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Classical harmonic oscillator with Dirac-like parameters and possible applications

HARET CODRATIAN ROSU OCTAVIO CORNEJO PEREZ ROMAN LOPEZ SANDOVAL (2004)

"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 Schr¨odinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of thesemodes. Generalizations to severalK 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 cavities."

Article

Quantum-mechanics Supersymmetry Equation Diffraction Modes Light CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA

FTIR and electrical characterization of a-Si:H layers deposited by PECVD at different boron ratios

ABDU ORDUÑA DIAZ CARLOS GERARDO TREVIÑO PALACIOS ALFONSO TORRES JACOME (2010)

Hydrogenated amorphous silicon (a-Si:H) has found applications in flat panel displays, photovoltaic solar cell and recently has been employed in boron doped microbolometer array.Wehave performed electrical and structural characterizations of a-Si:H layers prepared by plasma enhanced chemical vapor deposition (PECVD) method at 540K on glass substrates at different diborane (B₂H₆) flow ratios (500, 250, 150 and 50 sccm). Fourier transform infrared spectroscopy (FTIR) measurements obtained by specular reflectance sampling mode, show Si–Si, B–O, Si–H, and Si–O vibrational modes (611, 1300, 2100 and 1100cm⁻¹ respectively) with different strengths which are associated to hydrogen and boron content. The current–voltage curves show that at 250 sccm flow of boron the material shows the lowest resistivity, but for the 150 sccm boron flow it is obtained the highest temperature coefficient of resistance (TCR).

Article

Hydrogenated amorphous silicon Vibrational modes PECVD CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA ÓPTICA

Análisis y síntesis de campos ópticos con estructura Markoviana

Carina Gutiérrez Ojeda (2017)

We propose the implementation of a Markov chain type Ehrenfest process to describe the

evolution of the amplitude function associated to an optical field. As prototype, we use

a set of Bessel modes whose amplitude values have associated a probability vector for the

boundary condition. The partially coherent propagation of the optical field is studied by

analyzing the convergence of the process by means of the transition probability matrix

applied to an initial condition vector.

As a possible application, we describe the recording process with the interference of

two Markov modes. During the reconstruction process, the hologram is illuminated with a

Makovian mode which can be controlled through the evolution given by a transition matrix.

Computer simulations are presented.

Se propone implementar procesos estocásticos con las cadenas de Markov del tipo Ehrenfest

para describir la evolución de la función de amplitud asociada a un campo óptico. Como

prototipo, se usa un conjunto de modos Bessel cuyos valores de amplitud tienen asociados

un vector de probabilidad dada por las condiciones iniciales. La propagación de la

coherencia parcial del campo óptico es estudiada analizando la convergencia de los procesos

estocásticos por medio de una matriz de transición de probabilidades, aplicada a un vector

con las condiciones iniciales. Durante éste proceso las propiedades de entropía de los

campos ópticos son analizadas.

Como una posible aplicación, se describe el proceso de grabado de un holograma

con la interferencia de dos modos markovianos. Durante el proceso de reconstrucción el

campo con que se ilumina el holograma es un modo markoviano, que puede ser controlado

a través de la evolución dada por la matriz de transición estocástica

En cada caso se muestra una simulación numérica que predice los resultados

teóricos.

Master thesis

Coherence Stochastic processes Markov chains Optical Modes CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA HOLOGRAFÍA

FTIR and electrical characterization of a-Si:H layers deposited by PECVD at different boron ratios

Abdu Orduña Díaz CARLOS GERARDO TREVIÑO PALACIOS MARLON ROJAS LOPEZ RAUL JACOBO DELGADO MACUIL VALENTIN LOPEZ GAYOU ALFONSO TORRES JACOME (2010)

Hydrogenated amorphous silicon (a-Si:H) has found applications in flat panel displays, photovoltaic solar cell and recently has been employed in boron doped microbolometer array.Wehave performed electrical and structural characterizations of a-Si:H layers prepared by plasma enhanced chemical vapor deposition (PECVD) method at 540K on glass substrates at different diborane (B2H6) flow ratios (500, 250, 150 and 50 sccm). Fourier transform infrared spectroscopy (FTIR) measurements obtained by specular reflectance sampling mode, show Si–Si, B–O, Si–H, and Si–O vibrational modes (611, 1300, 2100 and 1100cm−1 respectively) with different strengths which are associated to hydrogen and boron content. The current–voltage curves show that at 250 sccm flow of boron the material shows the lowest resistivity, but for the 150 sccm boron flow it is obtained the highest temperature coefficient of resistance (TCR).

Article

Hydrogenated amorphous silicon Vibrational modes PECVD CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA ELECTRÓNICA

Stability analysis of orbital modes for a generalized Lane–Emden equation

Ronald Adams Stefan C. Mancas Haret Codratian Rosu (2019)

"We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial distributions of magnetically-trapped ultracold atomic clouds. A Lyapunov function is defined which helps us to prove that stable spatial structures in the atomic clouds exist only for the adiabatic index y = 1+1 /n with even n. In the case when n is odd we provide an instability result indicating the divergence of the density function for the atoms. Several numerical solutions, which according to our stability analysis are stable, are also presented."

