Maxwellian Distribution Research Articles

ON PERFORMANCE OF ACCEPTANCE SAMPLING PLANS USING SEQUENTIAL PROBABILITY RATIO TEST BASED ON TRUNCATED LIFE TESTS USING SOME DISTRIBUTION FUNCTION

Sequential sampling procedure constitute a powerful tool to achieve experimental efficiency a sequence of sample are taken from the lot and allow the number of samples to be determined entirely by the result of the sampling process, it forms the basis of numerous sequential technique for different applications which was the special case for multiple acceptance plans, the performance of sequential probability ratio test provides better detection for a wide range of source strength and useful in choosing the best statistical test, which take less time to make decision, was developed on the software reliability measure based on failure intensity for the life time random variable for a truncated life test. In this paper, we considered the performance of acceptance sampling plans using sequential probability ration (SPRT) based on truncated life tests on Maxwell distribution and exponential distribution function in terms of obtaining the minimum number of sample sizes necessary to obtain specified average life time under a given consumer’s and producer’s risk. The SPRT provide an alternative to fix the plans that can help diminish producer and consumer risk of reaching at a wrong decision.

Quasi-1D sedimentation of Brownian particles along optical line traps

We studied the Brownian motion of single 1 and 3 µm particles moving along optical line traps oriented in the gravity axis. The finite linear traps are formed using holographic optical tweezers which redistributes the incoming light beam into an elongated super Gaussian profile. Direct observation of the particle’s motion along the gravity axis allowed us to distinguish the non-equilibrium sedimentation of the particle, when the average velocity is 〈uz〉≠0, followed by equilibrium sedimentation when 〈uz〉=0 and the particle establishes the so-called gravitational length. We found that the bottom edge of the linear trap functions as a virtual “floor”, and subsequent Boltzmann distribution analysis of the equilibrium particle trajectories allows the estimation of the particle’s mass in the hundreds of femtograms range. In parallel, we also induced the physisorption of a macromolecule (hyaluronic acid) onto polystyrene microparticle in solution, detecting an increment of the particle’ mass of around 2 picograms. This suggests that the present technique can be used in surface chemistry, as it detects analyte absorption in solutions containing colloids by estimating the mass of both, the colloidal particle and the layer formed around it. On the other hand, we also found that when the longitudinal confinement established by the optical trap length is smaller than twice the particle gravitational length, particles remain suspended indefinitely even in the presence of a density mismatch with the medium, i.e., the notion of sedimentation disappears. Finally, we observed that the optical forces along the linear trap do not alter the Brownian motion of the particles significantly but can exert an extra pushing force on the smallest particles (1 µm) considered.

The local dark matter distribution in self-interacting dark matter halos

We study the effects of dark matter self-interactions on the local dark matter distribution in selected Milky Way-like galaxies in the EAGLE hydrodynamical simulations. The simulations were run with two different self-interacting dark matter models, a constant and velocity-dependent self-interaction cross-section. We find that the local dark matter velocity distribution of the Milky Way-like halos in the simulations with dark matter self-interactions and baryons are generally similar to those extracted from cold collisionless dark matter simulations with baryons. In both cases, the local dark matter speed distributions agree well with their best fit Maxwellian distributions. Including baryons in the simulations with or without dark matter self-interactions increases the local dark matter density and shifts the dark matter speed distributions to higher speeds. To study the implications for direct detection, we compute the dark matter halo integrals obtained directly from the simulations and compare them to those obtained from the best fit Maxwellian velocity distribution. We find that a Maxwellian distribution provides a good fit to the halo integrals of most halos, without any significant difference between the results of different dark matter self-interaction models.

Theory of ion holes in plasmas with flat-topped electron distributions

Coherent bipolar electric field structures with negative unipolar potentials are widely observed in space plasmas. These bipolar structures are often found to be ion Bernstein Greene Kruskal (BGK) modes or ion holes. Most theoretical models of ion holes assume them to be stationary with respect to the background plasma that follows either Maxwellian or kappa-type distribution. In this paper, we present a new theoretical model of ion holes where the structures are non-stationary, and electrons follow flat-topped distribution. We use the classical BGK approach to derive the inequality separating allowed and forbidden simultaneous values of amplitude and spatial width of ion holes. The model reveals that the parametric space for the existence of ion holes decreases with their speed. We applied the developed model to the largest available dataset of ion holes obtained from the magnetospheric multiscale spacecraft observations in the Earth's bow shock region.

