Search

It is well established that the knowledge about shock wave propagation in the free field cannot be applied to confined environments, especially when it comes to predicting the reflected shock wave. With the increase in accidental or intentional detonations of explosives in confined or urban environments, it is important to study and thoroughly understand the propagation of shock waves to provide behavior prediction tools. The present research focuses on understanding the influence of a variation in the explosion center in a confined room and how this variation affects the shock wave propagation and the reflection due to the confined environment. The shock waves were generated by the detonation of a stoichiometric hemispherical charge of propane–oxygen mixture. The charge was placed in a small-scale model (Hopkinson's scaling law) which represents a typical room in a building. The model was equipped with 29 pressure sensors distributed on the walls and the floor to record pressure history data. The aim of this study was to determine experimentally the evolution of the shock wave parameters such as the maximum overpressure or the arrival time and to predict the origin of the first three reflected peaks with the help of a simple and fast tool. [ABSTRACT FROM AUTHOR]

Forecasting 'Black Swan' events in ecosystems is an important but challenging task. Many ecosystems display aperiodic fluctuations in species abundance spanning orders of magnitude in scale, which have vast environmental and economic impact. Empirical evidence and theoretical analyses suggest that these dynamics are in a regime where system nonlinearities limit accurate forecasting of unprecedented events due to poor extrapolation of historical data to unsampled states. Leveraging increasingly available long-term high-frequency ecological tracking data, we analyze multiple natural and experimental ecosystems (marine plankton, intertidal mollusks, and deciduous forest), and recover hidden linearity embedded in universal 'scaling laws' of species dynamics. We then develop a method using these scaling laws to reduce data dependence in ecological forecasting and accurately predict extreme events beyond the span of historical observations in diverse ecosystems. Author summary: Rare large-amplitude 'Black Swan' fluctuation events have significant ecological and economic impact. In this work, we tackle the grand challenge in forecasting critical fluctuations in ecosystems, in particular in data sparse regimes. We take an unconventional approach by bridging the fields of statistical physics and ecological forecasting. We apply theory from avalanche systems (such as earthquakes) to analyze long-term monitoring data from diverse natural ecosystems, including marine plankton, intertidal mollusks, and deciduous forest. These datasets allow us to recover the clean power-law relations, or 'scaling laws' in statistical physics terms, in system fluctuations that are ubiquitous across species and communities. Leveraging these scaling laws, we extrapolate rare, extreme dynamics from limited historical data and accurately forecast unprecedented events. Therefore, our results have the potential to maximize data value in ecological forecasting with a broad set of applications. [ABSTRACT FROM AUTHOR]

In this paper, we quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter. Hashtags are special words used in social media to attract attention and to organize content. Looking at the collection of all hashtags used in a period of time, we identify the scaling laws underpinning the hashtag frequency distribution (Zipf's law), the number of unique hashtags as a function of sample size (Heaps' law), and the fluctuations around expected values (Taylor's law). While these scaling laws appear to be universal, in the sense that similar exponents are observed irrespective of when the sample is gathered, the volume and the nature of the hashtags depend strongly on time, with the appearance of bursts at the minute scale, fat-tailed noise, and long-range correlations. We quantify this dynamics by computing the Jensen–Shannon divergence between hashtag distributions obtained τ times apart and we find that the speed of change decays roughly as 1 / τ. Our findings are based on the analysis of 3.5 × 10 9 hashtags used between 2015 and 2016. [ABSTRACT FROM AUTHOR]

We investigate physical scaling laws for magnetic energy dissipation in solar flares, in the framework of the Sweet–Parker model and the Petschek model. We find that the total dissipated magnetic energy Ediss in a flare depends on the mean magnetic field component Bf associated with the free energy Ef, the length scale L of the magnetic area, the hydrostatic density scale height λ of the solar corona, the Alfvén Mach number MA = v1/vA (the ratio of the inflow speed v1 to the Alfvénic outflow speed vA), and the flare duration τf, i.e., , where the Alfvén speed depends on the nonpotential field strength Bnp and the mean electron density ne in the reconnection outflow. Using MDI/Solar Dynamics Observatory (SDO) and AIA/SDO observations and 3D magnetic field solutions obtained with the vertical-current approximation non-linear force-free field code we measure all physical parameters necessary to test scaling laws, which represents a new method to measure Alfvén Mach numbers MA, the reconnection rate, and the total free energy dissipated in solar flares. [ABSTRACT FROM AUTHOR]

Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades N, the traded volume V, the asset price P, the squared volatility σ 2 , the bid-ask spread S and the cost of trading C. Different reasonings result in simple proportionality relations ("scaling laws") between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., N ∼ σ 2 . More sophisticated relations are the so called 3/2-law N 3 / 2 ∼ σ P V / C and the intriguing scaling N ∼ (σ P / S) 2 . We prove that these "scaling laws" are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility σ , which turns out to be more subtle than one might naively expect. [ABSTRACT FROM AUTHOR]

