Variable Number Of Particles Research Articles

Two state particles, mixing entropy and negative temperatures revisited

The interrelation of thermodynamics and statistical properties of quantum systems can be demonstrated with comparatively little mathematical effort using two state systems (or two state particles). Basic results are summarized for this model system. The entropy can be interpreted as the entropy of mixing particles in their low and high energy state. Thus, an apparent single component system can be considered as a two component system with variable particle numbers. This result has recently been generalized for elementary bosonic and fermionic systems or particles with many different excited states. In this case, one has to take into account as many components as different internal states of the particles are available. The numbers of particles of each component, however, are not constant but depend on the temperature at thermal equilibrium according to statistical principles.In the literature, the concept of negative internal temperatures was previously introduced to characterize and describe special inverted occupation probabilities out of thermal equilibrium. This interpretation of inverted occupation numbers is revisited explicitly for nuclear spin systems. The interpretation of inverted occupancy by negative temperature is based on ignoring athermal contributions to the internal energy due to the inversion procedure. Accordingly, negative temperatures are not justified in the case of systems out of thermal equilibrium but seem to be misleading and confusing. Instead, the different states of the particles represent distinctive components possessing different chemical potentials, magnetic moments or other properties. The present paper intends to remove the confusion about negative temperatures. It shows how processes out of thermal equilibrium are described and understood without difficulties by balancing the different kinds of particles together with their energy and production of entropy within the framework of thermodynamics.

Toxicity of aged gasoline exhaust particles to normal and diseased airway epithelia.

Particulate matter (PM) pollution is a leading cause of premature death, particularly in those with pre-existing lung disease. A causative link between particle properties and adverse health effects remains unestablished mainly due to complex and variable physico-chemical PM parameters. Controlled laboratory experiments are required. Generating atmospherically realistic aerosols and performing cell-exposure studies at relevant particle-doses are challenging. Here we examine gasoline-exhaust particle toxicity from a Euro-5 passenger car in a uniquely realistic exposure scenario, combining a smog chamber simulating atmospheric ageing, an aerosol enrichment system varying particle number concentration independent of particle chemistry, and an aerosol deposition chamber physiologically delivering particles on air-liquid interface (ALI) cultures reproducing normal and susceptible health status. Gasoline-exhaust is an important PM source with largely unknown health effects. We investigated acute responses of fully-differentiated normal, distressed (antibiotics-treated) normal, and cystic fibrosis human bronchial epithelia (HBE), and a proliferating, single-cell type bronchial epithelial cell-line (BEAS-2B). We show that a single, short-term exposure to realistic doses of atmospherically-aged gasoline-exhaust particles impairs epithelial key-defence mechanisms, rendering it more vulnerable to subsequent hazards. We establish dose-response curves at realistic particle-concentration levels. Significant differences between cell models suggest the use of fully-differentiated HBE is most appropriate in future toxicity studies.

Investigation of thermodynamic properties of weakly interacting Fermi gas in weakly magnetic field by using the N-E-V distribution and pseudopotential method

Based on the fact that most of low temperature experiments of quantum systems are explored in an external field on condition that the particle numbers, volumes and energies of systems may be changed, the thermodynamic properties of weakly interacting Fermi systems in weak magnetic field are studied by using the statistical distribution of the completely open system with variable particle number, volume, and energy (N-E-V distribution). Firstly, the analytical expressions of internal energy and heat capacity, which are in the Fermi integral form, are obtained in the general case, and the analytical expressions and numerical results of energy and heat capacity are given under the extreme condition of supper-low temperature. The calculation results by the N-E-V distribution (with particle number density being variable) are compared with those by a pseudopotential method (with particle number density being unchanged). It can be found that the deviations of the internal energy and heat capacity calculated by the two different methods are very small, and the N-E-V distribution method can partially compensate for the error caused by the pseudo potential method. The most interesting point of the results obtained by the N-E-V distribution method is that there is a phase transition temperature in the weakly interacting Fermi system in weak magnetic field under the low temperature condition. The phase transition temperature is just in the range where occur the Fermi systems, Bose-Einstein condensation (BEC), Bardeen-Cooper-Schrieffer (BCS) phase transition, and BEC-BCS crossover, and does not vary with strength nor characteristic (attraction or repulsion) of the weak interaction, but it decreases with the strengthening of the external magnetic. When there is no external magnetic, the phase transition temperature is highest (more than 0.184 times Fermi temperature).

