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At least 685 records · Page 38

Cosmological density fluctuations and large-scale structure From N-point correlation functions to the probability distribution

Knowledge of N-point correlation functions for all N allows one to invert and obtain the probability distribution of mass fluctuations in a fixed volume. The hierarchical sequence of higher order is applied to correlations with dimensionless amplitudes suggested by the BBGKY equations. The resulting distribution is significantly non-Gaussian, even for quite small mean square fluctuations. The qualitative and to some degree quantitative results are to a large degree independent of the exact sequence of amplitudes. An ensemble of such models compared with N-body simulations fails in detail to account for the low-density frequency distribution.

Fry, J. N.↗

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Steely, Sidney L.↗

Probability density distribution of velocity differences at high Reynolds numbers

Recent understanding of fine-scale turbulence structure in high Reynolds number flows is mostly based on Kolmogorov's original and revised models. The main finding of these models is that intrinsic characteristics of fine-scale fluctuations are universal ones at high Reynolds numbers, i.e., the functional behavior of any small-scale parameter is the same in all flows if the Reynolds number is high enough. The only large-scale quantity that directly affects small-scale fluctuations is the energy flux through a cascade. In dynamical equilibrium between large- and small-scale motions, this flux is equal to the mean rate of energy dissipation epsilon. The pdd of velocity difference is a very important characteristic for both the basic understanding of fully developed turbulence and engineering problems. Hence, it is important to test the findings: (1) the functional behavior of the tails of the probability density distribution (pdd) represented by P(delta(u)) is proportional to exp(-b(r) absolute value of delta(u)/sigma(sub delta(u))) and (2) the logarithmic decrement b(r) scales as b(r) is proportional to r(sup 0.15) when separation r lies in the inertial subrange in high Reynolds number laboratory shear flows.

Praskovsky, Alexander A.↗

A reaction mechanism for plasma electrolysis of AgNO 3 forming silver nanoclusters and nanoparticles

In plasma-driven solution electrolysis (PDSE), gas-phase plasma-produced species interact with an electrolytic solution to produce, for example, nanoparticles. An atmospheric pressure plasma jet (APPJ) directed onto a liquid solution containing a metallic salt will promote reduction of metallic ions in solution, generating metallic clusters that nucleate to form nanoparticles. In this article, results from a computational investigation are discussed of a PDSE process in which a radio-frequency APPJ sustained in helium impinges on a silver nitrate solution, resulting in growth of silver nanoparticles. A reaction mechanism was developed and implemented in a global plasma chemistry model to predict nanoparticle growth. To develop the reaction mechanism, density functional theory was used to generate probable silver growth pathways up to Ag 9 . Neutral clusters larger than Ag 9 were classified as nanoparticles. Kinetic reaction rate coefficients for thermodynamically favorable growth pathways were estimated based on an existing, empirically determined base reaction mechanism for smaller Ag particle interactions. These rates were used in conjunction with diffusion-controlled reaction rate coefficients that were calculated for other Ag species. The role of anions in reduction of Agn ions in forming nanoparticles is also discussed. Oxygen containing impurities or admixtures to the helium, air entrainment into the APPJ, and dissociation of saturated water vapor above the solution can produce additional reactive oxygen species in solution, resulting in the production of anions and O 2 – in particular. For a given molarity, delivering a sufficient fluence of reducing species will produce similar nanoparticle densities and sizes for all applied power levels. In conclusion, comparisons are made to alternate models for nanoparticle formation, including charged nanoparticles and use of direct current plasmas.

36 MATERIALS SCIENCE↗

Fisher for complements: extracting cosmology and neutrino mass from the counts-in-cells PDF

In this work, we comprehensively analyse the cosmology dependence of counts-in-cells statistics. Furthermore, we focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass Mν and can disentangle it from the clustering amplitude σ 8 . Additionally, using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ 8 and the total neutrino mass Mν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ω m by a factor of 5 and σ 8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h -1 ) 3 . We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Helicity fluctuations in incompressible turbulent flows

Results from direct numerical simulations of several homogeneous flows and fully developed turbulent channel flow indicate that the probability distribution function (pdf) of relative helicity density exhibits at most a 20 percent deviation from a flat distribution. Isotropic flows exhibit a slight helical nature but the presence of mean strain in homogeneous turbulence suppresses helical behavior. All the homogeneous turbulent flows studied show no correlation between relative helicity density and the dissipation of turbulent kinetic energy. The channel flow simulations indicate that, except for low-dissipation regions near the outer edge of the buffer layer, there is no tendency for the flow to be helical. The strong peaks in the relative helicity density pdf and the association of these peaks with regions of low dissipation found in previous simulations by Pelz et al.(1985) are not observed.

