Relevant Distribution Functions Research Articles

Partition of free energy for a Brownian quantum oscillator: Effect of dissipation and magnetic field

Recently, the quantum counterpart of energy equipartition theorem has drawn considerable attention. Motivated by this, we formulate and investigate an analogous statement for the free energy of a quantum oscillator linearly coupled to a passive heat bath consisting of an infinite number of independent harmonic oscillators. We explicitly demonstrate that the free energy of the Brownian oscillator can be expressed in the form F(T)=〈f(ω,T)〉 where f(ω,T) is the free energy of an individual bath oscillator. The overall averaging process involves two distinct averages: the first one is over the canonical ensemble for the bath oscillators, whereas the second one signifies averaging over the entire bath spectrum of frequencies from zero to infinity. The latter is performed over a relevant probability distribution function P(ω) which can be derived from the knowledge of the generalized susceptibility encountered in linear response theory. The effect of different dissipation mechanisms is exhibited. We find two remarkable consequences of our results. First, the quantum counterpart of energy equipartition theorem follows naturally from our analysis. The second corollary we obtain is a natural derivation of the third law of thermodynamics for open quantum systems. Finally, we generalize the formalism to three spatial dimensions in the presence of an external magnetic field.

Optimal Planning of Multiple Renewable Energy-Integrated Distribution System With Uncertainties Using Artificial Hummingbird Algorithm

Appropriate installation of renewable energy-based distributed generation units (RDGs) is one of the most important challenges and current topics of interest in the optimal functioning of modern power networks. Due to the intermittent nature of renewable energy sources, optimal allocation and sizing of RDGs, particularly photovoltaic (PV) and wind turbine (WT), remains a critical task. Based on a new metaheuristic known as the Artificial hummingbird algorithm (AHA), this paper provides a novel approach for addressing the problem of RDG planning optimization. Considering various operational constraints, the optimization problem is developed with multiple objectives including power loss reduction, voltage stability margin (VSM) enhancement, voltage deviation minimization, and yearly economic savings. Furthermore, using relevant probability distribution functions, the ambiguities related with the stochastic nature of PV and WT output powers are evaluated. The proposed algorithm was compared to two of the recent metaheuristics applied in this domain known as improved harris hawks and particle swarm optimization algorithm (HHO-PSO) and hybrid of phasor particle swarm and gravitational search algorithm (PPSOGSA). The IEEE 33-bus and 69-bus systems are assessed as the test systems in this study. According to the findings, AHA delivers superior solutions and enhances the techno-economic benefits of distribution systems in all the scenarios evaluated.

On the algorithm to perform Monte Carlo simulations in cells with constant volume and variable shape

In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of the box on the fly in the course of the simulation as it may not be known ahead of time which geometry fits the studied system best. In this work we derive an algorithm for this task based on the condition that the distribution of specific geometrical parameter observed in simulations at a constant volume matches that observed in the constant-pressure ensemble. The proposed algorithm is tested for the system of hard-core ellipses which makes lattices of different types depending on the asphericity parameter of the particle. It is shown that the performance of the algorithm critically depends on the range of the sampled geometrical parameter. If the range is narrow, the impact of the sampling method is minimal. If the range is large, inadequate sampling can lead to significant distortions of the relevant distribution functions and, as a consequence, errors in the estimates of free energy.

Solvation of potential stable cations and anions originating from the Martian regolith in select ionic liquids

