Nonlinear second order ODE's: Factorizations and particular solutions

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we developed in Phys. Rev. E 71 (2005) 046607Comment: 6 pages, v3=published versio

Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations

In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential and Weierstrass functionsComment: 4 pages, some changes in the text according to referees' suggestions, added one reference, accepted at Central Europ. J. Phy

Riccati nonhermiticity with application to the Morse potential

A supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrodinger equations in particle physics is described at the general level. By this means we are able to introduce a nonhermitic Hamiltonian having the imaginary part proportional to the solution of a Riccati equation of the Witten type. The procedure is applied to the exactly solvable Morse potential introducing in this way the corresponding nonhermitic Morse problem. A possible application is to molecular diffraction in evanescent waves over nanostructured surfacesComment: 8 pages, 4 figure

Classical harmonic oscillator with Dirac-like parameters and possible applications

We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schroedinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavitiesComment: 14 pages, 9 figures, revised, accepted at J. Phys.

Supersymmetric methods in the traveling variable: inside neurons and at the brain scale

We apply the mathematical technique of factorization of differential operators to two different problems. First we review our results related to the supersymmetry of the Montroll kinks moving onto the microtubule walls as well as mentioning the sine-Gordon model for the microtubule nonlinear excitations. Second, we find analytic expressions for a class of one-parameter solutions of a sort of diffusion equation of Bessel type that is obtained by supersymmetry from the homogeneous form of a simple damped wave equations derived in the works of P.A. Robinson and collaborators for the corticothalamic system. We also present a possible interpretation of the diffusion equation in the brain contextComment: 14 pages, 1 figur

Neuroendocrine Regulation of Metabolism

Given the current environment in most developed countries, it is a challenge to maintain a good balance between calories consumed and calories burned, although maintenance of metabolic balance is key to good health. Therefore, understanding how metabolic regulation is achieved and how the dysregulation of metabolism affects health is an area of intense research. Most studies focus on the hypothalamus, which is a brain area that acts as a key regulator of metabolism. Among the nuclei that comprise the hypothalamus, the arcuate nucleus is one of the major mediators in the regulation of food intake. The regulation of energy balance is also a key factor ensuring the maintenance of any species as a result of the dependence of reproduction on energy stores. Adequate levels of energy reserves are necessary for the proper functioning of the hypothalamic-pituitary-gonadal axis. This review discusses valuable data presented in the 2015 edition of the International Workshop of Neuroendocrinology concerning the fundamental nature of the hormonal regulation of the hypothalamus and the impact on energy balance and reproduction.Fil: Cornejo, María Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Multidisciplinario de Biología Celular. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Multidisciplinario de Biología Celular. Universidad Nacional de La Plata. Instituto Multidisciplinario de Biología Celular; ArgentinaFil: Hentges, S.T.. State University of Colorado - Fort Collins; Estados UnidosFil: Maliqueo, M.. Universidad de Chile; ChileFil: Coirini, Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Becu Villalobos, D.. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Elias, C. F.. University of Michigan; Estados Unido

Supersymmetric free-damped oscillators: Adaptive observer estimation of the Riccati parameter

A supersymmetric class of free damped oscillators with three parameters has been obtained in 1998 by Rosu and Reyes through the factorization of the Newton equation. The supplementary parameter is the integration constant of the general Riccati solution. The estimation of the latter parameter is performed here by employing the recent adaptive observer scheme of Besancon et al., but applied in a nonstandard form in which a time-varying quantity containing the unknown Riccati parameter is estimated first. Results of computer simulations are presented to illustrate the good feasibility of this approach for a case in which the estimation is not easily accomplished by other meansComment: 8 pages, 6 figure

Supersymmetric pairing of kinks for polynomial nonlinearities

We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on reaction-diffusion equations in the travelling frame and damped-anharmonic-oscillator equations. We also report an interesting pairing of the kink solutions, a result obtained by reversing the factorization brackets in the supersymmetric quantum mechanical style. In this way, one gets ordinary differential equations with a different polynomial nonlinearity possessing kink solutions of different width but propagating at the same velocity as the kinks of the original equation. This pairing of kinks could have many applications. We illustrate the mathematical procedure with several important cases, among which the generalized Fisher equation, the FitzHugh-Nagumo equation, and the polymerization fronts of microtubulesComment: 13 pages, 2 figures, revised during the 2nd week of Dec. 200

Influence of a transverse static magnetic field on the magnetic hyperthermia properties and high-frequency hysteresis loops of ferromagnetic FeCo nanoparticles

The influence of a transverse static magnetic field on the magnetic hyperthermia properties is studied on a system of large-losses ferromagnetic FeCo nanoparticles. The simultaneous measurement of the high-frequency hysteresis loops and of the temperature rise provides an interesting insight into the losses and heating mechanisms. A static magnetic field of only 40 mT is enough to cancel the heating properties of the nanoparticles, a result reproduced using numerical simulations of hysteresis loops. These results cast doubt on the possibility to perform someday magnetic hyperthermia inside a magnetic resonance imaging setup.Comment: 6 pages, 3 figure

Factorization conditions for nonlinear second-order differential equations

For the case of nonlinear second-order differential equations with a constant coefficient of the first derivative term and polynomial nonlinearities, the factorization conditions of Rosu and Cornejo-Perez are approached in two ways: (i) by commuting the subindices of the factorization functions in the two factorization conditions and (ii) by leaving invariant only the first factorization condition achieved by using monomials or polynomial sequences. For the first case the factorization brackets commute and the generated equations are only equations of Ermakov-Pinney type. The second modification is non commuting, leading to nonlinear equations with different nonlinear force terms, but the same first-order part as the initially factored equation. It is illustrated for monomials with the examples of the generalized Fisher and FitzHugh-Nagumo initial equations. A polynomial sequence example is also included.Comment: 12 pages, 6 figures, 17 references, for NMMP-2022 proceeding