Miracle-dz/UniFAR-FTUs huggingface dataset:
Nonspecular effects and entropy change from complex media

The phenomena for which the laws of geometrical optics are invalid in the case of beams are already very well-known. Such effects are known as non-speculars and many works about them already exist in the literature. Classically, the angular and longitudinal displacements are considered the basic non-specular effects, but there are the focal and width changes that, in any sense, are related with the previous ones. The foundation of these non-specular effects are related with the energetic interchanges that take place at the inrerface between two media, and an entropic foundation has been developed recently. From the optical point of view, the non-specular effects have been studied because they are important for guided waves and integrated optics. An experimental verification is more simple in the microwaves region because the range in angular change has a small value (the order of magnitude is 10-3 radians), and the lateral displacement is comparable with the wavelength of the incident radiation. In this work, an impedance method (through the input impedance of the interface) is used to characterize different non-conventional structures: film on a medium with complex refraction index or multilayers with fractal distribution. The characterization of the reflection and transmission from the equivalent interface can be studied; also, very important is the relation between the angular and longitudinal changes with the entropy function for these cases.
Elimination of irradiation point defects in crystalline solids: Sink strengths

The rate theory of irradiation effects in crystalline solids rests on a set of two ordinary differential equations which, for each type of point defect (vacancy and self-interstitial), describe the balance between the production of defects on the one hand and their annihilation on the other. The latter process occurs either by mutual recombination, a bimolecular reaction, or by elimination on point defect sinks, a first-order reaction. The elimination rate is proportional to the defect concentration times the defect diffusion coefficient times a geometrical factor, the "sink strength. " The classical expression of sink strengths is obtained by solving the diffusion equation of point defects in a cell, which contains the sink, and ensuring that the mean value of the defect concentration in the cell equals the concentration in the rate theory. We propose an alternative criterion. Since the amplitude of the irradiation effects of practical relevance is dictated by the partitioning of the defect annihilation between mutual recombination and elimination on sinks, we propose that the value of the sink strength should give the correct value for the latter partitioning. The sink strengths so defined, scaled to their classical value, are evaluated for sink geometries of practical interest and expressed as a function of one dimensionless parameter, which is a function of the irradiation flux and temperature. Depending on the irradiation conditions, the correcting factors for individual sink strengths may be large (several orders of magnitude). When several types of sinks compete, we further impose that the partitioning of the elimination among the various types of sinks has the correct value. The sink strengths, as defined in this work, are additive, at variance with the classical ones. According to our definition, the dislocation bias, which measures the relative difference between the sink strengths of dislocations respectively for interstitials and vacancies, is shown to increase with the strength of neutral sinks around the dislocation. It ranges from zero when the dislocations are the only sinks to several 10 - 1 when the neutral sinks have a strength much larger than that of dislocations. The computation of the correcting factor is presented in such a way that it can be easily incorporated into the rate theory of irradiation effects.
The method of decoupling fields generalized to higher spatial derivatives.

This work studies the spatial derivatives of decoupling fields to strongly coupled forward-backward stochastic differential equations in a Brownian setting. We formally deduce the backward dynamics of the first and higher spatial derivatives. In addition, we study necessary conditions under which singularities in either one of them can occur while moving backwards in time.
Thermodynamic Coupled Modes in the Tropical Atmosphere–Ocean: An Analytical Solution

The present study provides a consistent and unified solution for the two types of thermodynamical coupled modes in the atmosphere-ocean climate system: the tropical meridional mode and the subtropical dipole mode. The solution is derived analytically from a linear model that couples a simple atmosphere to a slab ocean via the wind-evaporation-SST (WES) feedback. For a mean zonal wind, the results show that the wind (hence latent heat flux) anomaly and the SST anomaly differ in phase such that the tropical mode propagates downwind and the subtropical modes propagate upwind, with both modes being damped by the SST-driven component of latent heat flux. Despite the existence of positive WES feedback, the large-scale subtropical modes are always stable, while the tropical mode can become unstable only when the air-sea coupling is strong and the mean wind is easterly. Furthermore, the mean meridional winds break the equatorial symmetry and enable the coupled modes to intensify in the Southern (Northern) Hemisphere for a southerly (northerly) component. For realistic parameter values, these thermodynamical coupled modes have periods and damping time scales in years; hence, they may play important roles in the tropical interannual-to-decadal climate variability.
Metric Compatible or Noncompatible Finsler-Ricci Flows