Element recovery from the Martian regolith using ionic liquids (ILs) is an active area of research within the field of in-situ resource utilization. In this work, we performed a classical molecular dynamics (MD) simulation study to better understand the solvation thermodynamics and structures of potential cationic and anionic species originating from the Martian regolith in two select ILs, i.e., 1-ethyl-3-methylimidazolium acetate ([emim][Ac]) and 1-ethyl-3-methylimidazolium hydrogen sulfate ([emim][HSO4]), at two temperatures of 298.15 and 473.15 K. The studied cationic and anionic species represent the stable ions, i.e., a series of tetra-, tri-, di-, and monovalent cations, as well as several silicate, phosphate, chromate, titanate, and select halide anions, based on the mineral composition of the Martian regolith. We calculated the solvation free energies (SFEs) of these ionic species in the ILs using the free energy perturbation method. Moreover, we investigated the solvation environment of these ionic solutes by generating the relevant radial distribution functions and calculating the running coordination numbers of ILs' anions and cations surrounding the solutes. Overall, the average absolute values of the SFEs for cationic solutes increase with increasing ion valency (charge) and size of the solute at both temperatures. For anionic solutes, a more complex effect of anion molecular size and charge is responsible for the trends observed in the absolute values of the SFEs. For example, we found orthosilicate to be the most soluble anionic species in both ILs. On the other hand, the dichromate anion was found to be essentially insoluble in both ILs. Comparing between the solvation efficiencies of the ILs, [emim][Ac] shows larger negative SFE values than [emim][HSO4] for all cationic solutes at both temperatures. While the temperature effect on the solvation of cationic solutes is mixed, higher temperatures generally favor the dissolution of the anionic solutes in both ILs. Our results provide molecular insights into the solvation thermodynamics of various potential ionic species that may be extracted from the Martian regolith using suitable ILs.

Strategic planning of renewable distributed generation in radial distribution system using advanced MOPSO method

The integration of wind turbine, solar photovoltaic based distributed generation in low voltage distribution network has many advantages. However, the output power from wind turbine and solar PVs are intermittent in nature. The production of these intermittent power generations may introduce many challenges in distribution network such as increase in power losses, voltage deviation and instability. Therefore, this paper proposes optimal integration of these intermittent renewable DGs along with biomass and capacitor banks to optimize distribution network parameters. The real time wind speed and solar irradiance data are processed in time series mathematical model along with relevant probability distribution function (PDF) for calculating the accurate power output from these renewable resources. Later, an advanced multi-objective particle swarm optimization technique has been used to optimize the distribution network parameters such as power losses, voltage deviation and voltage stability index. The proposed model has been validates and tested on Portuguese 94 bus system. Moreover, the proposed model results revealed the power loss reduction up to 77.82%, voltage deviation 9.68% and voltage stability index 44.25%.

A study of the role of the PDF uncertainty on the LHC -boson mass measurement

The determination of the W-boson mass through an analysis of the decay charged-lepton transverse momentum distribution has a sizable uncertainty due to the imperfect knowledge of the relevant parton distribution functions (PDFs). In this paper, a quantitative assessment of the W-boson mass uncertainty at the LHC resulting from the PDF uncertainty is examined. We use the CT14 NNLO PDFs with a NNLL + NNLO calculation (ResBos) to simulate the W-boson production and decay kinematics. The uncertainty of the W-boson mass determination is then determined as a function of the boson and lepton kinematics. For W+ production using and (GeV) < 45, PDF uncertainties lead (at the 68% CL) to a mass uncertainty for the of MeV, MeV, and MeV, are determined at 7 TeV, 8 TeV and 13 TeV, respectively. The uncertainties of for the same cuts are found to be MeV, MeV and MeV, at 7 TeV, 8 TeV and 13 TeV, respectively.

Relaxation of one-dimensional collisionless gravitating systems

In an effort to better understand collisionless relaxation processes in gravitational systems, we investigate one-dimensional models. Taking advantage of a Hermite-Legendre expansion of relevant distribution functions, we present analytical and numerical behaviors of Maxwell-Boltzmann entropy. In particular, we modestly perturb systems about a separable-solution equilibrium and observe their collisionless evolution to a steady state. We verify the time-independence of fine-grained entropy in these systems before turning our attention to the behavior of coarse-grained entropy. We also verify that there is no analogue to the collisional H-theorem for these systems. Competing terms in the second-order coarse-grained entropy make it impossible to guarantee continuously increasing entropy. However, over dynamical time-scales the coarse-grained entropy generally increases, with small oscillations occurring. The lack of substantive differences between the entropies in test-particle and self-gravitating cases suggests that phase mixing, rather than violent relaxation associated with potential changes, more significantly drives the coarse-grained entropy evolution. The effects of violent relaxation can be better quantified through analysis of energy distributions rather than phase-space distributions.