Rogers, Michael M.↗

On minimizing the probability of misclassification for linear feature selection

The use of techniques for feature selection permits treatment of classification problems in spaces of reduced dimensions. A method is considered of linear feature selection for n-dimensional observation vectors which belong to one of two populations, where each population is described by a known multivariate normal density function. More specifically, the problem of finding a 1xn transformation matrix B for which the probability of misclassification with respect to the one-dimensional transformed density functions was minimized was considered. Theoretical results are presented which give rise to a numerically tractable expression for the variation in the probability of misclassification with respect to B. Using this expression a computational procedure is discussed for obtaining a B which minimizes the probability of misclassification. Preliminary numerical results are discussed.

Guseman, L. F., Jr.↗

On Orbital Elements of Extrasolar Planetary Candidates and Spectroscopic Binaries

We estimate probability densities of orbital elements, periods, and eccentricities, for the population of extrasolar planetary candidates (EPC) and, separately, for the population of spectroscopic binaries (SB) with solar-type primaries. We construct empirical cumulative distribution functions (CDFs) in order to infer probability distribution functions (PDFs) for orbital periods and eccentricities. We also derive a joint probability density for period-eccentricity pairs in each population. Comparison of respective distributions reveals that in all cases EPC and SB populations are, in the context of orbital elements, indistinguishable from each other to a high degree of statistical significance. Probability densities of orbital periods in both populations have P(exp -1) functional form, whereas the PDFs of eccentricities can he best characterized as a Gaussian with a mean of about 0.35 and standard deviation of about 0.2 turning into a flat distribution at small values of eccentricity. These remarkable similarities between EPC and SB must be taken into account by theories aimed at explaining the origin of extrasolar planetary candidates, and constitute an important clue us to their ultimate nature.

Stepinski, T. F.↗

On differentiating the probability of error in multipopular feature selection

A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities.

Peters, B. C.↗

Statistical characteristics of laser interference and its effect on IR optoelectronic observation systems

We consider statistical characteristics of laser interference recorded in the focal region of an IR optoelectronic observation system under field and out-of-field illumination by laser radiation. The applicability of the analytical description of experimental histograms of the laser interference signal distribution at the photodetector array output using the probability density approximations in the form of gamma distribution and the Gaussian function is substantiated. It is shown that the specific form of these functions is determined both by the mean value (mathematical expectation) of the interference signal and by the characteristic parameter M, which depends on the statistical properties of the laser interference. (laser applications and other issues in quantum electronics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

LFSPMC: Linear feature selection program using the probability of misclassification

The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.

Guseman, L. F., Jr.↗

The Aemulus Project. VI. Emulation of Beyond-standard Galaxy Clustering Statistics to Improve Cosmological Constraints

Abstract There is untapped cosmological information in galaxy redshift surveys in the nonlinear regime. In this work, we use the Aemulus suite of cosmological N -body simulations to construct Gaussian process emulators of galaxy clustering statistics at small scales (0.1–50 h −1 Mpc) in order to constrain cosmological and galaxy bias parameters. In addition to standard statistics—the projected correlation function w p ( r p ), the redshift-space monopole of the correlation function ξ 0 ( s ), and the quadrupole ξ 2 ( s )—we emulate statistics that include information about the local environment, namely the underdensity probability function P U ( s ) and the density-marked correlation function M ( s ). This extends the model of Aemulus III for redshift-space distortions by including new statistics sensitive to galaxy assembly bias. In recovery tests, we find that the beyond-standard statistics significantly increase the constraining power on cosmological parameters of interest: including P U ( s ) and M ( s ) improves the precision of our constraints on Ω m by 27%, σ 8 by 19%, and the growth of structure parameter, f σ 8 , by 12% compared to standard statistics. We additionally find that scales below ∼6 h −1 Mpc contain as much information as larger scales. The density-sensitive statistics also contribute to constraining halo occupation distribution parameters and a flexible environment-dependent assembly bias model, which is important for extracting the small-scale cosmological information as well as understanding the galaxy–halo connection. This analysis demonstrates the potential of emulating beyond-standard clustering statistics at small scales to constrain the growth of structure as a test of cosmic acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗

Gravitational microlensing - Powerful combination of ray-shooting and parametric representation of caustics

We present a combination of two very different methods for numerically calculating the effects of gravitational microlensing: the backward-ray-tracing that results in two-dimensional magnification patterns, and the parametric representation of caustic lines; they are in a way complementary to each other. The combination of these methods is much more powerful than the sum of its parts. It allows to determine the total magnification and the number of microimages as a function of source position. The mean number of microimages is calculated analytically and compared to the numerical results. The peaks in the lightcurves, as obtained from one-dimensional tracks through the magnification pattern, can now be divided into two groups: those which correspond to a source crossing a caustic, and those which are due to sources passing outside cusps. We determine the frequencies of those two types of events as a function of the surface mass density, and the probability distributions of their magnitudes. We find that for low surface mass density as many as 40 percent of all events in a lightcurve are not due to caustic crossings, but rather due to passings outside cusps.