It is known that static and spherically symmetric black hole solutions of general relativity in different spacetimes can be embedded into higher-dimensional flat spacetime. Given this result, we have explored the thermodynamic nature of black holes á la its embedding into flat spacetime. In particular, we have explicitly demonstrated that black hole temperature can indeed be determined starting from the embedding and hence mapping of the static observers in black hole spacetime to Rindler observers in flat spacetime. Furthermore, by considering the dynamics of a scalar field in the flat spacetime, it is indeed possible to arrive at the area scaling law for black hole entropy. Thus, by using the flat spacetime field theory, one can indeed provide a thermodynamic description of black holes. Implications are also discussed. [ABSTRACT FROM AUTHOR]

In the numerical simulation of induced seismicity, much attention is generally paid to the calibration of the frictional resistance of the causative fault to obtain a seismic moment consistent with that of the actual event, whereas sufficient investigation is not made in the estimation of the slip-weakening distance Dc as well as in the calibration of seismically radiated energy. The present study addresses this problem by numerically and analytically investigating the relation between Dc and seismic source parameters. First, this study performs the dynamic simulation of an induced seismic event caused by a decrease in the effective normal stress. The analysis demonstrated that seismic efficiency η can be used to improve the accuracy of estimating the critical slip-weakening distance and the coefficient of kinetic friction µd whilst considering not only seismic moment but also radiated energy in the calibration. This gave insight into the development of the new calibration method for induced seismicity that considers energy-related seismic source parameters. Furthermore, a new scaling law of the slip-weakening distance was derived from the theoretical expression of seismic efficiency η, considering seismic moment Mo and scaled energy e ^ . The proposed scaling law can yield the relation between Dc and Mo, which is shown to be similar to that obtained from a previous study, but additionally considers the relation between seismically radiated energy and Dc. The dependency of Dc on seismically radiated energy implied from the proposed scaling law has been verified from the dynamic analyses where η = 0.06 was used to place a constraint on Dc for seismic events with different magnitudes. The developed numerical simulation methodology of induced seismicity as well as the scaling law considering the energy indices significantly contributes to improving the accuracy of back-analysis, thus leading to a more accurate estimation of the mechanical properties of faults and/or shear zones in seismically active regions of deep underground mines or reservoirs composed of discontinuous hard rock masses. [ABSTRACT FROM AUTHOR]

One emerging application of machine learning methods is the inference of galaxy cluster masses. In this note, machine learning is used to directly combine five simulated multiwavelength measurements in order to find cluster masses. This is in contrast to finding mass estimates for each observable, normally by using a scaling relation, and then combining these scaling law based mass estimates using a likelihood. We also illustrate how the contributions of each observable to the accuracy of the resulting mass measurement can be compared via model-agnostic Importance Permutation values. Thirdly, as machine learning relies upon the accuracy of the training set in capturing observables, their correlations, and the observational selection function, and as the machine learning training set originates from simulations, two tests of whether a simulation's correlations are consistent with observations are suggested and explored as well. [ABSTRACT FROM AUTHOR]

Thermal stress weathering is now recognized to be an active and significant geomorphological process on airless bodies. This study aims to understand the key factors governing thermal stresses in rocks on airless bodies through extensive numerical calculations and analytic analyses. Microscopic (grain‐scale) thermal stresses are driven primarily by the maximum diurnal temperature variation at said depth. Macroscopic (rock‐scale) thermal stresses are more complex. For rock sizes larger than the thermal skin depth, macroscopic thermal stresses are driven primarily by second (and higher) order spatial gradients of temperature. For rock sizes smaller than the thermal skin depth, macroscopic thermal stresses are primarily driven by the ratio of rock size to thermal skin depth. Additionally, scaling relations for diurnal surface temperature variation, time‐rate‐of‐change of surface temperature, as well as peak microscopic (grain‐scale) and macroscopic (rock‐scale) thermal stresses are derived to provide a more accessible modeling tool. These scaling relations are remarkably accurate when compared to both the numerical calculations as well as three‐dimensional finite element calculations. The model formulation, results, and scaling relations provided here allow the estimation of diurnal temperatures and thermal stresses on rocks of various size and materials on airless bodies at any orbital distance with a broad spectrum of spin rates. Lastly, we postulate and confirm that there is a critical spin rate where macroscopic thermal stresses will be greatest. Key Points: The key factors governing thermal stresses in rocks on airless bodies are elucidatedScaling relations are derived to approximate diurnal temperature variations as a function of the thermal parameterScaling relations are derived to approximate thermal stresses as a function of diurnal temperature variations and thermal skin depth [ABSTRACT FROM AUTHOR]

The predictions of scaling laws for the structure and properties of defect clusters are generally limited to small defect clusters in their ground-state configurations. We investigated the size and geometrical configuration dependence of nano-sized defect clusters in niobium (Nb) using molecular dynamics. We studied the structure and stability of large clusters of size up to fifty defects for vacancies and one hundred defects for interstitials, as well as the role of helium and metastable configurations on the stability of these clusters. We compared three different interatomic potentials in order to determine the relative stability of these clusters as a function of their size and geometrical configurations. Additionally, we conducted a statistical analysis to predict the formation and binding energies of interstitial clusters as a function of both their size and configuration. We find that the size dependence of vacancy and interstitial clusters can be approximated by functional forms that account for bulk and surface effects as well as some considerations of elastic interactions. We also find that helium and metastable configurations can make vacancy and interstitial clusters thermally stable depending on the configuration. Our parameterized functional forms for the formation and binding energies are valid for a very broad range of defect sizes and configurations making it possible to be used directly in a coarse-grained modeling strategy such as Monte Carlo, cluster dynamics or dislocation dynamics which look at defect accumulation and evolution in microstructures. [ABSTRACT FROM AUTHOR]