Experimental investigations of the magnetic asymmetry effect in capacitively coupled radio frequency plasmas

The electrical asymmetry effect allows control of the discharge symmetry, the DC self-bias, and charged particle energy distribution functions electrically by driving a capacitive radio frequency discharge with multiple consecutive harmonics with fixed, but adjustable relative phases. Recently, Trieschmann et al (2013 J. Phys. D: Appl. Phys. 46 084016) and Yang et al (2017 Plasma Process. Polym. 14 1700087; 2018 Plasma Sources Sci. Technol. 27 035008) computationally predicted that the discharge symmetry can also be controlled magnetically via the magnetic asymmetry effect (MAE). By particle-in-cell simulations they demonstrated that a magnetic field, that is parallel to the electrodes and inhomogeneous in the direction perpendicular to the electrodes, induces a discharge asymmetry due to different ion densities adjacent to both electrodes. This, in turn, is predicted to lead to the generation of a DC self-bias as a function of the difference of the magnetic field at both electrodes. In this way the MAE should allow control of the mean ion energy at both electrodes as a function of the magnetic field configuration. Here, we present the first experimental investigation of the MAE. In a low pressure discharge operated in argon at 13.56 MHz, we use a magnetron-like magnetic field configuration at the powered electrode, which leads to an inhomogeneous profile of the magnetic field perpendicular to the electrodes. By measuring the DC self-bias and the ion flux-energy distribution function at the grounded electrode as a function of the magnetic field strength at the powered electrode, the driving voltage amplitude and the neutral gas pressure we experimentally verify the concept of the MAE and demonstrate this technology to be a powerful method to control the discharge symmetry and process relevant energy distribution functions.

Detection of an event and its location in a wireless sensor network

Wireless sensor networks (WSNs), which can often be installed quickly and fairly economically, are useful for detecting threats (or events) in a region of interest. As the data received from sensor nodes contain measurement and transmission errors, interpreting the data requires appropriate statistical methods and algorithms. In particular, deciding if an event is present in the network region or not and inferring the location of the event when it is deemed present are two important decision problems. We give a statistical framework for addressing these two problems and frame them as one estimation problem. We present a solution based on the maximum likelihood method and evaluate its performance by simulation. We also describe a Bayesian approach that can be used when relevant prior distribution and loss function are available.

Detection of an event and its location in a wireless sensor network

Wireless sensor networks WSNs, which can often be installed quickly and fairly economically, are useful for detecting threats or events in a region of interest. As the data received from sensor nodes contain measurement and transmission errors, interpreting the data requires appropriate statistical methods and algorithms. In particular, deciding if an event is present in the network region or not and inferring the location of the event when it is deemed present are two important decision problems. We give a statistical framework for addressing these two problems and frame them as one estimation problem. We present a solution based on the maximum likelihood method and evaluate its performance by simulation. We also describe a Bayesian approach that can be used when relevant prior distribution and loss function are available.

Methanol-methanol and methanol-water systems: the intermolecular interactions controlling the transition from small clusters to the liquid phase.

The present paper focuses on the characterization of the properties of methanol and water molecules in gas and liquid environments. A force field for methanol-methanol and methanol-water interactions, useful to be applied in Molecular Dynamics (MD) simulations, is proposed. The electrostatic interaction contributions, arising from permanent charge and/or from anisotropic charge distributions originating from permanent electric multipoles (Vel), different in gas and in liquid phases, are combined with the non electrostatic ones (Vnel), defined by means of Improved Lennard-Jones (ILJ) functions [F. Pirani et al., Phys. Chem. Chem. Phys., 2008, 10, 5489-5503]. Interestingly, the relevant parameters of the ILJ functions are not fitted to reproduce the selected properties of the systems but calculated from the molecular polarizability, which is considered the key property to define size (or Pauli) repulsion and dispersion and induction attractions. The constructed force field predicts binding energies and geometries of the methanol-methanol and methanol-water dimers, in good agreement with available data. On the other hand, several bulk and structural properties of liquid methanol, such as densities, vaporization enthalpies, diffusion coefficients, coefficients of cubic thermal expansion, heat capacities at constant pressure and some relevant radial distribution functions, calculated considering 2744 molecules and different conditions of pressure and temperature, have also been found to be in good agreement with experimental data. The study has been completed by calculating the density values at 298 K and 1 bar of some methanol-water mixtures, which have also been found to be in good agreement with experimental data.

Effective potentials in a bidimensional vibrated granular gas.

