Types Of Scaling Laws Research Articles

Casimir Effects in 2D Dirac Materials (Scientific Summary)

Fluctuation induced interactions originating from electromagnetic fields give rise to the Casimir force. Even though this is a universal interaction, because of the interplay between the response properties of interacting objects and their geometry the Casimir force can have many types of scaling laws, variations in magnitude and sign, and wide dependences on characteristic constants. The Casimir interaction is especially prominent in systems with reduced dimensions at micron and submicron scale separations. In recent years, examining this type of force for many nanostructured and chemically inert materials has become of great interest. Here, we review advances in the field of Casimir physics in the context of 2D layered materials with Dirac energy spectrum, such as graphene and related materials. The focus is on Casimir interactions and frictional effects with emphasis on the zero-point energy summation approach used for calculations. After giving an overview of this powerful technique, the optical response properties of graphene described with different models is presented. Numerical and analytical results in terms of characteristic behaviors for Casimir and Casimir-Polder interactions involving a stack of parallel layers are summarized. Other key results in the expanded graphene materials as well as their Casimir friction are also presented.

Scaling Laws for the Peak Overpressure of a Cannon Blast

For large cannons, blast overpressure can have a detrimental effect on the crew in the near field (i.e., within a distance of 50 tube diameters or calibers from the muzzle center) as well as on the support personnel and equipment in the far field (i.e., at a distance greater than 50 calibers). Therefore, an efficient method to determine the peak overpressure due to a cannon blast is highly desired. In this study, we investigate scaling laws for the peak overpressure, due to the primary blast of a large cannon, with the aim that they can be applied as an efficient method to evaluate the peak overpressure in the far field. We explore two types of scaling laws; each type is based on a power-law model involving a prefactor and an exponent as model parameters. The two types of the power-law models differ in the way they incorporate the polar angle dependence. The first type was proposed by Fansler and Schmidt (1983, “The Prediction of Gun Muzzle Blast Properties Utilizing Scaling,” U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, Report No. ARBRL-TR-02504). They developed a muzzle-center based scaling law (MCSL) in which the polar angle dependence was incorporated through a reference length scale to define a nondimensional or scaled radial distance from the muzzle center and the model parameters were independent of the polar angle. They calibrated the parameters by employing least-squares fit to a wide range of experimental data. In this study, we recalibrated or updated the parameters for the current cannon by using the numerical simulation data for the cannon blast in the near field. Additionally, we developed a second type of scaling law in which the radial distance is defined from the blast center (in contrast to the muzzle center) and scaled using the inner tube diameter. In this model, the angular dependence is incorporated directly into the model parameters. For this model too, we calibrated the parameters by using the numerical simulation data. We observe that both the modified version of the muzzle-center based scaling law as well as the blast-center based scaling law (BCSL) show a significantly closer fit to the numerical and experimental data and achieve a similar level of accuracy. This indicates that the current form or structure of the two types of power-law based scaling models is able to fit well with the near-field data; however, the current methodology requires a calibration process for a given cannon of interest. In the future, with far field data, we plan to evaluate predictions in the far field.

Study of compound particle production in 84Kr-emulsion interactions at 1.7 A GeV

The characteristics of compound particle multiplicity distribution and multiplicity correlations between the compound particle and the grey particle, black particle, shower particle and heavily ionized track particle are investigated in this paper. It is found that the average multiplicities of the grey particle, black particle, shower particle and heavily ionized track particle increase with an increase in the number of compound particles, which can be explained by the impact geometrical model. The compound multiplicity distribution is observed to obey a Koba-Nielson-Olesen (KNO) type of scaling law.

Shift of critical points in the parametrically modulated Hénon map with coexisting attractors

We study how the critical point positions change in the parametrically modulated Hénon map with coexisting period-1 and period-3 attractors. In particular, a new type of scaling law is found coinciding with that evidenced by laser experiments. We show that resonance phenomena play a crucial role in deformation of attractors and their basins of attraction.