The order-of-magnitude performance leaps of ECR ion sources over the past decades result from improvements to the magnetic plasma confinement, increases in the microwave heating frequency, and techniques to stabilize the plasma at high densities. Parallel to the technical development of the ion sources themselves, significant effort has been directed into the development of their plasma diagnostic tools. We review the recent results of Electron Cyclotron Resonance Ion Source (ECRIS) plasma diagnostics highlighting a number of selected examples of plasma density, electron energy distribution, and ion confinement time measurements, obtained mostly with the second-generation sources operating at frequencies from 10 to 18 GHz. The development of minimum-B ECR ion sources based on the superposition of solenoid and sextupole fields has long relied on semiempirical scaling laws for the strength of the magnetic field with increasing plasma heating frequency. This approach is becoming increasingly difficult with the looming limits of superconducting technologies being able to satisfy the magnetic field requirements at frequencies approaching 60 GHz. Thus, we discuss alternative ECRIS concepts and proposed modifications to existing sources that are supported by the current understanding derived from the plasma diagnostics experiments. [ABSTRACT FROM AUTHOR]

The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them, the presence of imperfect interfaces plays a central role being often at the origin of the scale effects. To describe real contacts between different phases, some classical schemes have been introduced in literature, namely the low and the high conducting interface models. Here, we introduce a generalized formalism, which is able to take into account the properties of both previous schemes and, at the same time, it implements more complex behaviors, already observed in recent investigations. We apply our models to the calculation of the effective conductivity in a paradigmatic structure composed of a dispersion of particles. In particular, we describe the conductivity dependence upon the size of the inclusions finding an unusual non-monotone scale effect with a pronounced peak at a given particle size. We introduce some intrinsic length scales governing the universal scaling laws. [ABSTRACT FROM AUTHOR]

Recent efforts have shown that the dynamic properties of a wide class of liquids can be mapped onto semi-universal scaling laws and constitutive relations that are motivated by thermodynamic analyses of much simpler models. In particular, it has been found that many systems exhibit dynamics whose behavior in state space closely follows that of soft-sphere particles interacting through an inverse power repulsion. In the present work, we show that a recently developed coarse-graining theory provides a natural way to understand how arbitrary liquids can be mapped onto effective soft-sphere models and hence how one might potentially be able to extract underlying dynamical scaling laws. The theory is based on the relative entropy, an information metric that quantifies how well a soft-sphere approximation to a liquid's multidimensional potential energy landscape performs. We show that optimization of the relative entropy not only enables one to extract effective soft-sphere potentials that suggest an inherent scaling of thermodynamic and dynamic properties in temperature-density space, but that also has rather interesting connections to excess entropy based theories of liquid dynamics. We apply the approach to a binary mixture of Lennard-Jones particles, and show that it gives effective soft-sphere scaling laws that well-describe the behavior of the diffusion constants. Our results suggest that the relative entropy formalism may be useful for 'perturbative' type theories of dynamics, offering a general strategy for systematically connecting complex energy landscapes to simpler reference ones with better understood dynamic behavior. [ABSTRACT FROM AUTHOR]

The results of micromagnetic simulations are presented, which examine the impact of thermal fluctuations on sweep rate dependent coercivities of both single-layer and exchange-coupled-composite (ECC) perpendicular magnetic recording media. M-H loops are calculated at four temperatures and sweep rates spanning five decades with fields applied normal to the plane and at 45°. The impact of interactions between grains is evaluated. The results indicate a significantly weaker sweep-rate dependence for ECC media suggesting more robustness to long-term thermal effects. Fitting the modeled results to Sharrock-like scaling proposed by Feng and Visscher [J. Appl. Phys. 95, 7043 (2004)] is successful only in the case of single-layer media with the field normal to the plane. [ABSTRACT FROM AUTHOR]

We present a continuum model for spontaneous twisting of graphene nanoribbons driven by compressive edge stresses. Based on a geometrically nonlinear theory of plates, we identify scaling laws for the dependence of twist angles on ribbon width. Strikingly, we find the existence of a critical width below which a ribbon will not undergo spontaneous twisting, preferring an in-plane stretching mode instead. The model predictions are shown to be in excellent qualitative and quantitative agreement with density-functional tight-binding simulations. More generally, our model provides a unifying picture of twisting in graphene nanoribbons with different edge orientations and chemical functionalizations that have been reported recently in the literature. [ABSTRACT FROM AUTHOR]

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si3N4. We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ∼ N2+ν for the unforced case and as τ ∼ N(1+2ν)/(1+ν) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ∼ 1/Vα, where α ≅ 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries. [ABSTRACT FROM AUTHOR]