There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math. Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that there are some models of Finsler gravity and geometric evolution theories with generalized Perelman's functionals, and correspondingly derived non-holonomic Hamilton evolution equations, when metric non-compatible Finsler connections are involved. Following such an approach, we have to consider distortion tensors, uniquely defined by the Finsler metric, from the Cartan and/or the canonical metric compatible connections. We conclude that, in general, it is not possible to elaborate self-consistent models of geometric evolution with arbitrary Finsler metric non-compatible connections.
Memory effect of ZnO nanocrystals embedded in an insulating polyimide layer

The memory effects of ZnO nanoparticles embedded in a polyimide (PI) matrix were investigated. Transmission electron microscopy images and selected area electron diffraction patterns showed that ZnO nanocrystals were created inside the PI layer. Capacitance-voltage (C-V) measurements on Al/PI/nanocrystalline ZnO∕PI∕p-Si structures at 300K showed a metal-insulator-semiconductor behavior with a flatband voltage shift due to the existence of the ZnO nanocrystals, indicative of trapping, storing, and emission in the electrons in the ZnO nanocrystals. Possible electronic structures corresponding to the writing and erasing operations for the Al/PI/nanocrystalline ZnO∕PI∕p-Si device are described on the basis of the C-V results.
A New Version of Huisken's Convergence Theorem for Mean Curvature Flow in Spheres

We prove that if the initial hypersurface of the mean curvature flow in spheres satisfies a sharp pinching condition, then the solution of the flow converges to a round point or a totally geodesic sphere. Our result improves the famous convergence theorem due to Huisken [9]. Moreover, we prove a convergence theorem under the weakly pinching condition. In particular, we obtain a classification theorem for weakly pinched hypersurfaces. It should be emphasized that our pinching condition implies that the Ricci curvature of the initial hypersurface is positive, but does not imply positivity of the sectional curvature.
Finite element modeling of microstructured optical fibers: leaky modes, twisted geometries, and spatial Kerr solitons

Microstructured optical fibers have much more degrees of freedom concerning the geometries and index contrasts than step-index fibers. This richness opens totally new fields of application for fiber optics. The finite element method appears as an extremely versatile tool to compute the propagation modes in such systems as it allows to take into account arbitrary geometries of the cross section and also anisotropic and inhomogeneous (i.e. not only piecewise constant) dielectric permittivities. In this paper, we review some more advanced features: how to compute leaky modes (crucial for the understanding of such kind of fibers) by using perfectly matched layers, how to use helicoidal coordinate systems to determine the influence of a twist on the modes via a two-dimensional model (using equivalent materials), and how to compute spatial solitons in fibers involving Kerr optical medium by taking into account the refractive index inhomogeneities caused by the nonlinearity.
Polynomial spectral collocation method for space fractional advection–diffusion equation

This article discusses the spectral collocation method for numerically solving nonlocal problems: one‐dimensional space fractional advection–diffusion equation; and two‐dimensional linear/nonlinear space fractional advection–diffusion equation. The differentiation matrixes of the left and right Riemann–Liouville and Caputo fractional derivatives are derived for any collocation points within any given bounded interval. Several numerical examples with different boundary conditions are computed to verify the efficiency of the numerical schemes and confirm the exponential convergence; the physical simulations for Lévy–Feller advection–diffusion equation and space fractional Fokker–Planck equation with initial δ‐peak and reflecting boundary conditions are performed; and the eigenvalue distributions of the iterative matrix for a variety of systems are displayed to illustrate the stabilities of the numerical schemes in more general cases. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 514–535, 2014
Scattering amplitude recursion relations in Batalin-Vilkovisky–quantizable theories

Tree-level scattering amplitudes in Yang-Mills theory satisfy a recursion relation due to Berends and Giele which yields e.g., the famous Parke-Taylor formula for maximally helicity violating amplitudes. We show that the origin of this recursion relation becomes clear in the Batalin-Vilkovisky (BV) formalism, which encodes a field theory in an L∞-algebra. The recursion relation is obtained in the transition to a smallest representative in the quasi-isomorphism class of that L∞-algebra, known as a minimal model. In fact, the quasi-isomorphism contains all the information about the scattering theory. As we explain, the computation of such a minimal model is readily performed in any BV quantizable theory, which, in turn, produces recursion relations for its tree-level scattering amplitudes.
Quantum Cohomology of Partial Flag Manifolds and a Residue Formula for Their Intersection Parings

As a generalization of our previous paper [GK], we formulate a residue formula and some simple behaviors of equivariant quantum cohomology applying to compute the quantum cohomology of partial flag manifolds $F_{k_1,\cdots , k_l} $with a try to give a rigorous definition of equivariant quantum cohomology.
On Bias and Rank.

