Application of ray-path geometry modification to the design of a collimating structure for LEDs

We investigate a system that is able to trace the ray path we decided previously, in particular, we would like to change a cylindrical raypath into a plane one after a given coordinate of the propagation axis. The technique we used is completely general, so we can calculate every kind of system to move some rays path in another one we want.     

On non-commutative geodesic motion

In this work we study the geodesic motion on a noncommutative space–time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury’s perihelion. In this way, we estimate the noncommutative parameter based in experimental data.     

Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects.     

Seeing in colour

Understanding perception of colour is challenging because what we see is not always what is there, which is a phenomenon we call illusions. Here we review the nature of colour vision, and the problems facing most current models and explanations. Focusing on our recent research on humans, bees and computers, we describe a new, more ecologically based explanation that provides a clear framework for why we see what we do.     

Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation

In this paper we prove the existence of doubly periodic solutions of certain nonlinear elliptic problems on ² and study the geometry of their nodal domains. In particular, we will show that if we perturb a nonlinear elliptic equation exhibiting a small amplitude doubly periodic solution whose nodal domains form a checkerboard pattern, then the perturbed equation will have a unique nearby solution which is still doubly periodic, but for which the nodal line structure breaks up. Moreover, we indicate what can happen if we start with a large amplitude doubly periodic solution whose nodal domains form a checkerboard pattern, and we relate these solutions to the Cahn-Hilliard equation and spinodal decomposition.     

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.     

Modulational instabilities in neutrino-antineutrino interactions

Using a semiclassical approach, we analyze the collective behavior of neutrinos and antineutrinos in a dense background. Applying the Wigner transform technique, we show that the interaction can be modeled by a coupled system of nonlinear Vlasov-like equations. From these equations, we derive a dispersion relation for neutrino-antineutrino interactions on a general background. The dispersion relation admits a novel modulational instability. Moreover, we investigate the modifications of the instability due to thermal effects. The results are examined, together with a numerical example, and we discuss the induced density inhomogeneities using parameters relevant to the early Universe.     

Exploring Evolutionary Fitness in Biological Systems Using Machine Learning Methods

Here, we propose a computational approach to explore evolutionary fitness in complex biological systems based on empirical data using artificial neural networks. The essence of our approach is the following. We first introduce a ranking order of inherited elements (behavioral strategies or/and life history traits) in considered self-reproducing systems: we use available empirical information on selective advantages of such elements. Next, we introduce evolutionary fitness, which is formally described as a certain function reflecting the introduced ranking order. Then, we approximate fitness in the space of key parameters using a Taylor expansion. To estimate the coefficients in the Taylor expansion, we utilize artificial neural networks: we construct a surface to separate the domains of superior and interior ranking of pair inherited elements in the space of parameters. Finally, we use the obtained approximation of the fitness surface to find the evolutionarily stable (optimal) strategy which maximizes fitness. As an ecologically important study case, we apply our approach to explore the evolutionarily stable diel vertical migration of zooplankton in marine and freshwater ecosystems. Using machine learning we reconstruct the fitness function of herbivorous zooplankton from empirical data and predict the daily trajectory of a dominant species in the northeastern Black Sea.     

Waves and rays in uniaxial birefringent crystals

In this paper, we present a more elaborate and complete way of the formalism that we have developed in successive steps for ray tracing through uniaxial birefringent media in view of the optical design. With the obtained formulas we analyze in detail what we see through a cleavage calcite crystal.     

On the Relationships Between the Moments of a POVM and the Generator of the von Neumann Algebra It Generates

In the present paper, we review some recent results about commutative positive operator valued measures (POVMs) and single out some open problems. We introduce a conjecture about the extension of some recent results and prove some important consequences of such conjecture. In particular, we prove that it implies the universal character of some of the mathematical objects we introduce, i.e., the fact that they do not depend on the POV measure we are considering. We analyze the relevance of this result. Finally, we point out that some of the results we present admit a constructive proof and we show the relevance of this fact to the theory of commutative POV measures.     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.     

一类延迟混沌系统沿主轴方向上Lyapunov指数的计算方法

提出了一种计算延迟混沌系统沿主轴方向上Lyapunov指数的方法：矩阵迭代法.给出了其计算方法的原理及推导过程;同时推导了一类泰勒展开法,介绍了已有的Wolf替代法计算延迟混沌系统的Lyapunov指数.分析了三种不同计算方法的优缺点,最后进行了数值模拟,验证方法的有效性. 关键词： Lyapunov指数 延迟混沌系统 矩阵迭代法 泰勒展开法     

Nonlinear electrohydrodynamic instability conditions of an interface between two fluids under the effect of a normal periodic electric field. III

A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal periodic electric field is subjected to nonlinear deformations. We use the method of multiple scales in order to solve the nonlinear equations. In the first-order problem we obtained Mathieu's differential equation. For the second order, we obtain the nonhomogeneous Mathieu equation and we use the method of multiple scales to obtain a sequence of equations. In the third order we obtain the second-order differential equation of periodic coefficients. Also, we obtain a formula for surface elevation. The stability conditions are determined.     