Given the exponentially scaling cost of full quantum calculations, approximations need to be employed for the simulation of the time evolution of chemical systems. We present a modified version of surface hopping that has the potential to treat larger systems. This is accomplished through an Ehrenfest-like treatment of the excited states, thereby reducing the dynamics to transitions between the ground state and a mean-field excited state. A simplified description of the excited states is achieved, while still allowing for an accurate description of disparate reaction channels. We test our mean-field approximation for the excited states on a series of model problems. Results are compared to the standard surface hopping procedure, with its explicit treatment of all excited states, and the traditional Ehrenfest approach, with its averaging together of all states. [ABSTRACT FROM AUTHOR]

Star polymers, as an important class of nonlinear macromolecules, process special thermodynamic properties for the existence of a common connecting point. The thermodynamic transitions of a single star polymer are systematically studied with the bond fluctuation model using Wang-Landau sampling techniques. A new analysis method employing the shape factor is proposed to locate the coil-globule (CG) and liquid-crystal (LC) transitions, which shows a higher efficiency and accuracy than the canonical specific heat function. The LC transition temperature is found to obey the identical scaling law as the linear polymers. However, the CG transition temperature shifts towards the LC transition with the increasing of the arm number. The reason is that for the star polymer a lower temperature is needed for the attractive force to overcome the excluded volume effect of the polymer chain because of its high arm density. This work clearly proves the structural distinction of the linear and star polymers can only affect the CG transition while has no influence on the LC transition. [ABSTRACT FROM AUTHOR]

Horizontally propagating fronts in the iodate-arsenous acid reaction are investigated experimentally in a vertically oriented Hele-Shaw cell by varying the height of liquid layer for various stoichiometry. At the preset conditions, a stable pattern develops which can be characterized by its mixing length defined as the standard deviation of the front position in the direction of propagation. The mixing length scales with the height of the reaction vessel, and although the exponent significantly changes by varying the ratio of the reactants, it has a universal value when the reaction front is thin and simple convection arises. [ABSTRACT FROM AUTHOR]

A thermodynamic scaling law for the relaxation times of complex liquids as a function of temperature and volume has been proposed in the literature: τ(T,V) = ƒ(TVγ), where γ is a material-dependent constant. We test this scaling for six materials, linear polystyrene, star polystyrene, two polycyanurate networks, poly(vinyl acetate), and poly(vinyl chloride), and compare the thermodynamic scaling to T - Tg scaling, where τ = ƒ(T - Tg). The thermodynamic scaling law successfully reduces the data for all of the samples; however, polymers with similar structures but different glass transition (Tg) and pressure-volume-temperature (PVT) behavior, i.e., the two polycyanurates, cannot be superposed unless the scaling law is normalized by TgVgγ. On the other hand, the T - Tg scaling successfully reduced data for all polymers, including those having similar microstructures. In addition, the T - Tg scaling is easier to implement since it does not require knowledge of the PVT behavior of the material. The relationship between TgVgγ/TVγ and T - Tg scaling is clarified and is found to be weakly dependent on pressure. [ABSTRACT FROM AUTHOR]

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function CN(t)≈∂t2hN(t)/2, measuring the curvature of the COM mean-square displacement hN(t). We demonstrate that CN(t) ≈ -(RN/TN)2(ρ*/ρ) f(x = t/TN) with N being the chain length (16 <= N <= 8192), RN ∼ N1/2 is the typical chain size, TN ∼ N2 is the longest chain relaxation time, ρ is the monomer density, ρ*≈N/RNd is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ∼ x-ω with ω = (d + 2) × α, where α = 1/4 for x < 1 and α = 1/2 for x > 1. We argue that the algebraic decay NCN(t) ∼ -t-5/4 for t < TN results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains. [ABSTRACT FROM AUTHOR]

A recently published alternative hierarchy of coupled-cluster approximations is reformulated as a perturbative correction. A single variant, a model for the total electronic energy based on the perfect quadruples model, is explored in detail. The computational scaling of the method developed is the same as canonical second order Mo\ller-Plesset perturbation theory (fifth order in the number of molecular orbitals), but its accuracy competes with the high-accuracy, high-cost standard CCSD(T), even when the latter is allowed to break spin-symmetry. The variation presented can be implemented without explicit calculation and storage of the most expensive energy contributions, thereby improving the range of systems which can be treated. The performance and scaling of the method are demonstrated with calculations on the water, fluorine, and oxirane molecules, and compared to the parent model. [ABSTRACT FROM AUTHOR]

The accuracy of dipole moments calculated from wave function methods based on second-order perturbation theory is investigated in the ground and electronically excited states. Results from the approximate coupled-cluster singles-and-doubles model, CC2, Mo\ller-Plesset perturbation theory, MP2, and the algebraic diagrammatic construction through second-order, ADC(2), are discussed together with the spin-component scaled and the scaled opposite-spin variants of these methods. The computed dipole moments show a very good correlation with data from high-resolution spectroscopy. Compared to the unscaled methods, the spin-component scaling increases the accuracy of the results and improves the robustness of the calculations. An accuracy about 0.2 to 0.1 D in the ground state and about 0.3 to 0.2 D in the electronically excited states can be achieved with these approaches. [ABSTRACT FROM AUTHOR]