Given a hypersurface $X\subset \mathbb{P}^{N+1}_{\mathbb{C}}$ Dimca gave a proof showing that the cohomologies of X are the same as the projective space in a range determined by the dimension of the singular locus of X. We prove the analog of Dimca's result case when $\mathbb{C}$ is replaced with an algebraically closed field of finite characteristic and singular cohomology is replaced with $\ell$-adic etale cohomology. The Weil conjectures allow relating results about eatle cohomology to counting problems over a finite field. Thus by applying this result, we are able to get a relationship between the algebraic properties of certain polynomials and the size of their zero set.
Black to white hole tunneling: An exact classical solution

We present a metric that describes conventional matter collapsing into a black hole, bouncing and emerging from a white hole, and that satisfies the vacuum Einstein equations everywhere, including in the interior of the black hole and the subsequent white hole, except for a small compact 4d “quantum tunneling” zone. This shows that a black hole can tunnel into a white hole without violating classical general relativity where this can be trusted. We observe that quantum gravity can affect the metric in a region outside the horizon without violating causality because small quantum effects might pile up over time. We study how quantum theory can determines the bouncing time.
The influence of reynolds number on the entry length and pressure drop for laminar pipe flow

A numerical analysis of the laminar flow of a Newtonian fluid in the inlet section of a circular pipe has been carried out for a Reynolds number range of 0 to 500, employing a finite element based CFD code. A new flow phenomenon has been identified at low Reynolds numbers (<50), viz, the existence of a peak in the axial pressure profile at a small distance from the entrance. Existing correlations for the entry length are shown to be insufficient and a new correlation for the entry length is proposed.
The influence of the coefficients of a system of coupled wave equations with fractional damping on its stabilization

In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using frequency domain approach combining with multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the ratio of the wave propagation speeds a, the order of the fractional damping. Indeed, under the equal speed propagation condition, we establish an optimal polynomial energy decay rate. Furthermore, when the wave propagate with different speeds, under some arithmetic conditions on the ratio of the wave propagation speeds, we prove that the energy of our system decays polynomially to zero.
The bilinear–biquadratic model on the complete graph

We study the spin-1 bilinear–biquadratic model on the complete graph of N sites, i.e. when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be rewritten as the linear combination of the quadratic Casimir operators of su(3) and su(2). Using group representation theory, we explicitly diagonalize the Hamiltonian and map out the ground-state phase diagram of the model. Furthermore, the complete energy spectrum, with degeneracies, is obtained analytically for any number of sites.
$K$ -theory of one-dimensional rings via pro-excision

Abstract This paper studies ‘pro-excision’ for the $K$ -theory of one-dimensional, usually semi-local, rings and its various applications. In particular, we prove Geller’s conjecture for equal characteristic rings over a perfect field of finite characteristic, give results towards Geller’s conjecture in mixed characteristic, and we establish various finiteness results for the $K$ -groups of singularities, covering both orders in number fields and singular curves over finite fields.
Molecular synthesis in interstellar clouds: Radiative association reactions of CH/sub 3//sup +/ ions

A survey of laboratory measurements of several binary and collision-stabilized association reactions of CH/sub 3//sup +/ ions is presented. It is shown that the association reactions can proceed via radiative stabilization at gas kinetic rates in interstellar clouds and that the products of the reactions can result in observed interstellar molecules.
Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

The paper by Liu (2010) introduces a method termed the canonical least-squares Monte Carlo (CLM) which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX) puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.
Interim Report IR-09-007 Modelling Household Energy Access in India

