited chargers, modeling the problem as an extension of the Vehicle Scheduling Problem and using a Benders' type decomposition approach to solve it. Feasibility cuts dynamically injected into the branch-and-bound tree help remove infeasible bus charging operations, with computational experiments showing the effectiveness of the approach over a single-stage model. Insights for planners include the marginal benefit of additional chargers or electric buses and the value added by a mixed fleet compared to a pure electric one.
TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW
(2021)
Article
Multidisciplinary Sciences
Yaroslav Erisov, Sergei Surudin, Fedor Grechnikov, Elena Lyamina
Summary: An axisymmetric boundary value problem for the flow of an incompressible material obeying Hill's orthotropic quadratic yield criterion and its associated flow rule is formulated and solved, with numerical techniques only necessary for evaluating ordinary integrals. The solution may exhibit singular behavior near the friction surface, with some strain rate components and plastic work rate approaching infinity. The effect of plastic anisotropy on the solution's behavior is discussed in detail.
Article
Mechanics
Langston L. Williams, Joseph Majdalani
Summary: This study focuses on the development of an internal potential flow solution in a hemispherically bounded cyclonic chamber using the Bragg-Hawthorne equation. The analysis results in deductions of various flow properties and identification of two different types of mantles based on the overarching spherical geometry.
Article
Computer Science, Interdisciplinary Applications
Zhi Yong Ai, Gan Lin Gu, Yong Zhi Zhao, Jun Jie Yang
Summary: This paper investigates the response of multilayered transversely isotropic poroelastic media under vertical rectangular moving loads using the extended precise integration method (PIM). The study derives governing equations, applies Fourier expansion and integral transform techniques, formulates solutions for multilayered media, and analyzes the impacts of various factors on dynamic response.
COMPUTERS AND GEOTECHNICS
(2021)
Article
Management
Stefano Nasini, Rabia Nessah
Summary: A new approach is proposed for deriving a lower bound for minimizing completion time variance in single machine scheduling problem, outperforming existing bounds and having an average difference of less than 0.01% from the optimal solution.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2021)