Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

The Phase Space as a New Representation of the Dynamical Behaviour of Temperature and Enthalpy in a Reefer monitored with a Multidistributed Sensors Network

The study of temperature gradients in cold stores and containers is a critical issue in the food industry for the quality assurance of products during transport, as well as forminimizing losses. The objective of this work is to develop a new methodology of data analysis based on phase space graphs of temperature and enthalpy, collected by means of multidistributed, low cost and autonomous wireless sensors and loggers. A transoceanic refrigerated transport of lemons in a reefer container ship from Montevideo (Uruguay) to Cartagena (Spain) was monitored with a network of 39 semi-passive TurboTag RFID loggers and 13 i-button loggers. Transport included intermodal transit from transoceanic to short shipping vessels and a truck trip. Data analysis is carried out using qualitative phase diagrams computed on the basis of Takens?Ruelle reconstruction of attractors. Fruit stress is quantified in terms of the phase diagram area which characterizes the cyclic behaviour of temperature. Areas within the enthalpy phase diagram computed for the short sea shipping transport were 5 times higher than those computed for the long sea shipping, with coefficients of variation above 100% for both periods. This new methodology for data analysis highlights the significant heterogeneity of thermohygrometric conditions at different locations in the container.

Representation of Neural Networks by Dynamical Systems

Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

Optimized harvest scheduling in eucalyptus plantations under operational, spatial and climatic constraints

The representation of sustainability concerns in industrial forests management plans, in relation to environmental, social and economic aspects, involve a great amount of details when analyzing and understanding the interaction among these aspects to reduce possible future impacts. At the tactical and operational planning levels, methods based on generic assumptions usually provide non-realistic solutions, impairing the decision making process. This study is aimed at improving current operational harvesting planning techniques, through the development of a mixed integer goal programming model. This allows the evaluation of different scenarios, subject to environmental and supply constraints, increase of operational capacity, and the spatial consequences of dispatching harvest crews to certain distances over the evaluation period. As a result, a set of performance indicators was selected to evaluate all optimal solutions provided to different possible scenarios and combinations of these scenarios, and to compare these outcomes with the real results observed by the mill in the study case area. Results showed that it is possible to elaborate a linear programming model that adequately represents harvesting limitations, production aspects and environmental and supply constraints. The comparison involving the evaluated scenarios and the real observed results showed the advantage of using more holistic approaches and that it is possible to improve the quality of the planning recommendations using linear programming techniques.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

Dynamical analysis of the global warming

Global warming is a major concern nowadays. Weather conditions are changing, and it seems that human activity is one of the main causes. In fact, since the beginning of the industrial revolution, the burning of fossil fuels has increased the nonnatural emissions of carbon dioxide to the atmosphere. Carbon dioxide is a greenhouse gas that absorbs the infrared radiation produced by the reflection of the sunlight on the Earth’s surface, trapping the heat in the atmosphere. Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic, and health aspects of human life. This paper studies the global warming trend in the perspective of dynamical systems and fractional calculus, which is a new standpoint in this context. Worldwide distributed meteorological stations and temperature records for the last 100 years are analysed. It is shown that the application of Fourier transforms and power law trend lines leads to an assertive representation of the global warming dynamics and a simpler analysis of its characteristics.

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

On the spinning axis representation

A new spinning axis representation is introduced. It allows us to calculate the evolution operator of a system with slowly varying time dependent Hamiltonian with the desired degree of approximation in the parameter used for describing its dynamical evolution. The procedure is compared with a previously existing one and applied to a simple example.

Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based On P

I present a novel design methodology for the synthesis of automatic controllers, together with a computational environment---the Control Engineer's Workbench---integrating a suite of programs that automatically analyze and design controllers for high-performance, global control of nonlinear systems. This work demonstrates that difficult control synthesis tasks can be automated, using programs that actively exploit and efficiently represent knowledge of nonlinear dynamics and phase space and effectively use the representation to guide and perform the control design. The Control Engineer's Workbench combines powerful numerical and symbolic computations with artificial intelligence reasoning techniques. As a demonstration, the Workbench automatically designed a high-quality maglev controller that outperforms a previous linear design by a factor of 20.

Stratospheric water vapor and climate: sensitivity to the representation in radiation codes

There has been considerable interest in the climate impact of trends in stratospheric water vapor (SWV). However, the representation of the radiative properties of water vapor under stratospheric conditions remains poorly constrained across different radiation codes. This study examines the sensitivity of a detailed line-by-line (LBL) code, a Malkmus narrow-band model and two broadband GCM radiation codes to a uniform perturbation in SWV in the longwave spectral region. The choice of sampling rate in wave number space (Δν) in the LBL code is shown to be important for calculations of the instantaneous change in heating rate (ΔQ) and the instantaneous longwave radiative forcing (ΔFtrop). ΔQ varies by up to 50% for values of Δν spanning 5 orders of magnitude, and ΔFtrop varies by up to 10%. In the three less detailed codes, ΔQ differs by up to 45% at 100 hPa and 50% at 1 hPa compared to a LBL calculation. This causes differences of up to 70% in the equilibrium fixed dynamical heating temperature change due to the SWV perturbation. The stratosphere-adjusted radiative forcing differs by up to 96% across the less detailed codes. The results highlight an important source of uncertainty in quantifying and modeling the links between SWV trends and climate.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Mean-field description of a dynamical collapse of a fermionic condensate in a trapped boson-fermion mixture

We suggest a time-dependent dynamical mean-field-hydrodynamic model for the collapse of a trapped boson-fermion condensate and perform numerical simulation based on it to understand some aspects of the experiment by Modugno et al. [Science 297, 2240 (2002)] on the collapse of the fermionic condensate in the K-40-Rb-87 mixture. We show that the mean-field model explains the formation of a stationary boson-fermion condensate at zero temperature with relative sizes compatible with experiment. This model is also found to yield a faithful representation of the collapse dynamics in qualitative agreement with experiment. In particular we consider the collapse of the fermionic condensate associated with (a) an increase of the number of bosonic atoms as in the experiment and (b) an increase of the attractive boson-fermion interaction using a Feshbach resonance. Suggestion for experiments of fermionic collapse using a Feshbach resonance is made.

Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)