The sound generated by a square cylinder with a splitter plate at low Reynolds number

The generation of aerodynamic sound by the interaction of flow at a Reynolds number of 150 and a Mach number of 0.2 with a rigid square cylinder attached to a rigid thin flat plate is numerically investigated. When the length of the plate is varied from L=0.5D to 6D, where D is the side length of the square cylinder, the results can be grouped into three distinct regimes. For the first regime (L?D), the sound levels decrease with increasing plate length. A 3 dB sound reduction is obtained when the length of the plate is D. For the second regime (1.25D?L?4.75D), the sound levels increase with increasing plate length. For the third regime (5D?L?6D), the sound levels decrease as the length of the plate increases but the levels are higher than for the other regimes. Results also show that the lift fluctuation is the dominant sound source. These acoustic results can be explained in terms of the fluid mechanics occurring in the near wake of the cylinder.     

A dynamical formulation of one-dimensional scattering theory and its applications in optics

We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrödinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility.     

The Smart 2-(2-Fluorobenzoyl)-N-(2-Methoxyphenyl)Hydrazinecarbothioamide Functionalized as Ni(II) Sensor in Micromolar Concentration Level and its Application in Live Cell Imaging

In recent years, fluorescent probes for the detection of environmentally and biologically important metal cations have received extensive attention for designing and development of fluorescent chemosensors. Herein, we report the photophysical results of 2-(2-fluorobenzoyl)-N-(2-methoxyphenyl) hydrazinecarbothioamide (4) functionalized as Ni (II) sensor in micromolar concentration level. Through fluorescence titration at 488 nm, we were confirmed that ligand 4 showed the remarkable emission by complexation between 4 and Ni (II) while it appeared no emission in case of the competitive ions (Cr³⁺, Fe²⁺, Co²⁺, Ba²⁺, Cu²⁺, Ca²⁺, Na⁺, K⁺, Cu⁺, Cs⁺). Furthermore, ligand 4 exhibited no toxicity with precise cell permeability toward normal living cells using L929 cell lines in bio imaging experiment investigated through confocal fluorescence microscope. The non-toxic behavior of ligand 4 (assessed by MTT assay) and its ability to track the Ni²⁺ in living cells suggest its possibility to use in biological system as nickel sensor.

Observation of long spin-relaxation times in bilayer graphene at room temperature

We report on the first systematic study of spin transport in bilayer graphene (BLG) as a function of mobility, minimum conductivity, charge density, and temperature. The spin-relaxation time τ(s) scales inversely with the mobility μ of BLG samples both at room temperature (RT) and at low temperature (LT). This indicates the importance of D'yakonov-Perel' spin scattering in BLG. Spin-relaxation times of up to 2 ns at RT are observed in samples with the lowest mobility. These times are an order of magnitude longer than any values previously reported for single-layer graphene (SLG). We discuss the role of intrinsic and extrinsic factors that could lead to the dominance of D'yakonov-Perel' spin scattering in BLG. In comparison to SLG, significant changes in the carrier density dependence of τ(s) are observed as a function of temperature.     

$${f(\mathcal R)}$$ quantum cosmology

We have quantized a flat cosmological model in the context of the metric models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.     

Optimal control theory of an age-structured coronavirus disease model and the dynamical analysis of the underlying ordinary differential equation model having constant parameters

This paper addresses the dynamics of COVID-19 using the approach of age-structured modeling. A particular case of the model is presented by taking into account age-free parameters. The sub-model consisting of ordinary differential equations (ODEs) is investigated for possible equilibria, and qualitative aspects of the model are rigorously presented. In order to control the spread of the disease, we considered two age- and time-dependent non-pharmaceutical control measures in the age-structured model, and an optimal control problem using a general maximum principle of Pontryagin type is achieved. Finally, sample simulations are plotted which support our theoretical work.     

Hartree-Fock energies of D and D doubly excited states of the lithium isoelectronic sequence

Hartree-Fock energies of 1s2snd ⁴D, 1s2pnp ⁴D and 1s2pnd ⁴D⁰, n=3–5 of lithium isoelectronic sequence from Li to Ne⁺⁷ are reported. These results in conjunction with the energy of the lowest ⁴P and ⁴P⁰ states of the lithium isoelectronic sequence as calculated by Holoien and Geltman, are used to check some proposed assignments of lines obtained in beamfoil spectroscopy of Be(II), C(IV) and N(V).     

On some problems of Petrich concerning Bruck and Reilly semigroups

For an inverse semigroupS with its idempotents dually well-ordered, we prove thatS is isomorphic to the semigroup of all one-to-one partial right translations ofS. Also, we prove for a Bruck semigroupS=B(T, α) thatS isE-unitary if and only ifT isE-unitary and α is an idempotent pure homomorphism. Moreover, we characterize allE-unitary covers ofB(T, α), whereT is a finite chain of groups.     

Spectral theory and L∞-time decay estimates for Klein–Gordon equations on two half axes with transmission: The tunnel effect

Consider two copies N₁, N₂ of the interval [0, ∞]. Consider Klein-Gordon equations with (different) constant coefficients on ? × N_j ( = time × space). Assume the coincidence of the values of the solution at the boundary points of the N_j for all times and a transmission condition relating its first (one-sided) space derivatives at these points. Under a symmetry condition, we extend the spatial part of the equation and the transmission conditions to a self-adjoint operator (by Friedrichs extension) and reformulate our problem in terms of an abstract wave equation in a suitable Hilbert space. We derive an expansion of the solution in generalized eigenfunctions of this self-adjoint extension and show, that the L^∞-norms (in space) of the solution and its first k space derivatives at the time t decay for t → ∞ at least as const. t^¼, if the initial conditions satisfy a compatibility condition of order k derived in this paper. The loss of decay rate in comparison with the full line case (const. t^?½, cf. [28]) is caused by the tunnel effect. Further we show that an abstract wave equation in a Hilbert space with a Friedrichs extension as spatial part can always be derived from a stationarity principle for an associated action-type functional. This yields a physical legitimation of our model by the principle of stationary action and moreover a criterion for the physical interpretability of all models created by the linear interaction concept [4, 6, 8, 10], in particular for the coupling of media of different dimension (alternative to [13, 16] for similar models).