Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

Motived by the necessity of explicit and reliable calculations, as a valid contribution to clarify the effectiveness and, possibly, the limits of the Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in nonextensive quantum statistical mechanics within the optimal Lagrange multiplier framework, focusing on the basic ingredients of the related Spectral Density Method. Besides, to show how the SDM works we have performed, to the lowest order of approximation, explicit calculations of the low-temperature properties for a quantum $d$-dimensional spin-1/2 Heisenberg ferromagnet with long-range interactions decaying as $1/r^{p}$ ($r$ is the distance between spins in the lattice)Comment: Contribution to Next-SigmaPhi conference in Kolymbari, Crete, Greece, August 13-18, 2005, 9 page

Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics

We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the $q$-spectral properties and the methods for a direct calculation of the two-time $q$% -Green's functions and the related $q$-spectral density ($q$ measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive ($q=1$) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the $q$-induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the $q$-induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the $q$ grand-partition function.Comment: 48 pages, no figure

The Classical Spectral Density Method at Work: The Heisenberg Ferromagnet

In this article we review a less known unperturbative and powerful many-body method in the framework of classical statistical mechanics and then we show how it works by means of explicit calculations for a nontrivial classical model. The formalism of two-time Green functions in classical statistical mechanics is presented in a form parallel to the well known quantum counterpart, focusing on the spectral properties which involve the important concept of spectral density. Furthermore, the general ingredients of the classical spectral density method (CSDM) are presented with insights for systematic nonperturbative approximations to study conveniently the macroscopic properties of a wide variety of classical many-body systems also involving phase transitions. The method is implemented by means of key ideas for exploring the spectrum of elementary excitations and the damping effects within a unified formalism. Then, the effectiveness of the CSDM is tested with explicit calculations for the classical $d$-dimensional spin-$S$ Heisenberg ferromagnetic model with long-range exchange interactions decaying as $r^{-p}$ ($p>d$) with distance $r$ between spins and in the presence of an external magnetic field. The analysis of the thermodynamic and critical properties, performed by means of the CSDM to the lowest order of approximation, shows clearly that nontrivial results can be obtained in a relatively simple manner already to this lower stage. The basic spectral density equations for the next higher order level are also presented and the damping of elementary spin excitations in the low temperature regime is studied. The results appear in reasonable agreement with available exact ones and Monte Carlo simulations and this supports the CSDM as a promising method of investigation in classical many-body theory.Comment: Latex, 58 pages, 12 figure

Phase separation in coupled chaotic maps on fractal networks

The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the phases. The persistence saturates and phase domains freeze for all values of the coupling parameter as a consequence of the fractal structure of the networks, in contrast to the phase transition behavior previously observed in regular Euclidean lattices. Several discontinuities and other features found in the saturation persistence curve as a function of the coupling are explained in terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE

On Exact and Approximate Solutions for Hard Problems: An Alternative Look

We discuss in an informal, general audience style the da Costa-Doria conjecture about the independence of the P = NP hypothesis and try to briefly assess its impact on practical situations in economics. The paper concludes with a discussion of the Coppe-Cosenza procedure, which is an approximate, partly heuristic algorithm for allocation problems.P vs. NP , allocation problem, assignment problem, traveling salesman, exact solution for NP problems, approximate solutions for NP problems, undecidability, incompleteness

Aeration control in membrane bioreactor for sustainable environmental footprint

In this study different scenarios were scrutinized to minimize the energy consumption of a membrane bioreactor system for wastewater treatment. Open-loop and closed-loop scenarios were investigated by two-step cascade control strategies based on dissolved oxygen, ammonia and nitrite concentrations. An integrated MBR model which includes also the greenhouse gas formation/emission processes was applied. A substantial energy consumption reduction was obtained for the closed-loop scenarios (32% for Scenario 1 and 82% for Scenario 2). The air flow control based on both ammonia and nitrite concentrations within the aerobic reactor (Scenario 2) provided excellent results in terms of reduction of operating cost reduction (64%), direct (10%) and indirect (81%) emissions

Uncertainty and sensitivity analysis for reducing greenhouse gas emissions from wastewater treatment plants