Article

Stability analysis Nonautonomous system Lyapunov function Numerical orbital modes Generalized Lane-Emden equation CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS MATEMÁTICAS

Shifted riccati procedure: application to conformal barotropic FRW cosmologies

HARET CODRATIAN ROSU (2011)

"In the case of barotropic FRW cosmologies, the Hubble parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. We consider these cosmologies in the framework of nonrelativistic supersymmetry that has been effective in the area of supersymmetric quantum mechanics."

Article

Factorization Shifted Riccati procedure Barotropic FRW cosmologies Cosmo-logical zero-modes CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

Global Conception Of Spherical Microresonators: Simulation And Optical Characterization

CARLOS ANDRES SAAVEDRA SALAZAR (2017)

Silica microresonators (MR) are closed surface structures which can con ne light for a few micro seconds of time. These cavities may support the phenomenon called whispering gallery modes (WGM) and have many photonic ap- plications. Using an experimental set-up implemented from zero, we studied and characterized optically the WGM of two different size silica spherical MR and compared results with the theory.

Master thesis

CLE- Maestría en Física CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Spherical Microresonators Silica microresonators Whispering gallery modes Q factor

Inhomogeneous barotropic FRW cosmologies with constant-shifted conformal hubble parameters

HARET CODRATIAN ROSU (2013)

"It is known that the barotropic FRW system of differential equations for zero cosmological constant can be reduced to simple harmonic oscillator (HO) differential equations in the conformal time variable. This is due to the fact that the Hubble rate parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. In previous works, we have used this mathematical result to set the barotropic HO equations in the nonrelativistic supersymmetric approach by factorizing them. If a constant additive parameter, denoted by S, is added to the common Riccati solution of these supersymmetric partner cosmologies one obtains inhomogeneous barotropic cosmologies with periodic singularities in their spatial curvature indices that are counterparts of the non-shifted supersymmetric partners. The zero-mode solutions of these cyclic singular cosmologies are reviewed here as a function of real and imaginary shift parameter. We also notice the modulated zero modes obtained by using the general Riccati solution and comment on their cosmological application."

Article

Barotropic FRW cosmologies Cosmological zero-modes Shifted Riccati procedure Factorization CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA

Free and forced Rossby normal modes in a rectangular gulf of arbitrary orientation

FEDERICO GRAEF ZIEHL (2016)

A free Rossby normal mode in a rectangular gulf of arbitrary orientation is constructed by considering the reflection of a Rossby mode in a channel at the head of the gulf. Therefore, it is the superposition of four Rossby waves in an otherwise unbounded ocean with the same frequency and wavenumbers perpendicular to the gulf axis whose difference is equal to 2m!/W, where m is a positive integer and W the gulf’s width. The lower (or higher) modes with small m (or large m) are oscillatory (evanescent) in the coordinate along the

gulf;these are elucidated geometrically. However for oceanographically realistic parameter values, most of the modes are evanescent.

When the gulf is forced at the mouth with a single Fourier component, the response is in general an infinite sum of modes that are needed to match the value of the streamfunction at the gulf’s entrance. The dominant mode of the response is the resonant one, which corresponds to forcing with a frequency ω and wavenumber normalto the gulf axis # appropriate to a gulf mode: # =− ˇ sin˛/(2ω) ± M!/W, where ˛ is the angle between the gulf’s axis and the eastern direction (+ve clockwise) and M the resonant’s mode number. For zonal gulfs ω drops out of the resonance condition.

For the special cases # = 0 in which the free surface goes up and down atthe mouth with no flow through it, or a flow with a sinusoidal profile, resonant modes can get excited for very specific frequencies (only for non-zonal gulfs in the # = 0 case). The resonant mode is around the annual frequency for a wide range of gulf orientations ˛ ∈ [40◦, 130◦] or ˛ ∈ [220◦,310◦] and gulf widths between 150 and 200 km; these include the Gulf of California and the Adriatic Sea. If # is imaginary, i.e. a flow with an exponential profile, there is no resonance. In general less modes get excited if the gulf is zonally oriented.

Article

Planetary waves, Gulf, Modes, Solutions CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA CIENCIAS DE LA TIERRA Y DEL ESPACIO OCEANOGRAFÍA OCEANOGRAFÍA FÍSICA (VE R 5603 .04) OCEANOGRAFÍA FÍSICA (VE R 5603 .04)

Nonlinear L2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

TOPACIO OSUNA ALTAMIRANO (2016)

"The L<sub>2</sub>-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possess L<sub>2</sub>-gain less than an a priori given disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase."

Article

Nonlinear, Hybrid systems, Sliding modes, ISS CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA