Narrow Results

In this paper we report our experimental study of dilute-dense transition in a 2-dimensional granular flow of particle size d₀ and channel width D with confined exit of width d. It is found that a maximum inflow rate Q_c exists, above which the outflow changes from dilute to dense and the outflow rate Q(t) drops abruptly from Q_c to a dense flow rate Q_d. The re-scaled critical rate q_c(≡Q_c/(D/d0)) is found to be a function of a scaling variable λ only, i.e. q_c~F(λ), and . The form of this new variable λ suggests that the dilute-to-dense transition is a global property of the flow; unlike the jamming transition, which depends only on . It is also found that this transition occurs when the area fraction of particles near the exit reaches a critical value 0.65±0.03.

An energy gain of the monoenergetic component of electrons γ were successfully increased to 25 MeV by decreasing an electron density n_e to 4 × 10¹⁹cm^-3 and increasing a laser power P_L to 4 TW. An empirical scaling law of the energy gain of γ ∝ P_L/n_e was derived from the experiment. A forward scattering spectrum of the laser pulse showed anti-Stokes satellite peaks up to third-order harmonics around a second harmonic light and a Stokes satellite peak around a laser wavelength, which indicated that a wakefield was excited in a self-modulation laser wakefield regime. A density modulation of wakefield was estimated at 60 ± 10 % from intensity ratios of satellite peaks. The empirical scaling law well agrees with results obtained at other institutes by using higher laser power of 10 ~ 30 TW.

The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction U_m and the derivative of superfluid density has a minimum at a certain interaction U_d. The critical point U_c can be quantified by the scaling analysis of either U_m or U_d. The transition point U_m tends to the critical point U_c from the region of U < U_c, while the U_d tends to the U_c from the region of U > U_c. The transition points U_m and U_d satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.

Magnetic critical current density was measured at various temperatures and fields for SmBa₂Cu₃O_7-x single crystal. Pronounced second peaks were observed at intermediate fields and temperatures. Normalized pinning force density exhibited a clear scaling law when H was normalized by H_max where the pinning force density has the maximum value. This is an indication that a single pinning mechanism exists in the investigated temperature region.

Urban traffic network is a typical complex system, in which movements of tremendous microscopic traffic participants (pedestrians, bicyclists and vehicles) form complicated spatial and temporal dynamics. We collected flow volumes data on the time-dependent activity of a typical urban traffic network, finding that the coupling between the average flux and the fluctuation on individual links obeys a certain scaling law, with a wide variety of scaling exponents between 1/2 and 1. These scaling phenomena can explain the interaction between the nodes' internal dynamics (i.e. queuing at intersections, car-following in driving) and changes in the external (network-wide) traffic demand (i.e. the every day increase of traffic amount during peak hours and shocking caused by traffic accidents), allowing us to further understand the mechanisms governing the transportation system's collective behavior. Multiscaling and hotspot features are observed in the traffic flow data as well. But the reason why the separated internal dynamics are comparable to the external dynamics in magnitude is still unclear and needs further investigations.

Turbulence structures are classified by defining the structure parameters. It is verified that the probabilities of these structure classes keep invariant at different scales within the inertial range. It is also shown that this scale-invariant property of turbulence leads to the existence of scaling laws for a series of physical quantities. From them we deduce the variation principle and the physical constraints to optimize the subgrid-scale stress model coefficients for large eddy simulation.

A sediment transport dynamic model, based on the consideration of streams confluence and/or diversion, is proposed to investigate the influence of water diversion on the mainstream. The simulated results accord qualitatively with the observed or experimental phenomenon in the Yellow River, that is, sedimentation will get more in the main channel as the water is diverted. Some interesting scaling laws describing the behavior of the erosion–sedimentation state in the process of sediment transport are observed, which may help us to get some understandings of sediment transport dynamics in a river network.

We present the scaling law of the pinning force F_P in intermediate and high temperature superconductors, the factors which influence its field and temperature dependence, the limitations imposed by the enlarged anisotropy and high operating temperatures, giant creep included. The theoretical developments which incorporate the new features of these classes of superconductors, most of them based on the Anderson–Kim theory, prove to be a useful source of information relative to the nature of the pinning and the characteristic fields. The use of models based on thermal activation integrates into scaling the tail of pinning force and also substantiates the use of the irreversibility field H_irr as scale field. Finally, the data on scaling law in the two class of superconductors are presented and discussed.

To solve the obscureness in measurement brought about from the weak ergodicity breaking appeared in anomalous diffusions, we have suggested the time-averaged mean squared displacement (MSD) with an integral interval depending linearly on the lag time τ. For the continuous time random walk describing a subdiffusive behavior, we have found that like that of the ensemble-averaged MSD, which makes it be possible to measure the proper exponent values through time-average in experiments like a single molecule tracking. Also, we have found that it has originated from the scaling nature of the MSD at an aging time in anomalous diffusion and confirmed them through numerical results of the other microscopic non-Markovian model showing subdiffusions and superdiffusions with the origin of memory enhancement.

A method is proposed for the estimation of computational errors in the fixed-step integration of nonlinear systems of differential equations. This method finds the bifurcation parameters from the characteristic values of the scheme-generated discrete set and then measures the deviation from expected values at well-defined bifurcation events. With the help of some nonlinear test models, it was found that this deviation or error obeys a scaling law function of the integration step with a characteristic noninteger exponent. Our results are in agreement with previously reported errors in first order schemes. The examination of bifurcation parameters as a function of both the step and initial conditions showed the presence of several attractors where a simpler dynamics was expected. Further considerations of shadowing effects and the presence of a limiting step size are consistent with a complex build up of computational error as manifested by the scaling law.

Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast–slow stochastic differential equations. A key assumption in many arguments for the existence of variance and auto-correlation growth before a tipping point is to use a linearization argument, i.e. the leading-order term governing the deterministic (or drift) part of a stochastic differential equation is linear. This assumption guarantees a local approximation via an Ornstein–Uhlenbeck process in the normally hyperbolic regime before, but sufficiently bounded away from, a bifurcation. In this paper, we generalize the situation to leading-order nonlinear terms for the setting of one fast variable. We work in the quasi-steady regime and prove that the fast variable has a well-defined stationary distribution and we calculate the scaling law for the variance as a bifurcation-induced tipping point is approached. We cross-validate the scaling law numerically. Furthermore, we provide a computational study for the predictability using early-warning signs for leading-order nonlinear terms based upon receiver-operator characteristic curves.

We consider crack propagation in brittle nonlinear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains nΩ on which the imposed boundary conditions scale according to Bažant's law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n → ∞) to the evolution of a crack in a brittle linear-elastic material.

The excited states of some odd A nuclei near the stability line have been systematically investigated from light to intermediate mass with the spherical relativistic mean field (RMF) model. The ratio between the valence nucleon root-mean-square (RMS) radius and the core rms radius, the separation energy and the density distribution have been deduced as signatures for halo or skin structure. We have presented the scaling laws of the ratio of valence particle rms radii and square-potential radii versus the scaled separation energies. The probability for a valence particle being out of the binding potential has also been extracted. We proposed a relaxed necessary condition for nuclear halo occurrence.

Estimation of maximum possible energy gain for a given energy of driver has always become a key point in inertial confinement fusion. It has direct impact on the cost of produced electricity. Here, we employ a hydrodynamics model to assess energy gain in the case of a symmetrical hydrodynamics implosion where a narrow fuel shell consisting of deuterium–tritium (DT), can experience an isentropic compression in a self-similar regime. Introducing a set of six state parameters {H_hs, T_hs, U_imp, α_c, ξ_hs and μ_hs}, the final fuel state close to ignition is fully described. It enables us to calculate energy gain curves for specific set of these state variables. The envelope of the energy gain family curves provide a limiting gain curve . Next, we took into account the inertial of cold surrounding fuel on the ignition process. It changes the limiting gain curve slope to 0.41. Finally, the analytical model results assessed and validated using numerical simulation code.

We show power-scaling behaviors for fluctuations in share volume, which no other studies have done so far. After analyzing a database of the daily transactions for all securities listed on the Tokyo Stock Exchange, we selected 1050 large companies that each had an unbroken series of daily trading activity from January 1975 to January 2002. We found that the cumulative distributions of daily fluctuations in share volumes can be well described by a power-law decay, and that the cumulative distributions for almost all of the companies can be characterized by an exponent within the stable Lévy domain 0 < α < 2. Furthermore, more than 35% of the cumulative distributions can be well approximated by Zipf's law, i.e. the cumulative distributions have an exponent close to unity.

The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.

Foamed concrete possesses characteristics such as high strength-to-weight ratio and low density, and widely used to reduce dead loads on the structure and foundation, contributes to energy conservation, and lowers the labor cost during construction. In this paper, the objective is to propose prediction relation for the compressive strength of foamed concrete by fractal theory. A theoretical relation was derived for the compressive strength relating to porosity based on the fractal model for foamed concrete. The proposed relation stands out compared to empirical model since it employs easily measurable parameter, the fractal dimension of porous structure in foamed concrete. The fractal dimension of porous structure can be calculated from the scaling law of the compressive strength of foamed concrete. The fractal model for porous structure serves as a simple and effective tool for predicting the compressive strength of foamed concrete because of its ease in application. The prediction relation of the compressive strength developed in this paper is found to match well with the measured strength.

The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner’s 2/3 law and Kleiber’s 3/4 law are two facets of the same truth, manifested across different scale approximations.

The objective of this study is to develop and validate similitude requirements and scaling laws for studying the real characteristics of structures easily and economically, especially for large structures. The generalized similitude requirements and the scaling law of orthogonally stiffened cylindrical panels and shells for buckling and free vibration are derived by applying the similitude transformation to the total energy of the structural system directly. In practice, due to either the difficulty of satisfying all of the similitude requirements simultaneously or to save experimental cost and time, distorted models with partial similarity are necessarily employed and approximate scaling laws are proposed. The partial similitude is mainly investigated first by using specific formulas of stiffness parameters and corresponding scaling laws are given. Also discussed herein are particular models with relaxations in the material properties of stiffeners, the materials of both the skin and the stiffeners and the material properties and geometry. The obtained results indicate that the distorted models are able to accurately predict the behavior of the prototype.

We use an atomic ratchet realized by applying short pulses of an optical standing-wave to a Bose–Einstein condensate to study the crossover between classical and quantum dynamics. The signature of the ratchet is the existence of a directed current of atoms, even though there is an absence of a net bias force. Provided that the pulse period is close to one of the resonances of the system, the ratchet behavior can be understood using a classical like theory which depends on a single variable containing many of the experimental parameters. Here we show that this theory is valid in both the true classical limit, when the pulse period is close to zero, as well as regimes when this period is close to other resonances where the usual scaled Planck's constant is nonzero. By smoothly changing the pulse period between these resonances we demonstrate how it is possible to tune the ratchet between quantum and classical types of behavior.