Unidirectional transport of ions and perturbation of plasma distribution functions by ion-acoustic solitons: Numerical simulation and analytical solution

New features of motion of background plasma ions in the presence of ion-acoustic solitons are analyzed by using a hydrodynamic model. Based on the ergodic hypothesis, ion velocity distribution functions are obtained analytically for the first time. It is shown that the initial Maxwellian distribution of ions takes a “beam-like” form in the region of plasmas occupied by solitons. Main parameters of the distribution functions of the background plasma corresponding to solitons of different amplitudes are determined. An important case of soliton trains motion, which often observed in experiments, as well as some other experimental aspects are also considered.

Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient

Two different kinetic theories [J. Solsvik and E. Manger (SM), Phys. Fluids 33, 043321 (2021) and Garzó et al. (GDH), Phys. Rev. E 76, 031303 (2007)] are considered to determine the shear viscosity η for a moderately dense granular binary mixture of smooth hard spheres. The mixture is subjected to a simple shear flow and heated by the action of an external driving force (Gaussian thermostat) that exactly compensates the energy dissipated in collisions. The set of Enskog kinetic equations is the starting point to obtain the dependence of η on the control parameters of the mixture: solid fraction, concentration, mass and diameter ratios, and coefficients of normal restitution. While the expression of η found in the SM-theory is based on the assumption of Maxwellian distributions for the velocity distribution functions of each species, the GDH-theory solves the Enskog equation by means of the Chapman–Enskog method to first order in the shear rate. To assess the accuracy of both kinetic theories, the Enskog equation is numerically solved by means of the direct simulation Monte Carlo method. The simulation is carried out for a mixture under simple shear flow, using the thermostat to control the cooling effects. Given that the SM-theory predicts a vanishing kinetic contribution to the shear viscosity, the comparison between theory and simulations is essentially made at the level of the collisional contribution ηc to the shear viscosity. The results clearly show that the GDH-theory compares with simulations much better than the SM-theory over a wide range of values of the coefficients of restitution, the volume fraction, and the parameters of the mixture (masses, diameters, and concentration).

Parameter Dependencies of Early‐Stage Tangential Discontinuity‐Driven Foreshock Bubbles in Local Hybrid Simulations

AbstractForeshock bubbles (FBs) are significant foreshock transients that can accelerate particles and disturb the magnetosphere‐ionosphere system. In the kinetic formation model, foreshock ions interact with the discontinuity by performing partial gyrations to generate currents that change the magnetic field topology around the discontinuity. However, how different foreshock ion properties affect the growth of the field variations is not well understood. Therefore, we use 2‐D local hybrid simulations to study the effects of different foreshock ion distributions and properties on the growth of tangential discontinuity (TD)‐driven FBs. We discover that for a gyrophase‐bunched distribution with an initial phase where the guiding center is on the other side of the TD, the foreshock ions gyrate together across the TD, causing more foreshock ions to cross the TD and leading to a faster expansion of the structure than for a Maxwellian distribution. A ring distribution also yields higher expansion speeds because of the higher projected velocity into the new perpendicular direction. For Maxwellian distributions, there are positive and linear correlations of the FB expansion speeds with the initial foreshock ion densities, thermal speeds, parallel speeds, and sine of the TD magnetic shear angles. These parameter dependencies grow in strength as the structures evolve with time. The foreshock ion distributions and properties that lead to stronger currents produce more significant magnetic field variations and higher expansion speeds. Our study helps quantify the formation and expansion of FBs to forecast their space weather effects and contribution to shock acceleration.

Cav2.1 channels divide into two populations at resting membrane potentials.

Voltage-gated CaV2.1 channels mediate P/Q-type currents and are the predominant CaV isoform in the brain, linking neuronal excitability to neurotransmitter release. Their pore-forming α1A subunit has four homologous, non-identical, voltage-sensing domains (VSDs) but their contributions to voltage-dependent regulation remain unclear. We utilized cut-open oocyte voltage-clamp fluorometry to optically track the activation of individual VSDs in conducting CaV2.1 complexes composed of the human α1A, together with α2δ and β2a, in the absence of Ca2+-dependent regulation. Previously, we showed that VSDs III and IV activate with a single Boltzmann distribution and have similar midpoint potentials (V0.5,III≈V0.5,IV≈−65mV).

Early Microjet Experimentation with Liquid Water in Vacuum.