In this work, we have tested the efficiency of two scaling approaches aiming at relating shear viscosity to a single thermodynamic quantity in dense fluids, namely the excess entropy and the thermodynamic scaling methods. Using accurate databases, we have applied these approaches first to a model fluid, the flexible Lennard-Jones chain fluid (from the monomer to the hexadecamer), then to real fluids, such as argon and normal alkanes. To enlarge noticeably the range of thermodynamics conditions for which these scaling methods are applicable, we have shown that the use of the residual viscosity instead of the total viscosity is preferable in the scaling procedures. It has been found that both approaches, using the adequate scaling, are suitable for the Lennard-Jones chain fluid model for a wide range of thermodynamic conditions whatever the chain length when scaling law exponents and prefactors are adjusted for each chain length. Furthermore, these results were found to be well respected by the corresponding real fluids. [ABSTRACT FROM AUTHOR]

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Mo\ller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported. [ABSTRACT FROM AUTHOR]

Coarse-grained models decrease the number of force sites and thus reduce computational requirements for molecular simulation. While these models are successful in describing structural properties, dynamic evolution is faster than the corresponding atomistic simulations or experiments. We consider coarse-grained models for four polymers and one polymer mixture, where accurate dynamics are obtained by scaling to match the mean-squared displacements of the corresponding atomistic descriptions. We show that the required scaling is dictated by local friction and that this scaling is only valid after the onset of continuous motion. [ABSTRACT FROM AUTHOR]

The relaxation of single grafted semiflexible chains freely rotating around the grafting point is investigated by means of two dimensional computer simulations and scaling arguments. Both free chains and chains surrounded by topological obstacles are considered. We compute the autocorrelation of the end-to-end vector for the whole chain and for terminal sections of various lengths. Our results are relevant for the relaxation of star polymers with stiff arms or branched semiflexible polymers moving in an array of obstacles. [ABSTRACT FROM AUTHOR]

We use molecular simulation to study the ability of entropy scaling relationships to describe the kinetic properties of two Lennard-Jones dumbbell models. We begin by examining the excess entropy, the key quantity used to correlate dynamic properties within entropy scaling strategies. We compute the thermodynamic excess entropy as well as contributions to the two-body excess entropy stemming from translational and orientational intermolecular correlations. Our results indicate that the total two-body contribution accounts for more than 70% of the thermodynamic excess entropy at all state conditions explored. For the two dumbbell models studied here, the orientational component of the two-body excess entropy dominates at moderate and high fluid densities. We next investigate the relationships between kinetic properties and various contributions to the excess entropy. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate-scattering function. We find that the thermodynamic excess entropy provides the best metric for describing kinetic properties. For each of the dynamic properties considered, reduced data collapse onto a common curve when expressed as a function of the thermodynamic excess entropy. The likelihood of a two-body contribution to the excess entropy serving as a reliable scaling variable is linked to the extent to which it correlates with the thermodynamic excess entropy. The total two-body term contributes significantly to the excess entropy, and therefore this quantity generally serves as a suitable scaling variable. [ABSTRACT FROM AUTHOR]

We study the scaling behavior of magnetic minor hysteresis loops in strain-induced ferromagnetic α′ martensites in an austenitic 316-type stainless steel. A scaling relationship between the hysteresis loss and the remanence, with a power law exponent of approximately 1.35, was found irrespective of the volume fraction of the α′ martensites as well as temperature. The coefficient of the power law largely decreases with volume fraction, whereas it increases with a decrease in temperature and exhibits a kink at around 40 K, close to the Néel temperature of an austenitic γ′ phase. The behavior of the coefficient was interpreted from the viewpoint of the morphology and exchange interaction of α′ martensites. [ABSTRACT FROM AUTHOR]

A qualitative model that relates the period of the surface roughness to the vertical and spherical growth rates of glancing angle deposited (GLAD) nanorods suggests that rod self-shadowing is responsible for the previously reported temperature dependence in the rod width. Atomic shadowing interactions between neighboring rods as well as surface islands on the rod growth fronts control the morphological evolution which is quantified by the growth exponent p that relates the rod width w (=Ahp) to their height h. An analytical formalism predicts linear dependences of p and A on the average island separation and provides an explanation for reported anomalous p values. Experimental validation using new and previously published GLAD data for Al, Cr, Nb, and Ta shows quantitative agreement for all metallic systems under consideration and confirms the predicted dependences. In addition, a discontinuity in the p versus homologous deposition temperature θ suggests a critical value θc=0.24±0.02 for a transition from two-dimensional to three-dimensional island growth, which is independently confirmed by a discontinuity in the measured island width. [ABSTRACT FROM AUTHOR]

