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Algae constitute a diverse group that is useful in many biotechnological areas. In this paper, the usefulness of Caulerpa sertularioides methanol extract in the synthesis of ZnO and Zn(OH)2 nanoparticles was explored. This work had two main objectives: (1) to use the extract in the synthesis as an organic harmless complexing agent, and (2) to enhance a photocatalytic effect over AZO dyes in wastewater from fabric industries without adding nanomaterial to the environment due to its toxicity. Caulerpa extract performed the expected complexing action, and nanoparticles were formed in a size range from 45 to 69 nm. X-ray diffraction analysis (XRD), transmission electron microscopy (TEM) and UV-Vis spectroscopy were used to characterize the system. It was demonstrated that the nanoparticles were useful to photocatalyst AZO dyes in the water, while contained in tetraethylorthosilicate composites. These could be used in industrial wastewater and are expected to have no environmental consequences because the composites do not add nanoparticles to the water.

This is a theoretical study to showcase the possibility of constructing a two-dimensional photonic crystal (PC) by placing a geometric array of hot spots on a dielectric layer that modify locally t...

Propagation of an electromagnetic pulse in a monolayer surface with a hot point is studied. Refractive index in the monolayer is changed locally. It is assumed that the perturbation to the ...

We present a classical and a quantum constant of motion used to study the behavior of an electron moving in the vicinity of a tridimensional charged nanostructure with electric dipole. It is the generalization of the bidimensional version studied in a previous work. The classical case is found by using two approaches: the Hamilton Jacobi equation and a Newtonian treatment. The quantum case is obtained by separating the Schrodinger equation in spherical coordinates. We use three quantum numbers to classify the states. The angular part is solved by using an expansion of spherical harmonics to get an eigenvalue equation for the new constant of motion. The solution shows that the probability density of the electron shifts toward the values where $\theta

This work approaches the Michaelis-Menten model for enzymatic reactions at a nanoscale, where we focus on the quasi-stationary state of the process. The entropy and the kinetics of the stochastic fluctuations are studied to obtain new understanding about the catalytic reaction. The treatment of this problem begins with a state space describing an initial amount of substrate and enzyme-substrate complex molecules. Using the van Kampen expansion, this state space is split into a deterministic one for the mean concentrations involved, and a stochastic one for the fluctuations of these concentrations. The probability density in the fluctuation space displays a behavior that can be described as a rotation, which can be better understood using the formalism of stochastic velocities. The key idea is to consider an ensemble of physical systems that can be handled as if they were a purely conceptual gas in the fluctuation space. The entropy of the system increases when the reaction starts and slightly diminishes once it is over, suggesting: 1. The existence of a rearrangement process during the reaction. 2. According to the second law of thermodynamics, the presence of an external energy source that causes the vibrations of the structure of the enzyme to vibrate, helping the catalytic process. For the sake of completeness and for a uniform notation throughout this work and the ones referenced, the initial sections are dedicated to a short examination of the master equation and the van Kampen method for the separation of the problem into a deterministic and stochastic parts. A Fokker-Planck equation (FPE) is obtained in the latter part, which is then used as grounds to discuss the formalism of stochastic velocities and the entropy of the system. The results are discussed based on the references cited in this work.

We study the behavior of an electron in the vicinity of a positively charged nanoparticle that has a permanent electric dipole and is of finite size (not point-like) in two dimensions. We place special attention to the fact that a constant of motion, as well as the energy, exists so that the wave functions result from an eigenvalue problem which are classified using two quantum numbers. The (GaAs)3 cluster is used as iconic case. The angular part is solved using Mathieu functions and the radial part by means of a numerical method. The solutions are plotted and the Einstein coefficients are calculated.

A new constant of the motion is found for an electric charge acted on by an electric dipole. The relation of the constant of the motion to the energy of the particle is found. Some properties of the motion are studied and known results are reproduced more simply. We discuss conditions for the appearance of bounded and unbounded trajectories, motion on a sphere, and on a plane. Small angular oscillations around a stable circular trajectory are also studied.

This chapter presents an attempt to compare the productivity of the Mexican banking sector in two different periods: the 2007-2011 period of global financial crisis and the 2003-2006 stage, which can be regarded as a relatively stable period. The purpose of this study is to disclose whether the global financial crisis affected Mexican banking productivity. Three Data Envelopment Models (DEA) are tested in order to assess whether there is a significant difference between the productivity patterns of Mexican banks before and after the financial crisis. Such models are the radial Malmquist Index, the non-radial and slacks-based model, and non-radial and non-oriented. Essentially, no significant difference of productivity indicators for both foreign and domestic banks was found. Likewise, no significant difference between the pre- and post-crisis periods was perceived, as far as productivity indicators are concerned. Therefore, the global financial crisis was effectless in banking operation.

