Width Of Distribution Function Research Articles

Novel low-macroscopic-field emission cathodes for electron probe spectroscopy systems

The current state of electron probe methods [including energy loss spectroscopy of inelastically scattered electrons (EELS)] is considered. The analysis concerning the issues of their application, challenges, and limitations is performed. Particular attention is paid to the fundamental limitations and the means to overcome those during electron probe methods’ subsequent development for the study of composite nanostructured materials. It is emphasized that the emitted electron energy spectrum dispersion (or electron energy distribution function width) is one of the main factors limiting a further increase in EELS energy resolution, although the use of direct detection sensors and monochromators allows one to approach the physical limit of this method. Novel low-macroscopic-field electron emitters are synthesized and investigated. Their properties are analyzed and compared with previously obtained specimens. Both energy and temporal resolutions of an EEL system utilizing the suggested cathodes are estimated. The comparison of its characteristics with the corresponding parameters of classical facilities is performed. The obtained results indicate the possibility to achieving a significant growth in energy and temporal resolutions as well as a decrease in the detection threshold of chemical elements with trace concentrations while maintaining relatively high emission current density values.

Exploration-imitation competition in well-mixed and structured populations.

Social physics is the mathematical study of how the flow of ideas can change the behavior of individuals. Models in social physics include processes for searching after new ideas and dispersing them inside the population. The present paper makes use of exploration and imitation processes for the mentioned purpose. A new type of imitation is employed here, in which the imitant strategy is not simply replaced by role model strategy, but rather moves toward it. Our exploration process is additive Gaussian noise. To study these processes, we both analyze and simulate the strategy distribution function. By combining exploration and soft imitation, the width of the strategy distribution function becomes stationary. In this model, regular imitation is a particular limit of soft imitation, where an imitant copies the role model, through which the stationary width of the distribution function disappears. As the network causes complex behavior, soft imitation and exploration have been studied in some complex networks as well. Simulation results show that for a small world, scale-free, random regular, and random network, and by selected parameters in this research, distribution function width reaches stationary states.

Determination of nanoparticle collision cross section distribution functions in low pressure plasma synthesis reactors via ion mobility spectrometry

Low pressure (<20 Torr) non-thermal plasma flow tube reactors are commonly used for the synthesis of high purity nanoparticles (NPs) via nucleation and subsequent growth from vapor phase precursors. In spite of their utility, process monitoring (i.e. output NP size characterization) in such reactors is difficult, as there is a dearth of techniques available for online NP size distribution function measurement. In this study, we developed and applied an ion mobility spectrometry (IMS) system consisting of a low pressure differential mobility analyzer (LPDMA) and electrical detector to determine the collision cross section distribution functions of Si NPs synthesized in a radio frequency non-thermal SiH4–Ar plasma operated at ∼2 Torr (266 Pa). The collision cross section, roughly proportional to projected area, is a parameter quantifying the size and structure of nanometer scale species in the vapor phase. We introduce the collision cross section distribution function as a metric for potential use in online process monitoring in NP synthesis. Proper inversion of the collision cross section distribution function requires a priori knowledge of the LPDMA transfer function. We utilized a tandem differential mobility analyzer approach, coupled with a Twomey–Markwoski based scheme to determine LPDMA transfer functions. Subsequent application of these transfer functions in collision cross section distribution function determination showed that at the outlet of the non-thermal plasma flow tube reactor, both negatively and positively charged Si NPs persisted with nearly identical collision cross section distribution functions. NPs were found to have mode ‘mobility equivalent’ diameters near 10 nm, and via TEM analysis were found to persist at the reactor outlet as small aggregates composed of ∼5 nm diameter primary particles. Size distribution functions inferred from collision cross section measurements were compared to size distribution functions inferred from TEM images; excellent agreements were found between IMS and TEM for both mean mobility equivalent diameter and distribution function width. In total, this study shows that (1) IMS is a viable approach for process monitoring in non-thermal plasma NP flow tube synthesis systems, (2) although NPs are modestly aggregated at low-pressure plasma reactor outlets, the extent of aggregation is considerably less than observed in most atmospheric pressure and equilibrium NP synthesis systems (e.g. flames), and (3) after exiting the plasma reactor, the decharging of NPs from highly negative charge levels to a bipolar charge distribution likely drives aggregation on the plasma boundary.