We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a nonstatic steady state via vertical shaking. The simulations explore a wide range of vertical accelerations, restitution coefficients, and packing fractions, always staying below the crystallization limit. From the simulations we obtain the relevant pair distribution functions (PDFs), and effective potentials for the interparticle interaction are extracted from these PDFs via the Ornstein-Zernike equation with the Percus-Yevick closure. The correlations in the granular structures originating from these effective potentials are checked against the originating PDF using standard Monte Carlo simulations, and we find in general an excellent agreement. The resulting effective potentials show an increase of the spatial correlation at contact with the decreasing values of the restitution coefficient, and a tendency of the potentials to display deeper wells for more dissipative dynamics. A general exception to this trend appears for a range of values of the forcing, which depends on the restitution coefficient, but not on the density, where resonant bouncing increases correlations, resulting in deeper potential wells. The nature of these resonances is explored and shown to be the result of synchronization in the parabolic flights of the particles.

A force field for acetone: the transition from small clusters to liquid phase investigated by molecular dynamics simulations

A new semiempirical force field for the intermolecular (CH $$_{3}$$ –CO–CH $$_{3}$$ )–(CH $$_{3}$$ –CO–CH $$_{3}$$ ) interaction has been built and applied to characterize the acetone behavior in different environments. Molecular dynamics simulations of some small clusters and liquid phase have been carried out. In particular, the behavior of the dimer and the trimer has been analyzed considering a microcanonical ensemble (NVE). Predictions of the (CH $$_{3}$$ –CO–CH $$_{3}$$ ) $$_{2-3}$$ binding energies have been provided by extrapolating to 0 K the mean potential energy values evaluated at low temperatures. The probability of isomerization processes has been also analyzed. Molecular dynamics simulations for liquid acetone have been performed, to test the generality of the force field formulation, considering an isothermal–isobaric (NpT ensemble) of 1000 molecules. Different conditions of pressure and temperature have been taken into account. Structural details of liquid have been analyzed through some relevant radial distribution functions, from which the coordination number has been evaluated. The model predictions for both small clusters and liquid acetone have been compared successfully with available experimental and/or theoretical results.

Bottom-Up Coarse-Graining of Peptide Ensembles and Helix-Coil Transitions.

This work investigates the capability of bottom-up methods for parametrizing minimal coarse-grained (CG) models of disordered and helical peptides. We consider four high-resolution peptide ensembles that demonstrate varying degrees of complexity. For each high-resolution ensemble, we parametrize a CG model via the multiscale coarse-graining (MS-CG) method, which employs a generalized Yvon-Born-Green (g-YBG) relation to determine potentials directly (i.e., without iteration) from the high-resolution ensemble. The MS-CG method accurately describes high-resolution models that fluctuate about a single conformation. However, given the minimal resolution and simple molecular mechanics potential, the MS-CG method provides a less accurate description for a high-resolution peptide model that samples a disordered ensemble with multiple distinct conformations. We employ an iterative g-YBG method to develop a CG model that more accurately describes the relevant distribution functions and free energy surfaces for this disordered ensemble. Nevertheless, this more accurate model does not reproduce the cooperative helix-coil transition that is sampled by the high resolution model. By comparing the different models, we demonstrate that the errors in the MS-CG model primarily stem from the lack of cooperative interactions afforded by the minimal representation and molecular mechanics potential. This work demonstrates the potential of the MS-CG method for accurately modeling complex biomolecular structures, but also highlights the importance of more complex potentials for modeling cooperative transitions with a minimal CG representation.

NO3(-) coordination in aqueous solutions by (15)N/(14)N and (18)O/(nat)O isotopic substitution: what can we learn from molecular simulation?

We explore the deconvolution of water-nitrate correlations by the first-order difference approach involving neutron diffraction of heavy- and null-aqueous solutions of KNO3 under (14)N/(15)N and (nat)O(N)/(18)O(N) substitutions to achieve a full characterization of the first water coordination around the nitrate ion. For that purpose we performed isobaric-isothermal simulations of 3.5 m KNO3 aqueous solutions at ambient conditions to generate the relevant radial distribution functions required in the analysis (a) to identify the individual partial contributions to the total neutron-weighted distribution function, (b) to isolate and assess the contribution of NO3(-)···K(+) pair formation, (c) to test the accuracy of the neutron diffraction with isotope substitution based coordination calculations and X-ray diffraction based assumptions, and (d) to describe the water coordination around both the nitrogen and oxygen sites of the nitrate ion.