Effect of sintering on the fractal prefactor of agglomerates

In a previous study different agglomerates composed by a variable number of primary particles corresponding to extreme and intermediate values of fractal dimension (Df=1, 2 and 3) were characterized to be used as reference shapes in a method for the determination of the fractal dimension of actual agglomerates. In that work, primary particles were assumed to be spherical and with no sintering or necking effects. In this work, the geometrical effect of processes such as coalescence, sintering, flattening, or surface growth is considered to evaluate the impact of these phenomena in the morphological parameters of fractal-like agglomerates. A sintering coefficient is firstly defined. Afterwards, the moment of inertia and radius of gyration of the agglomerate are determined and finally the prefactor of the power–law relationship is obtained as a function of the number of primary particles and the sintering coefficient. The equations proposed are used in a geometrical method to determine the fractal dimension of soot agglomerates, showing that sintering increases the prefactor significantly, which leads to a slight decrease in the fractal dimension of the agglomerates.

On the Validity of Janak’s Theorem and Ground State Energies of Ensembles of Interacting Quantum <i>N</i>-Particle Systems

It is established that for finite number of electrons, N ∞, and in the limit T = 0, the line of reasoning leading to the proof of Janak’s theorem is flawed, based on the incorrect treatment of a mixed state as a pure state. The derivative discontinuity at integral values of N of the total ground state energy, Ev[N], of an interacting N-particle system under an external single-particle potential, v(r), is shown to follow from general quantum principles governing the behavior of ensembles of systems with varying particle number, and its presence is shown to be independent of the particular approximation used in determining the total ground-state energy of an ensemble.

A comment on the paper “Systems with variable energy, volume and number of particles: Evaluation of partition function and thermodynamic quantities” by I.M. Stanković, V.M. Marković, and Lj.Z. Kolar-Anić [1

A comment on the paper “Systems with variable energy, volume and number of particles: Evaluation of partition function and thermodynamic quantities” by I.M. Stanković, V.M. Marković, and Lj.Z. Kolar-Anić [1

Exact results for non-integrable systems

Quantum mechanical many-body systems described by an arbitrary Hamiltonian () are analyzed. It is shown how positive semidefinite operator () properties are able to lead in this case to exact results related to the ground state and the low lying part of the excitation spectrum. This is done independent on dimensionality and integrability. The technique first casts the Hamiltonian in a positive semidefinite form in exact terms ( = + C, where C is a scalar). Second, the ground state is deduced by constructing the most general Hilbert space vector, on which applying , one obtains zero as a result. It is underlined, that the procedure, if applied for variable total number of particles N, allows to obtain information also related to the low lying part of the excitation spectrum. The uniqueness of the ground states can be demonstrated via the study of the kernel of ' = − C. The physical properties of the obtained phases are deduced based on ground state expectation values calculated in terms of the constructed ground states. Since for a fixed structure of , usually the transformation = + C is exact only in a restricted parameter space domain (\U0001d49f), the deduced ground states are present only in \U0001d49f. A global view on the phase diagram is obtained by different transformations of in positive semidefinite form.

System with variable energy, volume and number of particles: Evaluation of partition function and thermodynamic quantities

Partition function and thermodynamic parameters of the system open with respect to energy E, volume V and number of particles N, whereas temperature T, chemical potential μ and pressure P were kept constant, were considered by the procedure proposed by Gibbs. The mean values of variable energy, volume and number of particles were obtained by universal expression for such values. The entropy was determined by its general statistical definition. The thermodynamic potential and other thermodynamic quantities were also turned out naturally.

Geometrical determination of the lacunarity of agglomerates with integer fractal dimension

Different agglomerates composed by a variable number of spherical primary particles corresponding to extreme and intermediate values of fractal dimension ( D f = 1, D f = 2 and D f = 3) are analysed in this work. In each case, the moment of inertia, diameter of gyration and prefactor of the power-law relationship are determined as a function of the number of composing primary particles. The obtained results constitute the geometrical data base for the development of a method for the determination of the fractal dimension of individual agglomerates from their planar projections, although it is not the aim of this paper to describe the method itself. As a result of these calculations, the prefactor of the power-law relationship was shown not to be a constant parameter, but to tend asymptotically to a limit value with increasing number of primary particles. This limit value is closely related with the compactness of the initial geometrical arrangement in the agglomerate, this justifying the historical association of this parameter with the lacunarity of the agglomerate. A correlation for the determination of the prefactor as a function of the fractal dimension and the number of elementary structures is proposed and compared with other methods proposed in the literature.

