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1. Stability of Fluid Flow through a Channel with Flexible Walls

   https://doi.org/10.1155/2021/8825677  

   Shubov, Marianna A.; Edwards, Madeline M. (March 2021, International Journal of Mathematics and Mathematical Sciences)

   Solovjovs, Sergejs (Ed.)

   In the present paper, we summarize the results of the research devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls. The walls of the vessel are subject to traveling waves. Experimental data show that the energy of the flowing fluid can be transferred and consumed by the structure (the walls), inducing “traveling wave flutter.” The problem of stability of fluid-structure interaction splits into two parts: (a) stability of fluid flow in the channel with harmonically moving walls and (b) stability of solid structure participating in the energy exchange with the flow. Stability of fluid flow, the main focus of the research, is obtained by solving the initial boundary value problem for the stream function. The main findings of the paper are the following: (i) rigorous formulation of the initial boundary problem for the stream function, ψ x , y , t , induced by the fluid-structure interaction model, which takes into account the axisymmetric pattern of the flow and “no-slip” condition near the channel walls; (ii) application of a double integral transformation (the Fourier transformation and Laplace transformation) to both the equation and boundary and initial conditions, which reduces the original partial differential equation to a parameter-dependent ordinary differential equation; (iii) derivation of the explicit formula for the Fourier transform of the stream function, ψ ˜ k , y , t ; (iv) evaluation of the inverse Fourier transform of ψ ˜ k , y , t and proving that reconstruction of ψ x , y , t can be obtained through a limiting process in the complex k -plane, which allows us to use the Residue theorem and represent the solution in the form of an infinite series of residues. The result of this research is an analytical solution describing blood flowing through a channel with flexible walls that are being perturbed in the form of a traveling wave. 

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2. Non-perturbative Solution of the 1d Schrödinger Equation Describing Photoemission from a Sommerfeld Model Metal by an Oscillating Field

   https://doi.org/10.1007/s00220-023-04771-0  

   Costin, Ovidiu; Costin, Rodica; Jauslin, Ian; Lebowitz, Joel L (September 2023, Communications in Mathematical Physics)

   Springer (Ed.)

   We analyze non-perturbatively the one-dimensional Schrödinger equation describing the emission of electrons from a model metal surface by a classical oscillating electric field. Placing the metal in the half-space x 0, the Schrödinger equation of the system is i∂t ψ = − 2 1 ∂x 2 ψ + (x)(U − E x cos ωt)ψ, t > 0, x ∈ R, where (x) is the Heaviside function and U > 0 is the effective confining potential (we choose units so that m = e = = 1). The amplitude E of the external electric field and the frequency ω are arbitrary. We prove existence and uniqueness of classical solutions of the Schrödinger equation for general initial conditions ψ(x, 0) = f (x), x ∈ R. When 2the initial condition is in L the evolution is unitary and the wave function goes to zero at any fixed x as t → ∞. To show this we prove a RAGE type theorem and show that the discrete spectrum of the quasienergy operator is empty. To obtain positive electron current we consider non-L 2 initial conditions containing an incoming beam from the left. The beam is partially reflected and partially transmitted for all t > 0. For these initial conditions we show that the solution approaches in the large t limit a periodic state that satisfies an infinite set of equations formally derived, under the assumption that the solution is periodic by Faisal et al. (Phys Rev A 72:023412, 2005). Due to a number of pathological features of the Hamiltonian (among which unboundedness in the physical as well as the spatial Fourier domain) the existing methods to prove such results do not apply, and we introduce new, more general ones. The actual solution exhibits a very complex behavior, as seen both analytically and numerically. It shows a steep increase in the current as the frequency passes a threshold value ω = ωc , with ωc depending on the strength of the electric field. For small E, ωc represents the threshold in the classical photoelectric effect, as described by Einstein’s theory. 

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3. Observations of X-rays from Laboratory Sparks in Air at Atmospheric Pressure under Negative Switching Impulse Voltages

   https://doi.org/10.3390/atmos10040169  

   Rahman, Mahbubur; Hettiarachchi, Pasan; Cooray, Vernon; Dwyer, Joseph; Rakov, Vladimir; Rassoul, Hamid (April 2019, Atmosphere)

   We present observations of X-rays from laboratory sparks created in the air at atmospheric pressure by applying an impulse voltage with long (250 µs) rise-time. X-ray production in 35 and 46 cm gaps for three different electrode configurations was studied. The results demonstrate, for the first time, the production of X-rays in gaps subjected to switching impulses. The low rate of rise of the voltage in switching impulses does not significantly reduce the production of X-rays. Additionally, the timing of the X-ray occurrence suggests the possibility that the mechanism of X-ray production by sparks is related to the collision of streamers of opposite polarity. 

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4. QMol-grid : A MATLAB package for quantum-mechanical simulations in atomic and molecular systems

   https://doi.org/10.1016/j.softx.2024.101968  

   Mauger, François; Chandre, Cristel (December 2024, SoftwareX)

   The QMol-grid package provides a suite of routines for performing quantum-mechanical simulations in atomic and molecular systems, currently implemented in one spatial dimension. It supports ground- and excited-state calculations for the Schrödinger equation, density-functional theory, and Hartree–Fock levels of theory as well as propagators for field-free and field-driven time-dependent Schrödinger equation (TDSE) and real-time time-dependent density-functional theory (TDDFT), using symplectic-split schemes. The package is written using MATLAB’s object-oriented features and handle classes. It is designed to facilitate access to the wave function(s) (TDSE) and the Kohn–Sham orbitals (TDDFT) within MATLAB’s environment. 

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5. Ground state wave function overlap in superconductors and superfluids

   https://doi.org/10.1515/zna-2020-0277  

   Hertzberg, Mark P.; Jain, Mudit (November 2020, Zeitschrift für Naturforschung A)

   null (Ed.)

   Abstract In order to elucidate the quantum ground state structure of nonrelativistic condensates, we explicitly construct the ground state wave function for multiple species of bosons, describing either superconductivity or superfluidity. Since each field Ψ j carries a phase θ j and the Lagrangian is invariant under rotations θ j  →  θ j  +  α j for independent α j , one can investigate the corresponding wave function overlap between a pair of ground states $$\langle G\vert {G}^{\prime }\rangle $$ differing by these phases. We operate in the infinite volume limit and use a particular prescription to define these states by utilizing the position space kernel and regulating the UV modes. We show that this overlap vanishes for most pairs of rotations, including θ j  →  θ j  +  m j   ϵ , where m j is the mass of each species, while it is unchanged under the transformation θ j  →  θ j  +  q j   ϵ , where q j is the charge of each species. We explain that this is consistent with the distinction between a superfluid, in which there is a nontrivial conserved number, and the superconductor, in which the electric field and conserved charge is screened, while it is compatible with a nonzero order parameter in both cases. Moreover, we find that this bulk ground state wave function overlap directly reflects the Goldstone boson structure of the effective theory and provides a useful diagnostic of its physical phase. 

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