Scaling laws for magnetic minor hysteresis loops that are asymmetric and have their origin at an arbitrary point under a bias field have been examined for Fe single crystals with tensile deformation. We found that there exist power-law relations between field-dependent parameters of asymmetrical minor loops, which are the same as those for symmetrical ones observed previously. This agreement shows that the Bloch wall interaction with lattice defects is unchangeable irrespective of whether the Bloch walls move along the potential due to symmetrical or asymmetrical minor loops. The power-law relations were generalized on the basis of experimental results. [ABSTRACT FROM AUTHOR]

The dynamics of paraffin deposit formation on different surfaces was analyzed based on scaling laws. Carbon-based films were deposited onto silicon (Si) and stainless steel substrates from methane (CH4) gas using radio frequency plasma enhanced chemical vapor deposition. The different substrates were characterized with respect to their surface energy by contact angle measurements, surface roughness, and morphology. Paraffin thin films were obtained by the casting technique and were subsequently characterized by an atomic force microscope in noncontact mode. The results indicate that the morphology of paraffin deposits is strongly influenced by substrates used. Scaling laws analysis for coated substrates present two distinct dynamics: a local roughness exponent (αlocal) associated to short-range surface correlations and a global roughness exponent (αglobal) associated to long-range surface correlations. The local dynamics is described by the Wolf–Villain model, and a global dynamics is described by the Kardar–Parisi–Zhang model. A local correlation length (Llocal) defines the transition between the local and global dynamics with Llocal approximately 700 nm in accordance with the spacing of planes measured from atomic force micrographs. For uncoated substrates, the growth dynamics is related to Edwards–Wilkinson model. [ABSTRACT FROM AUTHOR]

In this third paper of the series, which started with Bailey et al. [J. Chem. Phys. 129, 184507 (2008); ibid. 129, 184508 (2008)], we continue the development of the theoretical understanding of strongly correlating liquids—those whose instantaneous potential energy and virial are more than 90% correlated in their thermal equilibrium fluctuations at constant volume. The existence of such liquids was detailed in previous work, which identified them, based on computer simulations, as a large class of liquids, including van der Waals liquids but not, e.g., hydrogen-bonded liquids. We here discuss the following: (1) the scaling properties of inverse power-law and extended inverse power-law potentials (the latter includes a linear term that “hides” the approximate scale invariance); (2) results from computer simulations of molecular models concerning out-of-equilibrium conditions; (3) ensemble dependence of the virial/potential-energy correlation coefficient; (4) connection to the Grüneisen parameter; and (5) interpretation of strong correlations in terms of the energy-bond formalism. [ABSTRACT FROM AUTHOR]

We present our investigation on the critical behavior of the spinel compound CdCr2S4 via the ac susceptibility and dc magnetization measurements. The analysis of ac susceptibility in terms of scaling behavior yields exponent values of δ=5.38±0.01, γ+β=1.77±0.03 and γ=1.44±0.02. Both δ and γ are slightly larger than that predicted by Heisenberg model. Detailed analyses of the inverse of the susceptibility and the electron spin resonance experiment reveal that the existence of correlated magnetic polarons has a key impact on the ferromagnetism of the spinel CdCr2S4. The abnormal critical exponent value of δ of CdCr2S4 may be attributed to the formation of the correlated magnetic polarons and abnormal spin-phonon coupling. [ABSTRACT FROM AUTHOR]

We present our investigation on the critical behavior of the spinel compound CdCr2S4 via the ac susceptibility and dc magnetization measurements. The analysis of ac susceptibility in terms of scaling behavior yields exponent values of δ=5.38±0.01, γ+β=1.77±0.03 and γ=1.44±0.02. Both δ and γ are slightly larger than that predicted by Heisenberg model. Detailed analyses of the inverse of the susceptibility and the electron spin resonance experiment reveal that the existence of correlated magnetic polarons has a key impact on the ferromagnetism of the spinel CdCr2S4. The abnormal critical exponent value of δ of CdCr2S4 may be attributed to the formation of the correlated magnetic polarons and abnormal spin-phonon coupling. [ABSTRACT FROM AUTHOR]

Of great interest to high power microwave, millimeter wave to terahertz sources, x-ray tubes, electrons guns, etc., is the electric field enhancement obtained from sharp emitting structures fabricated by various microfabrication methods. In this paper, we use conformal mapping to investigate the field enhancement of several rectilinear geometries, including a single rectangular ridge, a trapezoidal ridge, and their superposition, i.e., one ridge on top of another. We show that the composite field enhancement factor of the double ridge with a microprotrusion on top of a macroprotrusion is dominated by the product of the individual protrusions’ field enhancement factors over a very wide range of geometric aspect ratios, as conjectured by Schottky. Simplified scaling laws are proposed. Significant deviation from Schottky’s product rule occurs almost exclusively when the half-width of the macroprotrusion is less than the height of the microprotrusion. Accurate expressions of the divergent electric field near the sharp edges are derived. [ABSTRACT FROM AUTHOR]