ConspectusIn this brief look at the history of liquid microjets, I recollect some personal reminiscences on initial challenges for introduction of this method, as well as unexpected problems and exemplary results using this new tool for liquid evaporation and photoelectron spectroscopy studies.Many efficient and direct, atomic level diagnostic instruments in use at solid state surfaces and in gas-phase atom or cluster studies require high vacuum. They have therefore not been applied to investigations of aqueous solutions because liquid water both strongly evaporates and rapidly freezes in vacuum. Only fairly recently, over the past three decades, have liquid microjets been considered as practicable targets for research on liquid-water interfaces in vacuum. The working principle is analogous to the functioning of a free molecular beam source, where molecules enter through a small aperture into a vacuum without being disturbed by subsequent collisions in their original Maxwellian velocity distribution. Similarly, above a microjet surface in vacuum, water vapor molecules do not interact with each other, or with different probe particles, as long as the liquid jet diameter is small in relation to the mean free path of the liquids' vapor at equilibrium conditions. For pure liquid water, this constraint is Djet < λvap < 10 μm for 6.1 mbar vapor pressure at the triple point of water. A high streaming velocity of the liquid jet, >50 m/s, delays freezing and exposes a steadily renewed fresh vacuum surface for experiments.For experimental verification of the microjet free surface concept, H2O vapor velocities were measured in a molecular beam time-of-flight experiment. These studies showed Maxwellian velocity distributions with the expected local water-jet temperatures for 5 and 10 μm jets, whereas larger liquid jet diameters of 50 μm exhibit narrowed vapor velocity profiles. This narrowing is the known signature of incipient, collision dominated, supersonic hydrodynamic expansions in nozzle beam sources. As a completely unexpected new result in evaporation studies of carboxylic acid solutions, freely evaporating acetic acid dimers showed apparent non-equilibrium liquid surface source temperatures several hundred kelvin above the simultaneously measured monomer temperatures, a phenomenon shown to be correlated with surface tension.Continuing with improvements, the vacuum water microjets were implemented inside a photoelectron spectroscopy apparatus that was modified for handling large amounts of water vapor. After initial complications with liquid jet charging phenomena, the first partial liquid-water photoelectron spectra were recorded using 21 eV photons from a He I discharge lamp. In the next step, the equipment was taken to a synchrotron radiation beamline at BESSY II, resulting in substantial improvements of signal intensity and in photon tunability for narrow band monochromatic soft X-rays up to 1 keV. Two early examples of these continuing experiments are considered, briefly, for aqueous alkali halide salt solutions and for the pH-value dependent protonation of an NH2/NH3+ group in an amino acid directly in a photoelectron spectrum of a solution.In conclusion, liquid microjets have opened up a completely new approach to studies of arbitrary liquids with chemical and biological relevance.

Filtration of Interstellar Neutral Helium by Elastic and Charge Exchange Collisions in Heliospheric Boundaries

Interstellar neutral (ISN) helium atoms penetrating the heliosphere are used to find the flow velocity and temperature of the very local interstellar medium near the heliosphere. Recently, it was found that, in addition to charge exchange collisions, elastic collisions contribute to the filtration of these atoms outside the heliopause. Momentum exchange between colliding particles related to their angular scattering modifies the properties of the primary and secondary ISN helium populations before the atoms enter the heliosphere. Here, we calculate the transport of ISN helium atoms using plasma and neutral flows from a global three-dimensional heliosphere model. We confirm earlier results based on one-dimensional calculations that the primary population is slowed down and heated by the momentum exchange. Moreover, accounting for momentum exchange in charge exchange collisions results in a faster and warmer secondary population. The paper presents how the velocity and density of these populations vary over the entrance position to the heliosphere. We point out that Maxwell distributions cannot correctly describe these populations. Finally, we calculate the expected Interstellar Boundary Explorer (IBEX) count rates and show that the filtration processes change them significantly. Consequently, future studies of IBEX or Interstellar Mapping and Acceleration Probe (IMAP) observations of ISN atoms should account for these processes.