Omnivision-based KLD-Monte Carlo Localization

Mobile robots operating in real and populated environments usually execute tasks that require accurate knowledge on their position. Monte Carlo Localization (MCL) algorithms have been successfully applied for laser range finders. However, vision-based approaches present several problems with occlusions, real-time operation, and environment modifications. In this article, an omnivision-based MCL algorithm that solves these drawbacks is presented. The algorithm works with a variable number of particles through the use of the Kullback–Leibler divergence (KLD). The measurement model is based on an omnidirectional camera with a fish-eye lens. This model uses a feature-based map of the environment and the feature extraction process makes it robust to occlusions and changes in the environment. Moreover, the algorithm is scalable and works in real-time. Results on tracking, global localization and kidnapped robot problem show the excellent performance of the localization system in a real environment. In addition, experiments under severe and continuous occlusions reflect the ability of the algorithm to localize the robot in crowded environments.

Particle size and mineralogical composition of inorganic colloids in waters draining the adit of an abandoned mine, Goesdorf, Luxembourg

Particle size distributions and the mineralogy of inorganic colloids in waters draining the adit of an abandoned mine (Goesdorf, Luxembourg) were quantified by single particle counting based on light scattering (100 nm–2 μm) combined with transmission electronic microscopy coupled with energy dispersive spectroscopy and selected area electron diffraction. This water system was chosen as a surrogate for groundwaters. The dependence of the colloid number concentration on colloid diameters can be described by a power-law distribution in all cases. Power-law slopes ranged from −3.30 to −4.44, depending on water ionic strength and flow conditions. The same main mineral types were found in the different samples: 2:1 phyllosilicates (illite and mica), chlorite, feldspars (albite and orthoclase), calcite and quartz; with a variable number of Fe oxide particles. The colloid mineralogical composition closely resembles the composition of the parent rock. Spatial variations in the structure and composition of the rock in contact with the waters, i.e. fissured rock versus shear joints, are reflected in the colloid composition. The properties of the study colloids, as well as the processes influencing them, can be considered as representative of the colloids present in groundwaters.

Effect of particle number density in in-line digital holographic particle velocimetry

A digital in-line holographic particle tracking velocimetry (HPTV) system was developed to measure 3D (three-dimensional) velocity fields of turbulent flows. The digital HPTV (DHPTV) procedure consists of four steps: recording, numerical reconstruction, particle extraction and velocity extraction. In the recording step, a digital CCD camera was used as a recording device. Holograms contained many unwanted images or noise. To get clean holograms, digital image processing techniques were adopted. In the velocity extraction routine, we improved the HPTV algorithm to extract 3D displacement information of tracer particles. In general, the results obtained using HPTV were not fully acceptable due to technical limitations such as low spatial resolution, small volume size, and low numerical aperture (NA). The problems of spatial resolution and NA are closely related with a recording device. As one experimental parameter that can be optimized, we focused on the particle number density. Variation of the reconstruction efficiency and recovery ratio were compared quantitatively with varying particle number density to check performance of the developed in-line DHPTV system. The reconstruction efficiency represented the particle number distribution acquired through the numerical reconstruction procedure. In addition the recovery ratio showed the performance of 3D PTV algorithm employed for DHPTV measurements. The particle number density in the range of C o = 13–17 particles/mm3 was found to be optimum for the DHPTV system tested in this study.

Liquid Templating for Nanoparticle Organization into Complex Patterns

Dewetting of thin films of charged polymer solutions produces complex patterns that can be applied to direct nanoparticle organization on solid substrates. The morphology produced by dewetting can be controlled by the solution properties, temperature, and substrate wetting. In this work, new results on this liquid-template self-assembly system are presented, with special emphasis on producing large arrays of organized nanoparticles. On a hydrophilic substrate with complete wetting, the patterns include polygonal networks and parallel-track arrays that extend over several hundreds of microns. These large structures are formed under well-controlled drying conditions and characterized by scanning electron microscopy, which is better suited for the examination of large as well as small areas than atomic force microscopy. On partial wetting substrates, new patterns are observed, including a complex set of parallel curved bands with variable particle number densities.

Particle number renormalization in nearly half-filled Mott Hubbard superconductors

The effects of the Gutzwiller projection on a BCS wave function with varying particle number are considered. We show that a fugacity factor has to be introduced in these wave functions when they are Gutzwiller projected, and derive an expression for this factor within the Gutzwiller approximation. We examine the effects of the projection operator on BCS wave functions by calculating the average number of particles before and after projection. We also calculate particle number fluctuations in a projected BCS state. Finally, we point out the differences between projecting BCS wave functions in the canonical and grand canonical schemes, and discuss the relevance of our results for variational Monte Carlo studies.