The field dependence of the adiabatic temperature change ΔTad of second order phase transition materials is studied, both theoretically and experimentally. Using scaling laws, it is demonstrated that, at the Curie temperature, the field dependence of ΔTad is characterized by H1/Δ. Therefore, as the magnetic entropy change ΔSM follows a H(1-α)/Δ power law, these two dependencies coincide only in the case of a mean field model. A phenomenological construction of a universal curve for ΔTad is presented, and its theoretical justification is also given. This universal curve can be used to predict the response of materials in different conditions not available in the laboratory (extrapolations in field or temperature), for enhancing the resolution of the data and as a simple screening procedure for the characterization of materials. [ABSTRACT FROM AUTHOR]

Dynamic scaling behavior has been observed during the room-temperature growth of sputtered Pd films on SiO2 using the scanning electron microscopy technique. By the analyses of the dependence of the Pd grain size and surface density on the film thickness, the dynamical growth exponent z=4.2±0.3 was obtained, suggesting a conservative growth process. The analysis of the fraction of surface covered by Pd as a function of film thickness (up to a maximum of 8.5×1016 atoms/cm2, corresponding to 125 nm) allowed us to identify two different growth regimes in the investigated range: films thinner than 1.8×1016 atoms/cm2 (26.5 nm) that grow as an outside-cluster system and thicker film that exhibit an islandlike growth. [ABSTRACT FROM AUTHOR]

Dynamic scaling behavior has been observed during the room-temperature growth of sputtered Pd films on SiO2 using the scanning electron microscopy technique. By the analyses of the dependence of the Pd grain size and surface density on the film thickness, the dynamical growth exponent z=4.2±0.3 was obtained, suggesting a conservative growth process. The analysis of the fraction of surface covered by Pd as a function of film thickness (up to a maximum of 8.5×1016 atoms/cm2, corresponding to 125 nm) allowed us to identify two different growth regimes in the investigated range: films thinner than 1.8×1016 atoms/cm2 (26.5 nm) that grow as an outside-cluster system and thicker film that exhibit an islandlike growth. [ABSTRACT FROM AUTHOR]

We address room-temperature conductivities of chemically grown silver films. Disordered, granular silver films are grown using a modified Tollens reaction. Thick, polycrystalline films are transparent at visible wavelengths, with crystallinity similar to that of silver powders. The measured conductivities are close to those measured by I. V. Antonets, L. N. Kotov, S. V. Nekipelov, and Ye. A. Golubev, Tech. Phys. 49, 306 (2004) in amorphous silver films, however the thickness where bulk conductivity is reached is anomalously high. While measured resistance values do not obey a scaling relation in thickness, accounting for the films’ structural porosity through geometrical rescaling of the thickness leads to emergence of the well-known percolation power-law scaling, albeit that of two-dimensional percolating films. [ABSTRACT FROM AUTHOR]

A fractal analysis of effective thermal conductivity for unsaturated fractal porous media is presented based on the thermal-electrical analogy and statistical self-similarity of porous media. Here, we derive a dimensionless expression of effective thermal conductivity without any empirical constant. The effects of the parameters of fractal porous media on the dimensionless effective thermal conductivity are discussed. From this study, it is shown that, when the thermal conductivity of solid phase and wet phase are greater than that of the gas phase (viz., ks/kg>1, kw/kg>1), the dimensionless effective thermal conductivity of unsaturated fractal porous media decreases with decreasing degree of saturation (Sw) and increasing fractal dimension for pore area (Df), fractal dimension for tortuosity (Dt), and porosity ([lowercase_phi_synonym]); when the thermal conductivities of solid phase and wet phase are lower than that of the gas phase (viz., ks/kg<1, kw/kg<1), the trends were just opposite. Our model was validated by comparing the model prediction with existing experimental data. Excellent agreement was found except for the cases at very low level of saturation. [ABSTRACT FROM AUTHOR]

The electrical contact resistance is computed for a local constriction of finite length and finite transverse dimension in a conducting current channel. Conformal mapping is used for a rectangular current channel, and an electrostatic code is used for a cylindrical current channel. The connecting bridge, which models a local electrical contact, is assumed to be made of the same conducting material as the main current channel. Very simple analytic scaling laws for the contact resistance are constructed for a wide range of geometrical aspect ratios between the main current channel and its connecting bridge, which may assume a rectangular shape (for Cartesian channel), and a cylindrical or funnel shape (for cylindrical channel). These scaling laws have been confirmed by spot checks with numerical code results. They are generalizations of the classical theory of Holm and Timsit on the contact resistance of the “a-spot,” defined as a small circular area of zero thickness through which current can flow. Potential applications and extensions of the theory are indicated. [ABSTRACT FROM AUTHOR]

The present paper introduces a scaling law correlating three factors of ferroelectric materials in quite simple functions: the polarization (P), the electrical field (E), and the stress (T). The law is based on the physical symmetries of the problem and renders it possible to express the mechanical stress (T) as an electric field equivalent {Eeq=Th[P(E=0,T)]} and, as a consequence, also the relationship between strain (S) and polarization (P). Three materials with various phase structure (tetragonal, rhombohedral, and morphotropic) were used for the verification. It was found that such an approach permitted the prediction of the maximal stress using only purely electrical measurements [i.e., measurements of S(E) and P(E)]. Once this law was validated for the compressive stresses, the mapping could be extended in order to predict the polarization behavior in the tensile stress zone. It was shown that the polarization behaved differently as a function of the compressive and tensile stresses. The scaling law could also predict the piezoelectric constant (d33) under stress using only purely electrical measurements. Reciprocally, the dielectric constant ([variant_greek_epsilon]33) under an electrical field can be predicted using only purely mechanical measurements. Comparisons of hysteresis loops were made and a good agreement was found for the polarization versus electric field, compressive stresses, and, albeit to a lesser extent, for the coefficients ([variant_greek_epsilon]33) and d33. [ABSTRACT FROM AUTHOR]