Thermodynamics of a single mesoscopic phononic mode

In recent decades, the laws of thermodynamics have been pushed down to smaller and smaller scales, within the theoretical field of stochastic thermodynamics and state-of-the-art experiments performed on microfabricated mesoscopic systems. These measurements concern thermal properties of electrons, photons, and mesoscopic mechanical objects. Here we report on the measurements of thermal fluctuations of a single mechanical mode in equilibrium with a heat reservoir. The device under study is a nanomechanical beam with a first flexural mode resonating at $3.8\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$, cooled down to temperatures in the range from 100 to $400\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. The technique is constructed around a microwave optomechanical setup using a cryogenic high electron mobility transistor, and is based on two parametric amplifications implemented in series: an in-built optomechanical ``blue detuned'' pumping plus a traveling wave parametric amplifier stage. We demonstrate our ability to resolve energy fluctuations of the mechanical mode in real time up to the fastest relevant speed given by the mechanical relaxation rate. The energy probability distribution is then exponential, matching the expected Boltzmann distribution. The variance of fluctuations is found to be ${({k}_{B}T)}^{2}$ with no free parameters. Our microwave detection floor is about three times the standard quantum limit at $6\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$; the resolution of our fastest acquisition tracks reached about $100\phantom{\rule{0.16em}{0ex}}\mathrm{phonons}$, and is directly related to the rather poor optomechanical coupling of the device (${g}_{0}/2\ensuremath{\pi}\ensuremath{\approx}0.5\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$). This result is deeply in the classical regime, but shall be extended to the quantum case in the future with systems presenting a much larger ${g}_{0}$ (up to $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}250\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$), potentially reaching the resolution of a single mechanical quantum. We believe that it will open an experimental field, phonon-based quantum stochastic thermodynamics, with fundamental implications for quantum heat transport and macroscopic mechanical quantum coherence.

Sheath formation mechanism in collisional electronegative warm plasma with two-temperature non-extensive distributed electrons and ionization

The sheath formation mechanism is modeled in a four-component collisional electronegative warm plasma considering the behavior of positive ions by fluid equations and of negative ions by the Boltzmann distribution, along with non-extensive distributions of hot and cold electrons. For a more realistic situation, the ion source term and the ionization rate are also included in the basic equations that are solved numerically by applying appropriate boundary conditions. A concept of sheath thickness measurement is established based on two approaches, namely, the zero-electron-density approach and the floating potential approach. An identical behavior of the sheath thickness is observed based on these approaches, which means that the floating potential approach confirms the efficacy of the zero-electron-density approach. Finally, the effects of various parameters such as the temperature of all the plasma species, collisions, ionization rate, and non-extensivity are evaluated on the profiles of the densities of plasma species, electric potential, and net space charge density for better understanding of the sheath formation mechanism. In comparison to electropositive plasma, a sharp fall in the potential for the case of electronegative plasma has been depicted, or in other words, higher potential gradient is realized in the electronegative plasma. Also, increasing negative ion temperature results in the reduced sheath thickness and produces a stronger gradient in the potential.

Screening and relativistic effects on the stark broadening of hydrogenic ion lines in a plasma

In the present work, we compute the amplitude of the real part of the electronic collision operator for the electron broadening of hydrogenic ion lines in plasmas, taking into account the screening effects (the interaction between the free electron (perturber) and the ion (emitter) is governed by Debye potential) and relativistic effects in the dynamics of the perturbing electron. The screening effects are included using the cross section calculated by Debye potential instead of Rutherford cross section and the relativistic effects are included by the modification of the velocity distribution (Maxwell–Jûttner) instead of (Maxwell–Boltzmann) distribution and relativistic mass (mass depend on the velocity). The obtained results are compared with Griem’s theoretical work.

Interaction of organic pollutants with TiO2: a density functional theory study of carboxylic acids on the anatase (101) surface

Understanding the interaction of the carboxylic group with TiO2 is crucial for photocatalytic degradation of pollutants, because aromatic molecules containing carboxylic acid groups are among the most common micropollutants. This study investigated the interactions of the anatase TiO2 (101) surface with several aromatic carboxylic acids: benzoic, nicotinic, salicylic and anthranilic acid, using dispersion-corrected density functional theory (DFT) calculations. For all the molecules studied, we found higher stabilities of monodentate adsorbed configurations over bidentate. Dispersion was found to have a significant effect on adsorption energies. In particular, dispersion gave rise to a tilted monodentate adsorption configuration, where adsorption through interfacial covalent and hydrogen bonds was additionally stabilised by dispersion interactions of the aromatic ring with the surface. Comparative calculations using DFT with empirical dispersion correction and van der Waals-corrected functionals found the relative stabilities of adsorbed structures to be independent of the method of describing dispersion. Thermodynamic probabilities of different adsorption configurations were evaluated using the Boltzmann distribution, and the tilted dispersion-stabilised structures were predicted to be by far the most abundant. Finally, the optical absorption of TiO2-acid systems was modelled, and TiO2-aromatic acid complexes were found to have their optical absorption extended into the visible range.