Kinematics of stochastic mechanics is used to study diffusion problems at a more general level, without forcing a link to Newtonian mechanics. Stochastic velocities are taken from Nelson's kinematics to study nonlinear random systems. Random effects are systematically separated from the deterministic motion via a transformation to fluctuation variables. Then, closed expressions for stochastic velocities are written, and as a consequence, analytical applications can be developed. A system is studied to show the difference between detailed and nondetailed balance. Besides, a one-dimensional problem is considered to characterize the relaxation process. The concept of entropy is introduced to find an expression describing stationary processes, so that one has two kind of tools to study this type of problems. The final result is that a few simple techniques are put together to describe a wide amount of phenomena.

We consider a model for a one-dimensional photonic crystal formed by a succession of Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate the band structure and reflectance of this structure as a function of the incident wave intensity, and find two main behaviors: the appearance of prohibited bands, and the separation and narrowing of these bands. A system with these features is obtained by alternating very thin slabs of a soft matter material with thicker solid films, which can be used to design a device to control light propagation for specific wavelength intervals and light intensities., 6 pages, 6 figures

We consider a nematic liquid crystal constrained by two coaxial cylinders under the action of low-frequency axial or radial electric fields. Assuming an initially hybrid configuration, we find the equilibrium texture of the nematic subjected to weak anchoring boundary conditions on both cylindrical surfaces. We analyze the distinct textures of the nematic as a function of the strength of the interaction of the nematic with the sidewalls, the radii ratio of the cylinders, and the applied electric field. Also, for each radii ratio and strength of the nematic-surface interaction, we determine the critical field for which a complete alignment of the nematic liquid crystal occurs.

Se desarrolla un estudio analítico sistemático de los efectos de tamaño finito en modelos de redes separables, con dinámica secuencial lejos de la saturación. Se encuentran dos tipos de efectos: fluctuaciones térmicas y correcciones congeladas a las leyes de campo promedio. Se parte de que la dinámica microscópica de la red obedece una ecuación maestra conforme a la dinámica de Glauber y se demuestra que la dinámica macroscópica, con los traslapes o parámetros de orden como variables físicas, puede ser descrita en forma aproximada como un fenómeno de difusión. Se propone una descomposición de los traslapes como la suma de dos términos: uno determinista, que son las trayectorias de campo promedio, y otro fluctuante al azar, que es modelado mediante procesos de Ornstein y Uhlenbeck dependientes del tiempo. Estos últimos son procesos gaussianos, de modo que escribimos explícitamente la distribución de probabilidad conjunta de las fluctuaciones. Las ecuaciones diferenciales para describir sus momentos estadísticos forman sistemas no autónomos cuyas soluciones formales obtenemos. Entonces aplicamos la teoría a sistemas que se conducen como memorias asociativas, presentan relajación al equilibrio, cumplen con el balance detallado y con un teorema de fluctuación y disipación. También estudiamos dos sistemas fuera de equilibrio: uno donde existe un punto fijo de la red pero no hay balance detallado y otro donde las fluctuaciones aleatorias modifican cualitativamente su conducta dando lugar a un fenómeno en el cual el traslape se escapa de una cuenca a otra. Las predicciones teóricas son comparadas con simulaciones en computadora. An analytical and systematic study of finite size effects on separable neural networks withsequential dynamics is developed far away from saturation regime. Two kinds of effects are found: thermal fluctuations and frozen corrections to mean-field laws. It is considered that separable neural networksfollows microscopic Glauber dynamics goberned by a master equation and a macroscopic description is obtained by taking overlaps (or order parameters) as physical variables. A Fokker-Planck equation is found, so that diffusion phenomenaare useful to describe this macroscopic dynamics. A decomposition in two terms is proposed for the overlaps: one deterministic, given as the solutions to mean-field equations and other as random variables. It is found that these fluctuations can be modeled by time-dependent Ornstein-Uhlenbeck processes. Since these have gaussian behavior, one can write the joint probability distribution function for fluctuations. Differential equations as non-autonomous systemsare found to describe the timeevolution of the statistical moments of these fluctuations and their formal solutions are found. Thenour theory is applied to analize the dependenceoffinite size effects on detailed balance, scaling properties of fluctuations close to phase boundaries and escape processes in critical models which are driven by finite size effects. Finally, theoretical predictions are confirmed by numerical simulations in computers.

We considered a cholesteric slab whose axis is normal to their borders, when a uniform electric field is perpendicularly applied to the helix axis. We found the solution of the boundary value problem for the reflection and transmission of normally incident waves due to the slab. We showed that a left-circularly polarized thin reflection band is immersed in a wider right-circularly polarized band reflection, when the cholesteric is subjected to low amplitude fields. For larger field values, both reflection bands redshift simultaneously as the field increases. A device based on this phenomenon can be used as a electrically tunable universal filter.