Study of dielectric relaxation and hydrogen bonding in water + 2-butoxyethanol mixtures using TDR technique

The complex permittivity of 2-butoxyethanol (BE)–water mixtures over entire concentrations has been measured as a function of frequency from 10MHz to 30GHz. All spectra were fitted using Cole–Davidson (CD) relaxation spectral function which gives an asymmetric distribution of relaxation times. As composition of butoxyethanol in water increases the width of distribution function broadens. By using least squares fit method the dielectric parameters such as static dielectric constant (ɛ0), dielectric constant at high frequency (ɛ∞), relaxation time (τ) and relaxation distribution parameter (β) were extracted from complex permittivity spectra at temperature range from 25°C to 0°C. The heterogeneous interaction in unlike molecules and intramolecular interaction in same molecules has been discussed using the excess dielectric properties, Kirkwood correlation factor, thermodynamic properties and Bruggeman factor.

Specular refection at a non-stationary shock: A simple model

Analytic treatments of a particle encountering a collisionless shock have commonly been based on the assumption that the shock surface is quasi-planar with length scales larger than the particle gyroradius. Within this framework, the particle distribution function width is supposed to be conserved in any shock reflection process. It is well known, however, that the thermal energy associated with backstreaming ions upstream of Earth's bow shock is significantly larger than the incident solar wind thermal energy. In a previous study, we found that non-thermal features of ions reflected quasi-adiabatically can be accounted for by considering the effect of small, normally distributed fluctuations of the shock normal over short temporal or spatial scales. The strong dependence of the particle acceleration on shock geometry leads to an increase in the temperature and to a non-thermal tail. Here, we conduct a similar analysis to investigate the effects of small, normally distributed fluctuations in the shock normal direction for specularly reflected ions. This later mechanism is considered of first importance in the dissipation process occurring at quasi-perpendicular shocks. We have derived the probability distribution functions f ( v ∥ ) and f ( v ⊥ ) of ions issued from a specular reflection of incident solar wind in the presence of normal direction fluctuations. These distributions deviate weakly from a Maxwellian, in agreement with the observations. In particular, a qualitative agreement with the ion thermal energy is obtained for fluctuations of the normal orientation in the 5–8° range about the nominal direction. Also, we have found that the shock θ B n has a weak effect on the shape of the distribution. While, not a strong determinant of the reflected distribution characteristics, the dynamical shock structure at ion scales cannot be ignored when accounting for the shock-accelerated particle thermal energy.

Characterization of pore structure of chromatographic adsorbents employed in separation of monoclonal antibodies using size-exclusion techniques

Structural properties of commercial chromatographic adsorbents designated for separation of monoclonal antibodies were investigated using size-exclusion techniques. A batch technique provided the specific pore volumes distributed among small, medium and large pores. Inverse size-exclusion chromatography yielded the partition coefficients of dextran solute probes in medium pores. These data were fitted with one- and two-parametric models corresponding to different pore-size distribution functions and the suitability of the individual models for the characterization of the examined materials was then assessed. The reliability of estimation of the parameters of log-normal distribution of cylindrical pores was investigated. Large uncertainties and a strong correlation of the mean pore diameter and width of distribution function were observed.

Random Field Based Model for Calculation of the Properties of Relaxor Ferroelectric Thin Films

The model of relaxor ferroelectric films is proposed. Its basis is the theory of the random field. It destroys the polar long-range order and transforms it into mixed state of ferroelectric glass (FG) or dipole glass (DG). The spatial distribution of the physical properties of relaxor ferroelectric film was calculated with the random field distribution function. As an example the dependence of the order parameter on film thickness, temperature and distribution function width was obtained. The critical thickness and temperature of the size-driven phase transition from FG to DG state as a function of the film and distribution function were calculated.

Mode Selection Hypothesis in Diffusion-limited Aggregation

A hypothesis for the angular mode selection of diffusion-limited aggregation (DLA) is presented as the width of distribution function for sticking Brownian particles. The expected mode \(\sqrt{3}\pi\) agrees with a near pentagonal symmetry of 5.44 in an actual DLA. The mode-controlled DLA formed by anisotropic random walk is consistent with the mode derived on the basis of the hypothesis. The relationship between the preferred mode and fractal dimension is indicated.

Material-independent determination of anchoring properties on rubbed polyimide surfaces.

A material-independent method for determining liquid-crystal (LC) anchoring energy on rubbed polyimide (PI) surfaces has been devised. This method exploits the changes in the easy axis of rubbed PI film induced by exposure to linearly polarized UV (LPUV) light. The distribution of PI chains in a rubbed film is approximated by a Gaussian function and its width determined from the measured rotation of the LC easy axis as a function of exposure time. A quasimicroscopic free energy of the LC-substrate interface is used to model LC anchoring properties. The experimental and calculated values of the azimuthal anchoring energy are in good agreement and found to depend inversely on the width of the distribution function. The measurements of the width of the chain distribution function provide a simple LC material-independent method for determining the LC anchoring properties. With this method, it is also possible to calculate the strength of the interaction between PI chains and LC molecules.