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).     

Graphene to graphite; a layer by layer experimental measurements and density function theory calculations of electric conductivity

ABSTRACT

We measured the electric conductivity of large (25?×?50?mm) graphene films as a function of number of layers in the range of 1–20 layers. We also calculated the energy gap for such samples using density function theory. Our results showed a conductivity slightly above that of ITO for monolayer graphene and an exponential decrease as the number of graphene layers increased. Both experimental and simulation results showed a convergence of graphene into graphite at as little as 18–20 layers.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

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).     

Moment Systems Derived from Relativistic Kinetic Equations

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie algebras. We then extend this derivation to the classical case and general families of moments that obey the Galilean invariance are also constructed. It is remarkable that the set of formal classical limits of the so-obtained relativistic moment systems is not identical to the set of classical moments quoted in Ref. 21 and one could use a new physically relevant criterion to derive suitable moment systems in the classical case. Finally, the ultra-relativistic limit is considered.     

Hawking Absorption and Planck Absolute Entropy of Kerr-Newman Black Hole

We find the existence of a quantum thermal effect, “Hawking absorption.” near the inner horizon of the Kerr–Newman black hole. Redefining the entropy, temperature, angular velocity, and electric potential of the black hole, we give a new formulation of the Bekenstein–Smarr formula. The redefined entropy vanishes for absolute zero temperature of the black hole and hence it is interpreted as the Planck absolute entropy of the KN black hole.     

Mid-infrared supercontinuum generation to 4.5 microm in ZBLAN fluoride fibers by nanosecond diode pumping

A mid-infrared supercontinuum (SC) is generated in ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF...) fluoride fibers from amplified nanosecond laser diode pulses with a continuous spectrum from approximately 0.8 microm to beyond 4.5 microm. The SC has an average power of approximately 23 mW, a pump-to-SC power conversion efficiency exceeding 50%, and a spectral power density of approximately -20 dBm/nm over a large fraction of the spectrum. The SC generation is initiated by the breakup of nanosecond laser diode pulses into femtosecond pulses through modulation instability, and the spectrum is then broadened primarily through fiber nonlinearities in approximately 2-7 m lengths of ZBLAN fiber. The SC long-wavelength edge is consistent with the intrinsic ZBLAN material absorption.     

Waveguide electro-optic modulator in fused silica fabricated by femtosecond laser direct writing and thermal poling

An integrated electro-optic waveguide modulator is demonstrated in bulk fused silica. A Mach-Zehnder interferometer waveguide structure is fabricated by direct writing with a femtosecond laser followed by thermal poling. A 20 degrees electro-optic phase shift is achieved at an operating wavelength of 1.55 microm with an applied voltage of 400 V and an interaction length of 25.6 mm, which correspond to an estimated effective electro-optic coefficient of 0.17 pm/V for the TE-polarized mode.     

Anti-proliferative effects of gold nanoparticles functionalized with Semaphorin 3F

The new vessel formations play a vital role in growth and spread of cancer. Current anti-angiogenic therapies, predominantly based on vascular endothelial growth factor (VEGF) inhibition, can inhibit vascular development; however, they are usually ineffective against the primary tumor occurrence. The aim of this study was to assess anti-angiogenic effects of gold nanoparticles (AuNPs) functionalized with Semaphorin (Sema) 3F protein. The polyethylene glycol (PEG)-coated AuNPs were covalently functionalized with Sema 3F and labeled with the TAMRA fluorescent dye. The effect of the NPs on human umbilical vein endothelial cells (HUVECs) is probed in the way of internalization and viability assays. AuNP-Sema 3F bioconjugates showed great endothelial cell uptake. AuNP-Sema 3F bioconjugates reduced VEGF₁₆₅-induced endothelial cell proliferation more effectively than Sema 3F alone, suggesting that the therapeutic effects of Sema 3F can be improved by conjugation to AuNPs. Also, no significant toxicity effect was induced by bioconjugates. This is the first study that reports a covalent binding of full length Sema 3F to NPs. The exogenously administration of Sema 3F, which has both anti-angiogenic and anti-tumoral activity, to tumor vasculature via a carrying platform may not only lead to more effective anti-angiogenic treatment but also may make current approach more applicable in clinical use like drug delivery system.

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Graphical abstract Anti-proliferative effects of gold nanoparticles conjugated with Semaphorin 3F against VEGF₁₆₅-stimulated cell proliferation