Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems

This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the isolation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented

Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Multisensor change detection with nonlinear canonical correlation

The analysis of multi-modal and multi-sensor images is nowadays of paramount importance for Earth Observation (EO) applications. There exist a variety of methods that aim at fusing the different sources of information to obtain a compact representation of such datasets. However, for change detection existing methods are often unable to deal with heterogeneous image sources and very few consider possible nonlinearities in the data. Additionally, the availability of labeled information is very limited in change detection applications. For these reasons, we present the use of a semi-supervised kernel-based feature extraction technique. It incorporates a manifold regularization accounting for the geometric distribution and jointly addressing the small sample problem. An exhaustive example using Landsat 5 data illustrates the potential of the method for multi-sensor change detection.

Target Molecular Size and Sodium Dodecyl Sulfate-Polyacrylamide Gel Electrophoresis Analysis of the ATP-and Pyrophosphate-Dependent Proton Pumps from Maize Root Tonoplast.

Tonoplast-enriched membranes were prepared from maize (Zea mays L. cv LG 11) primary roots, using sucrose nonlinear gradients. The functional molecular size of the tonoplast ATP-and PPi-dependent proton pumps were analyzed by radiation inactivation. Glucose-6-phosphate dehydrogenase (G6PDH) was added as an internal standard. Frozen samples (-196 degrees C) of the membranes were irradiated with (60)Co for different periods of time. After thawing the samples, the activities of G6PDH, ATPase, and PPase were tested. By applying target theory, the functional sizes of the ATPase and PPase in situ were found to be around 540 and 160 kilodaltons, respectively. The two activities were solubilized and separated by gel filtration chromatography. The different polypeptides copurifying with the two pumps were analyzed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Two bands (around 59 and 65 kilodaltons) were associated with the ATPase activity, whereas a double band (around 40 kilodaltons) was recovered with the PPase activity.

Nonlinear inverse dynamic models of gas sensing systems based on chemical sensor arrays for quantitative measurements

Gas sensing systems based on low-cost chemical sensor arrays are gaining interest for the analysis of multicomponent gas mixtures. These sensors show different problems, e.g., nonlinearities and slow time-response, which can be partially solved by digital signal processing. Our approach is based on building a nonlinear inverse dynamic system. Results for different identification techniques, including artificial neural networks and Wiener series, are compared in terms of measurement accuracy.

Kinematically complete analysis of the CLAS data on the proton structure Function F2 in a Regge-Dual model

The recently measured inclusive electron-proton cross section in the nucleon resonance region, performed with the CLAS detector at the Thomas Jefferson Laboratory, has provided new data for the nucleon structure function F2 with previously unavailable precision. In this paper we propose a description of these experimental data based on a Regge-dual model for F2. The basic inputs in the model are nonlinear complex Regge trajectories producing both isobar resonances and a smooth background. The model is tested against the experimental data, and the Q2 dependence of the moments is calculated. The fitted model for the structure function (inclusive cross section) is a limiting case of the more general scattering amplitude equally applicable to deeply virtual Compton scattering. The connection between the two is discussed.

Soil infiltration based on bp neural network and grey relational analysis

Soil infiltration is a key link of the natural water cycle process. Studies on soil permeability are conducive for water resources assessment and estimation, runoff regulation and management, soil erosion modeling, nonpoint and point source pollution of farmland, among other aspects. The unequal influence of rainfall duration, rainfall intensity, antecedent soil moisture, vegetation cover, vegetation type, and slope gradient on soil cumulative infiltration was studied under simulated rainfall and different underlying surfaces. We established a six factor-model of soil cumulative infiltration by the improved back propagation (BP)-based artificial neural network algorithm with a momentum term and self-adjusting learning rate. Compared to the multiple nonlinear regression method, the stability and accuracy of the improved BP algorithm was better. Based on the improved BP model, the sensitive index of these six factors on soil cumulative infiltration was investigated. Secondly, the grey relational analysis method was used to individually study grey correlations among these six factors and soil cumulative infiltration. The results of the two methods were very similar. Rainfall duration was the most influential factor, followed by vegetation cover, vegetation type, rainfall intensity and antecedent soil moisture. The effect of slope gradient on soil cumulative infiltration was not significant.

Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models