This paper presents the sensitivity and uncertainty analysis of a plant-wide mathematical model for wastewater treatment plants (WWTPs). The mathematical model assesses direct and indirect (due to the energy consumption) greenhouse gases (GHG) emissions from a WWTP employing a whole-plant approach. The model includes: (i) the kinetic/mass-balance based model regarding nitrogen; (ii) two-step nitrification process; (iii) N2O formation both during nitrification and denitrification (as dissolved and off-gas concentration). Important model factors have been selected by using the Extended-Fourier Amplitude Sensitivity Testing (FAST) global sensitivity analysis method. A scenario analysis has been performed in order to evaluate the uncertainty related to all selected important model factors (scenario 1), important model factors related to the influent features (scenario 2) and important model factors related to the operational conditions (scenario 3). The main objective of this paper was to analyse the key factors and sources of uncertainty at a plant-wide scale influencing the most relevant model outputs: direct and indirect (DIR,CO2eq and IND,CO2eq, respectively), effluent quality index (EQI), chemical oxygen demand (COD) and total nitrogen (TN) effluent concentration (CODOUT and TNOUT, respectively). Sensitivity analysis shows that model factors related to the influent wastewater and primary effluent COD fractionation exhibit a significant impact on direct, indirect and EQI model factors. Uncertainty analysis reveals that outflow TNOUT has the highest uncertainty in terms of relative uncertainty band for scenario 1 and scenario 2. Therefore, uncertainty of influential model factors and influent fractionation factors has a relevant role on total nitrogen prediction. Results of the uncertainty analysis show that the uncertainty of model prediction decreases after fixing stoichiometric/kinetic model factors

Antiproliferative effects of Ceratonia siliqua L. on mouse hepatocellular carcinoma cell line

Extracts from pods and leaves of carob (Ceratonia siliqua L.) were tested for their ability to inhibit cell proliferation of mouse hepatocellular carcinoma cell line (T1). The two extracts showed a marked alteration of T1 cell proliferation in a dose-related fashion reaching the maximal effect at 1 mg/ml. Moreover, we demonstrated that leaf and pod extracts were able to induce apoptosis in T1 cell lines after 24-h treatment mediating a direct activation of the caspase 3 pathway. HPLC analysis revealed the presence of gallic acid, epigallocatechin-3-gallate and (-) epi catechin - 3 -gallate in pod and leaf extracts, compounds well known to exert antiproliferative effects. Their concentration reached 6.28 mg/g in carob leaves and 1.36 mg/g in carob pods extract. The discovery that carob pod and leaf extracts contained antiproliferative agents could be of practical importance in the development of functional foods and/or chemopreventive drugs

Attentional biases in problem and non-problem gamblers

Background: From a cognitive perspective, attentional biases are deemed as factors responsible in the onset and development of gambling disorder. However, knowledge relating to attentional processes in gambling is scarce and studies to date have reported contrasting results. Moreover, no study has ever examined which component and what type of bias are involved in attentional polarization in gambling. Methods: In the present study, 108 Italian participants, equally divided into problem and non-problem gamblers were administered a modified Posner Task, an attentional paradigm in which – through the manipulation of stimuli presentation time – it is possible to measure both initial orienting and maintenance of attention. In addition to the experimental task, participants completed self-report measures involving (i) craving (Gambling Craving Scale), (ii) depression, anxiety and stress (Depression Anxiety Stress Scale) and (iii) emotional dysregulation (Difficulties in Emotion Regulation Scale). Results: Analyses revealed facilitation in detecting gambling-related stimuli at the encoding level in problem gamblers but not in non-problem gamblers. Compared to non-problem gamblers, problem gamblers also reported higher levels of craving, emotional dysregulation, and negative mood states. Furthermore, all measures correlated with the gambling severity. Limitations: The use of indirect measure of attentional bias could be less accurate compared to direct measures. Conclusions: The facilitation in detecting gambling-related stimuli in problem gamblers and the correlation between subjective craving and facilitation bias suggests that attentional polarization could not be due to a conditioning process but that motivational factors such as craving could induce addicted-related seeking-behaviors

Attentional bias in non-problem gamblers, problem gamblers, and abstinent pathological gamblers: an experimental study

Background Attentional biases have been recognized as factors responsible for the maintenance of gambling problems. To date, no study has ever assessed the attentional biases among problem gamblers that have discontinued gambling (e.g., abstinent gamblers in treatment). Methods The sample consisted of 75 participants comprising three groups: non-problem gamblers, problem gamblers, and abstinent pathological gamblers undergoing treatment. The groups were discriminated using South Oaks Gambling Screen scores, with the exception of the abstinent pathological gamblers that already had a DSM-5 diagnosis for gambling disorder. Participants carried out a modified Posner Task for the assessment of attentional bias for gambling stimuli and completed the Depression Anxiety Stress Scale and the Gambling Craving Scale. Results Abstinent pathological gamblers showed an avoidance bias in the maintenance of attention, whereas problem gamblers exhibited a facilitation in detecting gambling stimuli. No biases were detected in non-problem gamblers. The results also demonstrated that compared to the other groups, abstinent pathological gamblers showed high emotional stress and problem gamblers reported a higher level of craving. Limitations The sample size limits the generalizability of results. Conclusions The present study demonstrated that attentional biases affect the maintenance and the discontinuation of gambling activities, and that the subjective feeling of craving for gambling may facilitate problem gamblers’ attention towards gambling stimuli