Scale Mixture of Maxwell-Boltzmann Distribution

This paper presents a new distribution, the product of the mixture between Maxwell-Boltzmann and a particular case of the generalized gamma distributions. The resulting distribution, called the Scale Mixture Maxwell-Boltzmann, presents greater kurtosis than the recently introduced slash Maxwell-Boltzmann distribution. We obtained closed-form expressions for its probability density and cumulative distribution functions. We studied some of its properties and moments, as well as its skewness and kurtosis coefficients. Parameters were estimated by the moments and maximum likelihood methods, via the Expectation-Maximization algorithm for the latter case. A simulation study was performed to illustrate the parameter recovery. The results of an application to a real data set indicate that the new model performs very well in the presence of outliers compared with other alternatives in the literature.

New Control Chart Based On Neutrosophic Maxwell Distribution with Decision Making Applications

New Control Chart Based On Neutrosophic Maxwell Distribution with Decision Making Applications

A reactivity-controlled epitaxial growth strategy for synthesizing large nanocrystals

Large ZnSe nanocrystals are expected to be promising blue-light emitters with an emission peak of 455–475 nm, which is important for the construction of display apparatus. The final size of ZnSe nanocrystals via one-step injection can be varied by the reactivity of the Zn and Se precursors; however, it has a limit of <5 nm. To describe the key factors in determining the final size of ZnSe nanocrystals, we proposed a nuclei number-considered LaMer model based on the Maxwell–Boltzmann distribution of crystal embryos. As a result, a general strategy of reactivity-controlled epitaxial growth was developed to synthesize large ZnSe nanocrystals through sequential injection of high-reactivity and low-reactivity Zn and Se precursors. The resultant ZnSe nanocrystals achieved pure blue emission between 455 and 470 nm. We further fabricated stable, large ZnSe/ZnS core–shell nanocrystals with photoluminescence quantum yields up to approximately 60%. Moreover, the reactivity-controlled epitaxial growth strategy is versatile and could be used to synthesize large ZnSe, CdSe and PbSe nanocrystals with average sizes up to 35 nm, 76 nm and 87 nm, respectively. The control of quantum-confined and classical effects in these large semiconductor nanocrystals will open up new directions for fundamental research and application exploration. Synthesizing Se-based nanocrystals with large diameters remains challenging. Here, a reactivity-controlled epitaxial growth strategy was demonstrated to synthesize nanocrystals of ZnSe, CdSe and PbSe with average diameters of 35 nm, 76 nm and 87 nm, respectively. The large ZnSe nanocrystals emitted pure blue light, which is important for display technology.

Kinetic simulations of ignited mode cesium vapor thermionic converters

Cesium vapor thermionic converters are an attractive method of converting high-temperature heat directly to electricity, but theoretical descriptions of the systems have been difficult due to the multi-step ionization of Cs through inelastic electron–neutral collisions. This work presents particle-in-cell simulations of these converters, using a direct simulation Monte Carlo collision model to track 52 excited states of Cs. These simulations show the dominant role of multi-step ionization, which also varies significantly based on both the applied voltage bias and pressure. The electron energy distribution functions are shown to be highly non-Maxwellian in the cases analyzed here. A comparison with previous approaches is presented, and large differences are found in ionization rates due especially to the fact that previous approaches have assumed Maxwellian electron distributions. Finally, an open question regarding the nature of the plasma sheaths in the obstructed regime is discussed. The one-dimensional simulations did not produce stable obstructed regime operation and thereby do not support the double-sheath hypothesis.

Integrable 3D lattice model in M-theory

It is argued that the supersymmetric index of a certain system of branes in M-theory is equal to the partition function of an integrable three-dimensional lattice model. The local Boltzmann weights of the lattice model satisfy a generalization of Zamolodchikov’s tetrahedron equation. In a special case the model is described by a solution of the tetrahedron equation discovered by Kapranov and Voevodsky and by Bazhanov and Sergeev.

Solving Poisson equation with slowing-down equilibrium distribution for global gyrokinetic simulation

Fusion-born alpha particles in burning plasmas are usually regarded as have a slowing-down distribution, which differs significantly from the Maxwellian distribution of thermal particles in velocity space. A generalized multi-point average method has been developed for gyrokinetic Poisson equation with slowing-down equilibrium distribution using optimization in Fourier space. Its accuracy is verified in both long and short wavelength limits. The influence of changing equilibrium distribution from Maxwellian to slowing-down on gyrokinetic Poisson equation is analyzed to illustrate the significance of the new method. The effect of critical speed in the slowing-down distribution on the field solver is also presented. This method forms an important basis for global gyrokinetic simulation of low-frequency drift Alfvénic turbulence in burning plasmas.