Restricted Percolation Critical Exponents in High Dimensions

Despite great progress in the study of critical percolation on ℤ^d for d large, properties of critical clusters in high-dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions. Closely related models such as critical branching random walk give natural conjectures for the value of the relevant high-dimensional critical exponents; see in particular the conjecture by Kozma-Nachmias that the probability that 0 and (n, n, n, …) are connected within [−n, n]^d scales as n^{−2 − 2d} . In this paper, we study the properties of critical clusters in high-dimensional half-spaces and boxes. In half-spaces, we show that the probability of an open connection (“arm”) from 0 to the boundary of a sidelength n box scales as n⁻³ . We also find the scaling of the half-space two-point function (the probability of an open connection between two vertices) and the tail of the cluster size distribution. In boxes, we obtain the scaling of the two-point function between vertices which are any macroscopic distance away from the boundary. Our argument involves a new application of the “mass transport" principle which we expect will be useful to obtain quantitative estimates for a range of other problems. © 2020 Wiley Periodicals LLC     

Features of dual fluorescence of 1, 2, 3, 4- tetrahydroisoquinoline

In polar and nonpolar solvents, tetrahydroisoquinoline emits S₂ (ππ¹) → S₀ and S₁ (ππ¹) → S₀ dual fluorescence and T₁ (ππ¹) → S₀ phosphorescence on S₂ (ππ¹) ← S₀ excitation. When excited by S₁ (ππ¹) ← S₀ the molecule yields S₁ (ππ¹) → S₀ fluorescence and T₁ (ππ¹) → S₀ phosphorescence in nonpolar solvent but only fluorescence in polar solvents. Probable participation of intermediate S₁ (nπ¹), T₁(nπ¹) states in intersystem crossing and internal conversion processes and its significance in interpreting the results are discussed.     

A new representation of the heavy ion Coulomb potential

The Coulomb potential between two heavy ions at their interpretation condition has been represented in terms of two point charges with reduced effective charge, dependent on overlap volume. This representation enables visualization of the dynamic development of the deformations of the colliding nuclei as a function of the degree of overlap. The potential has been compared with well known potentials for heavy-ion collisions. This Coulomb potential gave good agreement in reproducing excitation functions for fusion for a large number of heavy-ion systems.     

Scattering of light by a periodic structure in the presence of randomness IV. Limit of detection by curve fitting

In the context of scattering of light, we determine the extent of randomness within which a hidden periodic part can still be detected. The detection is carried out using a technique called the extended matched filtering, first introduced by us in this context. The earlier prediction, before our technique was introduced, had placed the limit of detection, by intensity measurements alone, at (r ₀/Λ) ∼ 0.33, where r₀ is the coherence length of light for scattering by the rough part of the surface and Λ is the wavelength of the periodic part of the surface. In our earlier works we have shown that by intensity measurements alone, the limit of detection can be taken to a much lower value of (r ₀/Λ), when the extended matched filtering method is employed. In this paper we follow the extended matched filtering method, and try to reach the lowest possible value of detection in (r ₀/Λ) by fitting the data to a polynomial. It is concluded by our numerical work that the lowest possible limit for detection from intensity measurements alone is (r ₀/Λ) = 0.11.     

Generation of 6.8–7.7 µm radiation in lithium iodate

Generation of infrared radiation in ts-infrared transmission window (6.8–7.7 µm) is reported for the first time by non-collinear difference-frequency mixing of the Nd: YAG second harmonic and the same-pumped dye (Rh-610) laser radiation in a lithium-iodate crystal. The spectrum of polythene sheets was run with the generated radiation.     

Homogeneous cosmological model for a Kaluza-Klein-type metric

Cosmological solutions are obtained for a homogeneous, spatially isotropic five-dimensional (5D) Kaluza-Klein-type metric with variable rest mass. The dynamical behavior of the model is studied and a comparison made with the corresponding solution in Einstein's 4D theory. Some important Cosmological parameters are also calculated for this model.     

The Simplest Resonance Capture Problem,Using Harmonic Balance Based Averaging

We study the dynamics of capture into, or escape from, resonance in a strongly nonlinear oscillator with weak damping and forcing, using harmonic balance based averaging (HBBA). This system provides the simplest example of resonance capture that we know of. The HBBA technique, here adapted to tackle nonlinear resonances, provides a harmonic balance assisted approximation to the underlying, asymptotically correct, averaged dynamics. Allowing the harmonic balance approximation makes a variety of systems analytically tractable which might otherwise be intractable. The evolution equations for amplitude and phase of oscillations are derived first. Restricting attention near the primary resonance, the slow flow equations are approximately averaged. The resulting flow transparently shows the stable and unstable primary resonant solutions, as well as the trajectories that get captured into resonance and the ones that escape. Good agreement with numerics is obtained, showing the utility of HBBA near resonance manifolds.     

Investigations on compton scattering: New directions

Although inelastic (Compton) scattering of a photon off a free electron was well understood about 80 years ago, inelastic scattering off bound electrons remains an incompletely understood process. The availability of synchrotron light sources has led a great enhancement in the precision of experimental measurements involving this process. As a result, approximations made in obtaining numerical predictions of physical observables are being reexamined by theorists. In this article, we present a comparison of experimental measurements to theoretical predictions to assess the need for future advances in both experiment and theory.     

C-Field Cosmology in Higher Dimensions

Hoyle and Narlikar's C-field cosmology is extended in the framework of higher dimensional spacetime and a class of exact solutions is obtained. Adjusting the arbitrary constants of integration one can show that our model is amenable to the desirable property of dimensional reduction so that the universe ends up in an effective 4D one. Further with matter creation from the C-field the mass density steadies with time and the usual bigbang singularity is avoided. An alternative mechanism is also suggested which seems to provide matter creation in the 4D spacetime although total matter in the 5D world remains conserved. Quintessence phenomenon and energy conditions are also discussed and it is found that in line with the physical requirements our model admits a solution with a decelerating phase in the early era followed by an accelerated expansion later. Moreover, as the contribution from the C-field is made negligible a class of our solutions reduces to the previously known higher dimensional models in the framework of Einstein's theory.     

Reagenzien

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