Mario Schönberg e a introdução do espaço de Fock na física estatística clássica

Há cerca de cinqüenta anos, numa série pioneira de trabalhos, Mario Schönberg utilizou métodos de segunda quantização para generalizar o teorema de Liouville, introduzindo a idéia de indistinguibilidade entre partículas clássicas. O espaço de Fock, que era considerado um atributo paradigmático dos sistemas quânticos, foi utilizado com rigor matemático e consistência física para construir um formalismo da mecânica estatística clássica descrevendo um sistema com número variável de partículas. Abordagens semelhantes foram redescobertas ao longo das últimas três décadas, em particular no contexto de modelos estocásticos, incluindo processos irreversíveis em redes de spins e reações químicas. Apresentamos uma descrição da teoria de Schönberg, estabelecendo conexões com desenvolvimentos mais recentes. O nosso trabalho é uma contribuição pedagógica, enfatizando a consistência física da utilização da representação número de ocupação em contextos clássicos.

Understanding temperature and chemical potential using computer simulations

Several Monte Carlo algorithms and applications that are useful for understanding the concepts of temperature and chemical potential are discussed. We then introduce a generalization of the demon algorithm that measures the chemical potential and is suitable for simulating systems with variable particle number.

On some properties of Markov processes and Monte Carlo methods for inhomogeneous Boltzmann equation

We consider Markov jump processes, Continuous Time Monte Carlo methods [A. I. Khisamutdinov, Simulation statistical modelling of the kinetic equation of rarefied gases. Dokl. Akad. Nauk SSSR (1988) 302, 75–79 (in Russian).] based on these processes, and the inhomogeneous smoothed Boltzmann equation. In the first place, integral forms of a system of master equations for the processes are constructed and general properties of the solution of the system are inspected. Secondly, we investigate unbiased simulation estimators for the computation of linear functionals on the phase density of the average number of particles; and we investigate the asymptotic behaviour of the variance of one of these estimators when the mean initial number density of particles increases. Third, we touch upon the convergence of the phase density to the solution to the Boltzmann equation. The paper considers the general case of a variable number of particles in the system and describes an example of the application of the methods. The results have relation to the known Direct Simulation Monte Carlo methods.

On some properties of Markov processes and Monte Carlo methods for inhomogeneous Boltzmann equation

We consider Markov jump processes, Continuous Time Monte Carlo methods [A. I. Khisamutdinov, Simulation statistical modelling of the kinetic equation of rarefied gases. Dokl. Akad. Nauk SSSR (1988) 302, 75–79 (in Russian).] based on these processes, and the inhomogeneous smoothed Boltzmann equation. In the first place, integral forms of a system of master equations for the processes are constructed and general properties of the solution of the system are inspected. Secondly, we investigate unbiased simulation estimators for the computation of linear functionals on the phase density of the average number of particles; and we investigate the asymptotic behaviour of the variance of one of these estimators when the mean initial number density of particles increases. Third, we touch upon the convergence of the phase density to the solution to the Boltzmann equation. The paper considers the general case of a variable number of particles in the system and describes an example of the application of the methods. The results have relation to the known Direct Simulation Monte Carlo methods.

Virus‐Associated Trichodysplasia Spinulosa

Background: Virus‐associated trichodysplasia spinulosa (VATD) is a relatively new entity associated with a distinctive histologic picture of distended follicles with excessive production of inner root sheath material. Only two patients have thus far been reported. Both had developed the condition after a kidney transplant. Observation: We report two additional cases of VATD. One is a nineteen year‐old man with a history of acute lymphocytic leukemia, who developed a papular facial eruption as well as madarosis. The other is a nine year‐old boy, who presented with facial papules after a kidney transplant. Histologic examination of both cases reveals characteristic findings for trichodysplasia spinulosa, but also indicates a spectrum of histologic alterations. Ultrastructural studies confirm the presence of a variable number of intranuclear viral particles. Conclusions: Our cases illustrate the histologic spectrum seen in association with VATD. The severity of histologic alterations corresponds to the viral load seen by electron microscopy. This report documents for the first time that VATD can be found in patients without a solid organ transplant. Increased awareness of the distinct histologic picture associated with VATD will likely lead to more frequent diagnosis of this under‐recognized entity.

Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid - Mott insulator cross-over and its analog for attractive interactions is recognized.