Disentangling Intra- and Interlayer Disorder in Disordered Carbons via Pair-Angle Distribution Function Analysis

Sklar's Theorem Revisited: An Elaboration of the RRschendorf Transform Approach

Many natural fluids, including crude oils, are complex mixtures of molecules with a broad range of sizes and chemical properties. In such systems, the molecular dynamics is complex and the relaxation and diffusion behavior cannot be described by a single relaxation time or diffusion coefficient. Nevertheless, low field NMR relaxation and diffusion measurements have become powerful tools for the study of such fluids. The complexity can be overcome by analyzing the measurements in terms of one- and two-dimensional distribution functions. The one-dimensional relaxation and diffusion distribution functions are directly related to the composition of the fluids. We also show that from the analysis of the shape of the relaxation and diffusion decay, it is possible to predict the temperature dependence of viscosity. Two-dimensional distribution functions probe further aspects of the molecular dynamics. The correlation between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> relaxation behavior can be used to detect the presence of slow motion and to probe the aggregation of molecules into supermolecular structures. Diffusion–relaxation distribution functions give information about the chemical composition of the fluid.

14 - Copulas and quasi-copulas: An introduction to their properties and applications

In this paper I examine graphical comparisons of one-dimensional (or marginal) distribution functions of alternative estimators. It is shown that areas under the c.d.f. (cumulative distribution function) curve can be given a decision-theoretic interpretation as risk under a bounded absolute-error loss function. I also show that by a simple rescaling of the graph's axes, graphical areas are created which can be interpreted as risk under bounded squared-error loss. The bounded loss functions are applied to compare graphically and numerically the risk of exact distributions of the limited-information maximum likelihood and two-stage least-squares estimators in a simultaneous equations model.

Model-Based Fitting of Single-Channel Dwell-Time Distributions

It is shown that the one-dimensional alpha particle velocity distribution function can be determined from the fluctuation- dissipation theorem based on measurements of lower hybrid wave fluctuations in an equilibrium plasma. This method uses collective Thomson scattering data with large signal-to-noise ratio, but it is applicable only when the alpha particles have an isotropic velocity distribution. 16 refs., 1 fig.

It is shown that the one-dimensional alpha particle velocity distribution function can be determined from a first-order differential equation based on measurements of lower-hybrid wave fluctuations in an equilibrium plasma. This method uses collective Thomson scattering data from an array of detectors placed on a prescribed curve. It is applicable only when the alpha particles have an isotropic velocity distribution.

This paper describes a shape signature that captures the intrinsic geometric structure of 3D objects. The primary motivation of the proposed approach is to encode a 3D shape into a one-dimensional geodesic distribution function. This compact and computationally simple representation is based on a global geodesic distance defined on the object surface, and takes the form of a kernel density estimate. To gain further insight into the geodesic shape distribution and its practicality in 3D computer imagery, some numerical experiments are provided to demonstrate the potential and the much improved performance of the proposed methodology in 3D object matching. This is carried out using an information-theoretic measure of dissimilarity between probabilistic shape distributions.

The anisotropic hypernetted chain approximation is used to calculate the one- and two-particle distribution functions for an ionic fluid confined between two charged surfaces. Particular attention is given to the anisotropic distribution functions g(R,R′), c(R,R′), and ρ(R)g(R,R′) (where g, c, and ρ are the pair distribution, direct correlation, and density functions, respectively). They are plotted for various cases and are used to illustrate the mechanisms of the double-layer interaction and other aspects of the system. The effects of image charges (when each surface is a dielectric boundary) and discrete surface charges are investigated.

The dispersion characteristics of electromagnetic waves in a relativistic plasma having a one-dimensional distribution function established through radiation losses in a strong magnetic field are studied. It is shown that the longitudinal waves in such a plasma exist in a certain frequency interval near the plasma frequency, they propagate at small angles to the external magnetic field, and their phase velocities exceed the velocity of light, as a consequence of which the longitudinal waves do not have clear advantages over other types of waves in terms of generation (their ''Cherenkov'' generation is impossible). The dispersion properties of the electromagnetic waves in the low-frequency intervals of ..omega../sub Hi/ less than ..omega.. less than ..omega../sub He/ and ..omega.. much less than ..omega../sub Hi/ in the ''quasivacuum'' approximation (parallel bar n/sup 2/ -- 1 parallel bar much less than 1) are analogous to the properties of normal waves in a cold plasma in the corresponding frequency intervals. A distinguishing feature of a relativistic plasma is the attenuation of the waves caused by the presence in it of a continuous spectrum of gyrofrequencies and strong spatial dispersion. The instability increments of Alfven and fast magnetosonic waves, connected with the one-dimensionality of the distribution function,more » are found for quasilongitudinal propagation.« less

The evolution of a one-dimensional velocity distribution is studied in the presence of a monochromatic large-amplitude periodic force which is turned on adiabatically. The periodic Vlasov-Poisson equations are solved in the presence of a linearized Fokker-Planck collision term. For a constant driving force, the system is found to approach, after transient oscillations, a steady state which is maintained by one wave at the driving frequency. This is in contrast to the result in the absence of collisions where the steady state tends to be supported by several waves. An analytical solution for the steady-state distribution function in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powers of a small parameter \ensuremath{\Gamma} proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-averaged distribution function correct to first order in \ensuremath{\Gamma}. Comparison with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good accuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined.