Wambsganss, J.↗

Anisotropy in Thermal Conductivity of Ga2O3 under Irradiation: Ab-initio Investigations

Ga2O3 is a wide-bandgap semiconducting material known for its high breakdown electric field and thermal stability. Its various crystalline forms have shown great potential in power electronics, optoelectronics, and high-temperature applications. Specifically, ß-Ga2O3 has been recognized for its suitability in neutron and gamma radiation detection, making it ideal for sensor and detector applications [1]. Notably, ß-Ga2O3 exhibits anisotropic thermal conductivity, meaning that the magnitude of thermal conductivity varies with the crystallographic direction [2]. Under neutron irradiation, Ga2O3 undergoes a significant phenomenon, resulting in the formation of Helium bubbles within its crystalline matrix. The presence of Helium in Ga2O3 has been found to influence the material's anisotropic thermal conductivity. In this study, the objectives were twofold: firstly, to employ Density Functional Theory (DFT) to determine the most probable sites of Helium occupation in ß-Ga2O3, and secondly, to investigate the anisotropic variation in thermal conductivity when Helium is present in the crystalline matrix of ß-Ga2O3. These ab-initio DFT studies provide crucial insights into understanding the behavior of Helium in Ga2O3 and its impact on thermal conductivity, which can contribute to further advancements in sensor and detector applications based on this wide-bandgap semiconductor.

36 MATERIALS SCIENCE↗

Generalized Maximum Entropy

A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].

Cheeseman, Peter↗

Prospects for Surrogate Neutron Capture Measurements with Radioactive Ion Beams and GODDESS

Neutron capture reactions are responsible for the synthesis of almost all of the elements heavier than iron through the slow s-process, that proceeds close to the line of stability, and the rapid r-process, with very neutron-rich waiting points. Uncertainties in (n,γ) rates in neutron rich nuclei, especially near closed neu- tron shells, can have significant impact [1] on the predictions of final abundances for different astrophysical scenarios for the r process. Understanding (n,γ) rates on neutron-rich fission fragments is also important for nuclear forensics and stockpile stewardship science. Ratkiewicz et al. [2 and references therein] has recently demonstrated that the (d,pγ) reaction is a valid surrogate for (n,γ), where the formation of the compound nucleus from the breakup of the deuteron has been calculated in a reaction model and the subsequent measured gamma-decay probabilities are reproduced with standard level density and strength functions in a Bayesian approach. In parallel to the surrogate validation efforts, we have demonstrated that the (d,pγ) reaction can be measured in inverse kinematics with Gammasphere ORRUBA: Dual Detectors for Experimental Structure Studies (GODDESS) [3] where the Gammasphere array of Compton-suppressed HPGe detectors is coupled to the Oak Ridge Rutgers University Barrel Array of position-sensitive silicon strip detectors. During the commissioning campaign we measured the (d,pγ) reaction with 134 Xe and 95 Mo beams, the latter to demonstrate the surrogate method in inverse kinematics. The present talk will present preliminary results from this campaign including γ-decay probabilities and prospects for surrogate (n,γ) measurements with 143 Ba fission-fragment beams.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dynamic Restructuring Induced Oxygen Activation on AgCu Near Surface Alloys

Recent studies have shown that the addition of Cu to Ag catalysts improves their epoxidation performance by increasing the overall selectivity of the bimetallic catalyst. We have prepared AgCu near-surface alloys and used scanning tunneling microscopy to gain an atomistic picture of O 2 dissociation on the bimetallic system. These data reveal a higher dissociative sticking probability for O 2 on AgCu than Ag(111), and density functional theory (DFT) confirms that the O 2 dissociation barrier is 0.17 eV lower on the alloy. Surprisingly, we find that after a slow initial uptake of O 2 , the sticking probability increases exponentially. Further DFT calculations indicate that surface oxygen reverses the segregation energy for AgCu, stabilizing Cu atoms in the Ag layer. These single Cu atoms in the Ag surface are found to significantly lower the O 2 dissociation barrier. Altogether, these results explain nonlinear effects in the activation of O 2 on this catalytically relevant surface alloy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the normality and accuracy of simulated random processes.

Efficient methods of simulating stationary and nonstationary random processes and envelopes, by using a series of sine or cosine functions or by using the fast Fourier transform, have been proposed previously. Without applying the central limit theorem, it is shown in this paper that the simulated random processes are asymptotically Gaussian processes as the number of terms, N, of sine or cosine functions approaches infinity. The accuracy of the first-order probability densities of the simulated random processes is investigated by using the fast Fourier transform. Numerical results are computed with respect to the variation of the number of terms, N, of sine or cosine functions used for simulation. It is shown that within the practical range of N, such as 500, the accuracy is remarkably satisfactory even outside the region of 3 standard deviations.

Yang, J.-N.↗