Hawking radiation and propagation of massive charged scalar field on a three-dimensional Gödel black hole

In this paper we consider the three-dimensional Gödel black hole as a background and we study the vector particle tunneling from this background in order to obtain the Hawking temperature. Then, we study the propagation of a massive charged scalar field and we find the quasinormal modes analytically, which turns out be unstable as a consequence of the existence of closed time-like curves. Also, we consider the flux at the horizon and at infinity, and we compute the reflection and transmission coefficients as well as the absorption cross section. Mainly, we show that massive charged scalar waves can be superradiantly amplified by the three-dimensional Gödel black hole and that the coefficients have an oscillatory behavior. Moreover, the absorption cross section is null at the high frequency limit and for certain values of the frequency.     

Theory of strong interactions. I. Kinematics

This paper is the first of a series devoted to strong interaction theory. As a general introduction to the series, we give a critical survey of theories and models presently in force.In a previous paper, we studied the kinematics of a single unstable hadron, the state of which was described as an incoherent superposition of states with different masses. To such a state there corresponds a function on the Poincaré group, called a characteristic function. Here we take up these old results anew, we work them out, and we go more thoroughly into their physical foundations. Then we describe the kinematics of several particles.The theory of strong interactions must take into account two opposed features of unstable hadrons: their identity and their difference with stable hadrons. The identity implies that an unstable hadron is in a certain state, described by a density operator; the difference is that this state has a mass spectrum, whose width cannot be neglected.We make the further assumption that the state is an incoherent superposition of components with different masses. This assumption is compared to the statistics experiment of Baton and Laurens, in which the components with different masses have been effectively separated.We define the characteristic function of such a state, and we point out its analogy with a usual characteristic function in probability theory. The physical meaning of characteristic functions is studied on the example of a spin, then in the general case.Then we study the characteristic function of several hadrons, and we define two notions: the global particle and the inclusive characteristic function.     

Microwave-Triggered Metal-Enhanced Chemiluminescence (MT-MEC): Application to Ultra-fast and Ultra-sensitive Clinical Assays

In this rapid communication we describe a new approach to protein detection with chemiluminescence. By combining common practices in protein detection with chemiluminescence, microwave technology, and metal-enhanced chemiluminescence, we show that we can use low power microwaves to substantially increase enzymatic chemiluminescent reaction rates on metal substrates. As a result, we have found that we can in essence trigger chemiluminescence with low power microwave (Mw) pulses and ultimately, perform on-demand protein detection assays. Using microwave triggered metal-enhanced chemiluminescence (MT-MEC), we not only improve the sensitivity of immunoassays with enhanced signal-to-noise ratios, but we also show that we can accurately quantify protein concentrations by integrating the photon flux for discrete time intervals.     

Teaching a laser beam to go straight

In classical physics a beam of light propagates in a perfectly straight line and this means that we can measure small displacements with unlimited accuracy. However, this is not correct for real laser beams when we take the quantum properties of light into account. Spatial measurements will be limited by quantum noise, similar to the limitations for optical communication and sensing. Here we derive the spatial quantum noise limit and show how to measure it. Next we demonstrate that we can use specially prepared light with quantum correlations, so-called squeezed light, to improve spatial measurements to below this quantum limit. In this way we prepare a beam which goes in a straighter line than the output of any conventional laser.     

Construction of a unitary analytic scattering amplitude (I). Scalar particles

By imposing cos θ analyticity, we extend earlier investigations into the problem of constructing a unitary scattering amplitude from experimental measurements. The new approach is superior to earlier work, inasmuch as (a) the partial waves fall off exponentially, (b) we can handle cross sections with zeros, (c) we have a convergent Newton-Kantorovich interaction even when the fixed-point theorems do not apply, (d) we can study bifurcation points, (e) in the inelastic region, we find that analyticity does not remove the continuum ambiguity, (f) for quasi-elastic reactions (e.g. photoproduction) we resolve the Watson ambiguity for the phase shifts. We work at fixed energy, and throughout this first paper we neglect spin and isospin.     

On the Long Time Behavior of a Particle in an Infinitely Extended System in One Dimension

We study the long time behavior of a non-equilibrium infinite particle system in one dimension. First, we show that the velocity of a particle increases at most linearly in time. Then we discuss at a heuristic level the displacement of a particle when the mutual interaction is singular. Finally we study the motion of a fast particle interacting with a background of slow particles and we prove that the velocity of the fast particle remains almost unchanged for a long time (at least proportional to the velocity itself).