Comparison of steady-state and strongly chaotic thermal convection at high Rayleigh number.

Steady-state and time-dependent two-dimensional thermal convection in a Boussinesq, infinite-Prandtl-number fluid with stress-free boundaries has been investigated. Two independent numerical methods have been employed to calculate the evolution of convective flows in a rectangular box with aspect ratio \ensuremath{\lambda}=1.8 in a Rayleigh-number (Ra) range of ${10}^{6}$${10}^{9}$. With increasing Ra, greater than ${10}^{7}$, the flow reveals the presence of disconnected thermals, rather than connected plumes, driven by a persistent large-scale circulation. Such features have also been reported from laboratory convection experiments in the regime of hard turbulence. Extensive calculations were performed (up to 140 overturns) in order to reach the statistically stationary regime for strongly chaotic flows. A Gaussian distribution with a mean value ${\mathrm{Nu}}_{\mathit{t}}$ was derived from the time history of the Nusselt (Nu) numbers. The value of ${\mathrm{Nu}}_{\mathit{t}}$ can be directly obtained by solving the steady-state equations via an iteration procedure. Thus the stationary flow obtained from the steady-state method resembles the turbulent flow in a statistical sense. Since the iteration procedure is about ${10}^{4}$ times faster than calculating the full time-dependent evolution, it allows for the systematic investigation of the heat-transfer Nu-Ra relationship and other types of scaling laws. The steady-state and time-dependent experiments indicate that a power-law exponent of \ensuremath{\beta}=0.315 holds for the Nu-Ra relation for stress-free boundaries in the entire range of Ra. No indication of a jump in the exponent was found in the transition to hard turbulence.

Features of compound multiplicity in heavy-ion interactions at 4.5AGeV/c

This paper mainly deals with some important features of compound multiplicity in the inelastic nuclear reactions induced by 4.5{ital A} GeV/{ital c} carbon and silicon ions in nuclear emulsion. The characteristics of this parameter observed in the present study are compared with the corresponding values obtained for proton-emulsion interactions at the same incident momentum per nucleon. The average compound multiplicity is found to vary linearly with black and heavy particle multiplicities. Finally, the compound multiplicity distributions for carbon- and silicon-emulsion interactions are observed to obey a Koba-Nielsen-Olesen (KNO) type of scaling law.

Fluctuation Spectrum for a New Type of Intermittency in a Coupled Electronic Circuit

A new type of intermittency associated with the transition from uniform to nonuniform chaos in a coupled electronic circuit is studied by means of the fluctuation spectrum theory. The time series are constructed by taking the n -th power of original experimental data obtained near the intermittent transition point. The intermittent behavior is enhanced as the power n is increased. Two types of scaling laws are found for the fluctuation spectra σ(α)'s.

Entropy and redundancy scaling in multihadron production

It was recently proposed by Simak, Sumbera and Zborovsky that the experimental multiplicity distributions at different energies may obey a new type of scaling law when using entropy per unit of rapidity. In this paper we discuss the questions of this proposal concerning the definition of entropy and introduce a characteristic quantity, redundancy, to replace it.

Simplified Scale Modeling Of Turbulent Flame Spread With Implication To Wildland Fires

Scale-model experiments were performed to measure rates of horizontal and up-slope flame spread for models of stem fires (fires of the tree crowns and the fibrous bark on the tree boles) and grass fires and radiant heat flux to the environments. This work was motivated by previous studies of stationary fires in which two different types of scaling laws were proposed, both of which were applicable for turbulent flame spread. Data obtained include radiant heat fluxes, flame heights and depths, and pyrolysis front locations. Comparisons of the measurements with the scaling laws aid understanding of scaling effects on turbulent flame spread; scaling laws for the flame spread in the wildland are suggested.

New type of scaling law and the Bloom-Gilman duality

A new scaling law is studied in accommodation with Bloom-Gilman duality, which forces us to use a new scaling variable. We test the new scaling by using electroproduction data and find that it presents a beautiful description of the pattern of scaling violations.