We study the scaling laws of affinity-based biosensors. In particular, we examine the implications of scaling on the response time, signal-to-noise ratio (SNR), and dynamic range (DR) of biosensor systems. Initially, using stochastic differential methods and particularly Fokker¿Planck (FP) equation, we formulate the analyte capturing process and derive its uncertainty by computing the probability distribution function of the captured analytes as a function of time. Subsequently, we examine the effects of scaling on the solution to the FP equation and the signal fluctuation, which demonstrates that scaling down significantly reduces the achievable SNR and DR of biosensors. We argue that these results question the advantages of excessive miniaturization of biosensors, especially the fundamental SNR limitation, which transpire in the micro- and nanoregimes. [ABSTRACT FROM AUTHOR]

In recent experiments, the temporal average C(t) of the mean square displacement for nanorods moving through a chemical monolayer was explored. The results showed a scaling C(t)∼t1.6, which suggest the existence of superdiffusive motion for these particles. In this paper, we interpret these results by means of a continuous-time random walk (CTRW) model from which we can reproduce the exponent 1.6 and the curve C(t) versus time found in the experiments. We show that the behavior observed arises as a consequence of the superposition of different transport mechanisms: directional propulsion plus translational and rotational diffusion. Our model reveals that this superdiffusive-like scaling may also be found in other systems as in chemotactic biological motion, provided that the characteristic times for translational and rotational diffusions are very different. [ABSTRACT FROM AUTHOR]

Vibrational zero-point energies (ZPEs) determined from ab initio calculations are often scaled by empirical factors. An empirical scaling factor partially compensates for the effects arising from vibrational anharmonicity and incomplete treatment of electron correlation. These effects are not random but are systematic. We report scaling factors for 32 combinations of theory and basis set, intended for predicting ZPEs from computed harmonic frequencies. An empirical scaling factor carries uncertainty. We quantify and report, for the first time, the uncertainties associated with scaling factors for ZPE. The uncertainties are larger than generally acknowledged; the scaling factors have only two significant digits. For example, the scaling factor for B3LYP/6-31G(d) is 0.9757±0.0224 (standard uncertainty). The uncertainties in the scaling factors lead to corresponding uncertainties in predicted ZPEs. The proposed method for quantifying the uncertainties associated with scaling factors is based upon the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization. We also present a new reference set of 60 diatomic and 15 polyatomic “experimental” ZPEs that includes estimated uncertainties. [ABSTRACT FROM AUTHOR]

A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn–Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability. [ABSTRACT FROM AUTHOR]

A fast algorithm for dealing with electrostatic interactions in partially periodic systems that are confined along the nonperiodic direction by two planar dielectric interfaces is presented. The method is a generalization of the electrostatic layer correction (ELC) method of Arnold et al. [J. Chem. Phys. 117, 2496 (2002)], and employs an exact relation between the 2D+h system and a three-dimensional (3D) periodic system. The terms connecting the two systems can be evaluated linearly in the number of charges. Thus, the method shows overall the scaling of the underlying method employed to handle the Coulombic 3D case. Moreover, our algorithm can accurately handle multiple polarization image charges due to the dielectric interfaces as well as all the periodic images due to the periodic boundary conditions and has full control over the errors depending on the underlying method used for the 3D periodic case. [ABSTRACT FROM AUTHOR]

Recently, we developed a generalized ensemble based free energy simulation technique, the simulated scaling (SS) method [Li et al., J. Chem. Phys. 126, 024106 (2007)]. In the SS simulations, random walks in the scaling parameter space are realized and free energy values can be conveniently estimated based on trial biasing weights. To improve free energy convergence in the SS simulations, we adopt a recent adaptive algorithm to systematically optimize the scaling parameter intervals; here, the optimization target is the round-trip rate between two end chemical states. As demonstrated in our model studies on the solvation of chloride ion and methane, free energy convergence can be greatly improved when the round-trip rates are accelerated. [ABSTRACT FROM AUTHOR]

An efficient implementation of vibrational coupled cluster theory with two-mode excitations and a two-mode Hamiltonian is described. The algorithm is shown to scale cubically with respect to the number of modes which is identical to the scaling of the corresponding vibrational configuration interaction algorithm. This is achieved through the use of special intermediates. The same algorithm can also be used in vibrational Mo\ller–Plesset calculations. To improve performance, screening techniques have been implemented as well. Test calculations on polyaromatic hydrocarbons with up to 264 coupled modes and model systems with up to 1140 modes are used to illustrate the various features of the algorithm. [ABSTRACT FROM AUTHOR]