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.

An introductory review on gravitational-deformation induced structures, fabrics and modeling

Recent studies have pointed out a similarity between tectonics and slope tectonic-induced structures. Numerous studies have demonstrated that structures and fabrics previously interpreted as of purely geodynamical origin are instead the result of large slope deformation, and this led in the past to erroneous interpretations. Nevertheless, their limit seems not clearly defined, but it is somehow transitional. Some studies point out continuity between failures developing at surface with upper crust movements. In this contribution, the main studies which examine the link between rock structures and slope movements are reviewed. The aspects regarding model and scale of observation are discussed together with the role of pre-existing weaknesses in the rock mass. As slope failures can develop through progressive failure, structures and their changes in time and space can be recognized. Furthermore, recognition of the origin of these structures can help in avoiding misinterpretations of regional geology. This also suggests the importance of integrating different slope movement classifications based on distribution and pattern of deformation and the application of structural geology techniques. A structural geology approach in the landslide community is a tool that can greatly support the hazard quantification and related risks, because most of the physical parameters, which are used for landslide modeling, are derived from geotechnical tests or the emerging geophysical approaches.

Detailed assessment of the deep-seated gravitational deformation at Stampa above Flåm, Norway

The unstable rock slope above the village of Flåm shows signs of active and postglacial gravitational deformation over an area of 11 km2. We performed detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, and generated a detailed topographic model based on airborne and terrestrial laser scanning. Kinematic analyses of the structural data indicates that deformation is complex and varies over the slope. Both sliding and toppling are locally feasible. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points show an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks. Large fractures indicate deep-seated gravitational deformation of volumes up to 80 million m3, but the movement rates in these areas are below 2 mm/year. Based upon these combined observations, we interpret that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes >100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A large collapse involving more than 10 million m3, however, is of very low likelihood at present.

Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale: some case studies

Every year, debris flows cause huge damage in mountainous areas. Due to population pressure in hazardous zones, the socio-economic impact is much higher than in the past. Therefore, the development of indicative susceptibility hazard maps is of primary importance, particularly in developing countries. However, the complexity of the phenomenon and the variability of local controlling factors limit the use of processbased models for a first assessment. A debris flow model has been developed for regional susceptibility assessments using digital elevation model (DEM) with a GIS-based approach.. The automatic identification of source areas and the estimation of debris flow spreading, based on GIS tools, provide a substantial basis for a preliminary susceptibility assessment at a regional scale. One of the main advantages of this model is its workability. In fact, everything is open to the user, from the data choice to the selection of the algorithms and their parameters. The Flow-R model was tested in three different contexts: two in Switzerland and one in Pakistan, for indicative susceptibility hazard mapping. It was shown that the quality of the DEM is the most important parameter to obtain reliable results for propagation, but also to identify the potential debris flows sources.

Watching television: a previously unrecognized powerful trigger of λ waves.

OBJECTIVE: To assess whether lambda waves are elicited by watching television (TV) and their association with demographical and EEG features. METHODS: We retrospectively compared lambda wave occurrence in prolonged EEG monitorings of outpatients who were allowed to watch TV and in standard EEGs recorded in TV-free rooms. All EEGs were interpreted by the same two electroencephalographers. RESULTS: Of 2,072 standard EEG reports, 36 (1.7 %) mentioned lambda waves versus 46 (32.2%) of 143 prolonged EEG monitoring reports (P < 0.001). Multivariable comparison of prolonged EEG monitorings and standard EEGs disclosed that recordings performed in rooms with a TV (odds ratio, 20.6; 95% confidence interval, 4.8-88.0) and normal EEGs (odds ratio, 3.03; 95% confidence interval, 1.5-6.25) were independently associated with lambda waves. In the prolonged EEG monitoring group, all recordings with lambda waves also had positive occipital sharp transients of sleep. CONCLUSIONS: Watching TV likely represents a powerful and previously unrecognized stimulus for lambda waves. Furthermore, this study confirms the benign nature of this EEG variant and its strong association with positive occipital sharp transients of sleep.

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

Two waves of recombinase gene expression in developing thymocytes.

During T cell development in the thymus, T cell receptor (TCR) alpha, beta, gamma, and delta genes are rearranged and expressed. TCR rearrangement strictly depends upon the coordinate activity of two recombinase activating genes, Rag-1 and Rag-2. In this study we have followed the expression of these genes at different stages of intrathymic development. The results indicate that there are two periods of high Rag-1 and Rag-2 mRNA expression. The first wave peaks early at the CD25+CD4-CD8-CD3- stage of development and coincides with the initial appearance of transcripts derived from fully rearranged TCR beta, gamma, and delta genes, whereas the second wave occurs later at the CD4+CD8+ stage coincident with full-length TCR alpha mRNA expression. Active downregulation of Rag-1 and Rag-2 mRNA expression appears to occur in vivo between the two peaks of recombinase activity. This phenomenon can be mimicked in vitro in response to artificial stimuli such as phorbol myristate acetate and calcium ionophore. Collectively our data suggest that recombinase expression is actively regulated during early thymus development independently of cell surface expression of a mature heterodimeric TCR protein complex.

Influence of structural heterogeneities and of large scale topography on imbricate gravitational rock slope failures: New insights from 3-D physical modeling and geomorphological analysis

Initial topography and inherited structural discontinuities are known to play a dominant role in rock slope stability. Previous 2-D physical modeling results demonstrated that even if few preexisting fractures are activated/propagated during gravitational failure all of those heterogeneities had a great influence on mobilized volume and its kinematics. The question we address in the present study is to determine if such a result is also observed in 3-D. As in 2-D previous models we examine geologically stable model configuration, based upon the well documented landslide at Randa, Switzerland. The 3-D models consisted of a homogeneous material in which several fracture zones were introduced in order to study simplified but realistic configurations of discontinuities (e.g. based on natural example rather than a parametric study). Results showed that the type of gravitational failure (deep-seated landslide or sequential failure) and resulting slope morphology evolution are the result of the interplay of initial topography and inherited preexisting fractures (orientation and density). The three main results are i) the initial topography exerts a strong control on gravitational slope failure. Indeed in each tested configuration (even in the isotropic one without fractures) the model is affected by a rock slide, ii) the number of simulated fracture sets greatly influences the volume mobilized and its kinematics, and iii) the failure zone involved in the 1991 event is smaller than the results produced by the analog modeling. This failure may indicate that the zone mobilized in 1991 is potentially only a part of a larger deep-seated landslide and/or wider deep seated gravitational slope deformation.

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

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small