Improving access to aﬀordable modern energy is deemed to be a critical factor in improving living standards in the developing world. Particularly rural households in India are rely-ing mostly on traditional biomass to satisfy their basic energy needs with adverse eﬀects on human health through indoor air pollution, but also on land degradation and labor productivity. This study presents a new generic modeling approach with the aim to explore response strategies for energy poverty eradication for India. The modeling approach explores characteristics of fuel consumption of the poorest through explicit representation of the main determinants of urban and rural energy fuel choice, including the eﬀect of income distributions and capital scarcity on energy use as well as traditionally more in-tangible factors such as ”inconvenience costs” or private discount rates. The methodology is applied to explore how diﬀerent policy mechanisms such as fuel subsidies and micro-ﬁnancing can enhance the diﬀusion of clean and aﬀordable energy in India. This draft summarizes preliminary initial results focusing on the attainable transition to clean and modern fuels. As a next step, a sensitivity analysis for the main uncertain parameters and an assessment of the number of households and their exposure is planned. Implications for life-expectancy will be assessed through collaboration with APD.
On Random Knots

In this paper, we consider knotting of Gaussian random polygons in 3-space. A Gaussian random polygon is a piecewise linear circle with n edges in which the length of the edges follows a Gaussian distribution. We prove a continuum version of Kesten's Pattern Theorem for these polygons, and use this to prove that the probability that a Gaussian random polygon of n edges in 3-space is knotted tends to one exponentially rapidly as n tends to infinity. We study the properties of Gaussian random knots, and prove that the entanglement complexity of Gaussian random knots gets arbitrarily large as n tends to infinity. We also prove that almost all Gaussian random knots are chiral.
Projections, multipliers and decomposable maps on noncommutative $\mathrm{L}^p$-spaces

We describe a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $L^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are identical. We also describe precisely the regular norm of several classes of regular multipliers. This includes Schur multipliers, Fourier multipliers on some unimodular locally compact groups which can be approximated by discrete groups in various senses. On the other hand, we show the existence of bounded Fourier multipliers which cannot be approximated by regular operators, on large classes of locally compact groups, including all infinite abelian locally compact groups. We finish by introducing a general procedure for proving positive results on selfadjoint contractively decomposable Fourier multipliers, beyond the amenable case.
Covariant Linearization of elasticity.

In this paper we derive a general linearized theory for first-order continuum dynamics on manifolds with particular application to incompatible elasticity. We adopt a global approach viewing the equations of motion as a $1$-form on the configuration space which is the Banach manifold of $C^1$ time-dependent embeddings of a body manifold $\B$ into a space manifold $\S$. The linearization is done by differentiating the equations 1-form with respect to an affine connection which we construct and study extensively. We provide detailed coordinate computations for the linearized equations of a large class of problems in continuum dynamics on manifolds.
PK-Graph: Partitioned K2-Tree Graph

Graphs are becoming increasingly larger, having millions of vertices and billions (or even trillions) of edges in some cases. As a result, it’s becoming harder and harder to fit the entire graph into the mainmemory of a single machine. This may lead to significant overhead by having to read the graph from secondary storage. Thus causing an impact in the performance of queries and the storage requirements of the system. It is relevant to try to minimize the storage requirements of the graph data without degrading access time and, ideally, even improving it. Current graph storage systems store their graphs in an uncompressed format, either in a shared architecture, leading to high space overhead and the inability to store the entire graph in main memory or a distributed architecture, in which the entire graph is partitioned over a cluster of machines and each machine stores only a fragment of the graph in main memory. Our solution extends a distributed graph processing system to utilize a compressed representation of a graph while still allowing to update the graph data, all while maintaining the same processing performance and ideally even improving it.
On the Size-Ramsey Number of Cycles

Abstract For given graphs G1,…, Gk, the size-Ramsey number $\hat R({G_1}, \ldots ,{G_k})$ is the smallest integer m for which there exists a graph H on m edges such that in every k-edge colouring of H with colours 1,…,k, H contains a monochromatic copy of Gi of colour i for some 1 ≤ i ≤ k. We denote $\hat R({G_1}, \ldots ,{G_k})$ by ${\hat R_k}(G)$ when G1 = ⋯ = Gk = G. Haxell, Kohayakawa and Łuczak showed that the size-Ramsey number of a cycle Cn is linear in n, ${\hat R_k}({C_n}) \le {c_k}n$ for some constant ck. Their proof, however, is based on Szemerédi’s regularity lemma so no specific constant ck is known. In this paper, we give various upper bounds for the size-Ramsey numbers of cycles. We provide an alternative proof of ${\hat R_k}({C_n}) \le {c_k}n$ , avoiding use of the regularity lemma, where ck is exponential and doubly exponential in k, when n is even and odd, respectively. In particular, we show that for sufficiently large n we have ${\hat R_2}({C_n}) \le {10^5} \times cn$ , where c = 6.5 if n is even and c = 1989 otherwise.