Electrochemical impedance spectroscopy (EIS) is a useful method for characterizing the interfacial characteristics of materials such as a passive layer underneath the surface of a titanium-based metal-oxide anode. Conventionally EIS data were interpreted by fitting them with electrically equivalent circuit. However, this method requires the initial knowledge of the structure of the tested material. It is also impossible to model a system with continuous variation of layers. Normally, an electrode with finite dielectric layers can be represented by a series of RC circuits plus an interfacial impedance. To cope with the difficulty of systems with continuous variation, a distribution function may be assumed to describe the distribution of time constant along the thickness of the layers [1]. Still, this approach needs to assume a profile to which the system is restricted. A reverse approach was proposed [2]. Within a layered material, a distribution function g(τ) of the resistance over the time-constant (τ=RC) may result from the discrete or continuous variation of the composition (Figure1). By simply fitting the EIS data into Equation 1, one may obtain the function g(τ), which is directly related to the layered structures of the electrode. This method was previously applied to study a transient passive layer in the Ti-supported metal oxide anode, and showed a continuum over the time constant spectrum [2]. However, direct correlation between the bands and the physically observed layers was not well established. Thus the interpretation method by time-constant domain needs to be validated. In the present work, the growth of a titanium oxide film on top of Ti was studied. This reaction is well studied. The growth kinetics and characterization of the titanium oxide film is well established [3]. Therefore it is considered to be a suitable system to test and validate the use of time-constant spectra for the interpretation of EIS. Commercially pure titanium was polarized in a pH=7 buffer containing phosphate. Preliminary data confirmed that the system showed the growth of a resistance band with a characteristic time constant (Figure 2). This band is different from the other peak representing the surface charge-transfer process. Its position was almost stationary at all voltages. Judging by its increase, it was considered to be related to the dielectric film developed on top of the Ti. Further work will focus on correlating the data with physical data, including thickness and composition information from the literature.

The thermal resistance of soldered Insulated-Gate Bipolar Transistor (IGBT) modules is commonly calculated using a fixed interlayer heat transfer angle, which can lead to junction temperature errors due to inaccurate thermal resistance extraction—especially under varying operating conditions. To address this issue, this paper investigates the internal heat transfer characteristics of soldered IGBT modules and introduces a Transverse Temperature Distribution (TTD) function, defined as a two-dimensional Gaussian function fitted from each material layer temperature data. The TTD function captures the lateral temperature distribution within each material layer and can be updated in real time. By computing the parameters of the TTD function, both transverse and longitudinal heat fluxes at specific coordinate points are derived, allowing the dynamic estimation of local heat flux angles and correction of thermal resistances. Finally, a Cauer thermal network model with real-time thermal resistance adjustment is employed to accurately predict the junction temperature.

The concept of the equivalence of a hard particle (depending on the number of dimensions: hard sphere, disk, or rod, with no attractive interaction) of diameter a in a system of hard particles, and a spherical cavity of radius at least a, is extended to define distribution functions, γn(r1, ···rn), for sets of n cavities in a hard-particle system. A new theorem, relating the excess chemical potential of a hard-particle system to the distribution function of two cavities at zero separation, γ2(r12)|τ12–0, as well as corresponding theorems for higher-order distributions, are derived. The theorems for γ2(r12) and γ3(r1, r2, r3), and some simple physical arguments are used to obtain an approximation to the exact Born–Green–Yvon equation for γ2(r12), the “pair stress approximation” (PSA). The resulting simple equation of state yields very good approximate values for the fourth and fifth virial coefficients for hard disks, and for the fourth virial coefficient for hard spheres. The corresponding zero-separation theorems for higher-order distribution functions yield successively higher- and higher-order approximations to the equation of state and pair distribution function of hard-particle systems. The next-order approximation after PSA results in an integral equation whose solution would yield equations of state exact through the fourth virial coefficient. A rough approximation to the solution of that equation results in an equation of state which agrees very well with molecular dynamics computer calculations, within the entire fluid range, both for hard spheres and hard disks. The equation of state yields minimum specific volumes for both systems, between the fluid and crystal specific volumes at phase transitions observed by molecular dynamics computer calculations. All these approximations become exact for hard rods in one dimension, and the method yields the known expressions for the equation of state and pair distribution function for this system in a particularly simple way.

Multidimensional discrete distributions of probabilities of independent random values were received. Their one-dimensional distribution is widely used in probability theory. Producing functions of those multidimensional distributions were also received.