TOWARDS DATA MINING TEMPORAL PATTERNS FOR ANOMALY INTRUSION DETECTION SYSTEMS

A reasonably light-weight host and net-centric Network IDS architecture model is indicated. The model is anomaly based on a state-driven notion of “anomaly”. Therefore, the relevant distribution function need not remain constant; it could migrate from states to states without any a priori warning so long as its residency time at a next steady state is sufficiently long to make valid observations there. Only those intrusion events (basically DOS and DDOS variety) capable of triggering anomalous streams of attacks/response both near and/or far of target monitoring point(s) are considered at the first level of detection. At the next level of detection, the filtered states could be fine-combed in a batch mode to mine unacceptable strings of commands or known attack signatures.

PHYSICAL ORIGIN OF THE POWER-LAW TAILED STATISTICAL DISTRIBUTIONS

Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell–Boltzmann distribution and of the Boltzmann entropy, respectively, and define the statistical mechanics presented in [Phys. Rev. E66 (2002) 056125] and [Phys. Rev. E72 (2005) 036108]. The achievements of the present effort, support the idea that the experimentally observed power-law tailed statistical distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics.

Selection effects in the black hole-bulge relation and its evolution

We present an investigation of sample selection effects that influence the observed black hole - bulge relations and its evolution with redshift. We provide a common framework in which all kinds of selection effects on the BH-bulge relations can be investigated, but our main emphasis is on the consequences of using broad-line AGN and their host galaxies to search for evolution in the BH-bulge relation. We identified relevant sources of bias that were not discussed in the literature so far. A particularly important effect is caused by the fact that the active fraction among SMBHs varies considerably with BH mass, in the sense that high-mass BHs are less likely to be active than lower mass ones. In the connection with intrinsic scatter of the BH-bulge relation this effect implies a bias towards a low BH mass at given bulge property. This effect adds to the bias caused by working with luminosity or flux limited samples that were already discussed by others. A quantitative prediction of these biases requires (i) a realistic model of the sample selection function, and (ii) knowledge of relevant underlying distribution functions. For low-redshift AGN samples we can naturally reproduce the flattening of the relation observed in some studies. When extending our analysis to higher redshift samples we are clearly hampered by limited empirical constraints on the various relevant distribution functions. Using a best-guess approach for these distributions we estimate the expected magnitude of sample selection biases for a number of recent observational attempts to study the BH-bulge evolution. In no case do we find statistically significant evidence for an evolving BH-bulge relation. We suggest a possible practical approach to circumvent several of the most problematic issues connected with AGN selection; this could become a powerful diagnostic in future investigations (abridged).

ON SMALL-SIGNAL AMPLIFICATION IN A GYRO-TWT

The corrected dispersion relation governing the linear interaction of a TE mode in a circular cylindrical wave guide with an annular beam of gyrating electrons in a gyro-TWT conflguration is derived. The derivation of the correct dispersion relation no longer involves any integration with respect to the radial coordinate ro of the electron guiding center as the relevant equilibrium distribution function turns out to be independent of ro. When the cyclotron resonance condition is satisfled by the TE mode for a positive s-number, the small-signal theory is shown to predict an initial exponential growth of the mode with interaction length over a small but flnite band of frequencies around the design frequency.

A bi-variate Kernel Estimation Model for Travel Time and Activity Duration

The activity duration in activity-based approach typically has been analyzed by various types of regression models, which manifest relationships between socio-economic variables for independent variables and activity duration for dependent variable. Among various approaches, the most frequently adopted model is the hazard-based model, which is a parametric approach because it assumes the probability distribution of the dependent variable prior to model estimation. Since the distribution is not usually aware of, the assumption of distribution function prior to estimation is sometimes very strong restriction. Especially, when the true distribution has a unique pattern (for example, bimodality shape), we have difficulty in choosing the relevant probability distribution functions. This study aims to develop the activity duration models using kernel density estimator (hereafter „KDE‟). KDE is a type of nonparametric estimation methods and can construct the probability distribution including some special features, which parametric methods hardly