Universal scaling relations in molecular superconductors

Scaling relations between the superconducting transition temperature T(c), the superfluid stiffness rho(s), and the normal state conductivity sigma(0)(T(c)) are identified within the class of molecular superconductors. These new scaling properties hold as T(c) varies over 2 orders of magnitude for materials with differing dimensionality and contrasting molecular structure and are dramatically different from the equivalent scaling properties observed for cuprate superconductors. These scaling relations place strong constraints on theories for molecular superconductivity.     

Universal scaling behaviors of meteorological variables’ volatility and relations with original records

Volatility series (defined as the magnitude of the increments between successive elements) of five different meteorological variables over China are analyzed by means of detrended fluctuation analysis (DFA for short). Universal scaling behaviors are found in all volatility records, whose scaling exponents take similar distributions with similar mean values and standard deviations. To reconfirm the relation between long-range correlations in volatility and nonlinearity in original series, DFA is also applied to the magnitude records (defined as the absolute values of the original records). The results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series.     

Universal scaling in transient creep

We present experimental evidence that pressure solution creep does not establish a steady-state interface microstructure as previously thought. Conversely, pressure solution controlled strain and the characteristic length scale of interface microstructures grow as the cubic root of time. Transient creep with the same scaling is known in metallurgy (Andrade creep). The apparent universal scaling of pressure solution transient creep is explained using an analogy with spinodal dewetting.     

Intermittency and scaling relations

We show that to a very good approximation there exists in general an equivalence between intermittency and the assumption that the first factorial correlatorF ₁₁ is independent of bin size. We further show that strict bin size independence imposes for the possible values of the intermittency index?, ?=0, or?=1.     

Universal scaling law in human behavioral organization

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.     

Universal scaling behaviour in weighted trade networks

Identifying universal patterns in complex economic systems can reveal the dynamics and organizing principles underlying the process of system evolution. We investigate the scaling behaviours that have emerged in the international trade system by describing them as a series of evolving weighted trade networks. The maximum-flow spanning trees (constructed by maximizing the total weight of the edges) of these networks exhibit two universal scaling exponents: (1) topological scaling exponent η = 1.30 and (2) flow scaling exponent ζ = 1.03.     

Optical properties of strongly anisotropic metamaterials

We study the behavior of wave propagation in strongly anisotropic metamaterials with different principal dielectric constants. Analytical expressions of the dispersion relation, Poynting vector, and group velocity are derived theoretically. The light propagation properties for TM and TE waves in these metamaterials are explored, in which the backward wave, negative refraction, phase-compensation effects, and far-field propagation wave carrying subwavelength information are discussed. These theoretical results are supported by numerical simulation.     

Self-gravitating darkon fluid with anisotropic scaling

The fluid model for the dark sector of the universe (darkon fluid), introduced previously in Phys. Rev. D 80, 083513, 2009, is reformulated as a modified model involving only variables from the physical phase space. The Lagrangian of the model does not possess a free particle limit and hence the particles it describes, darkons, exist only as a self-gravitating fluid. This darkon fluid presents a dynamical realization of the zero-mass Galilean algebra extended by anisotropic dilational symmetry with dynamical exponent z=\frac53z=\frac{5}{3}. The model possesses cosmologically relevant solutions which are identical to those in the previous paper. We derive also the equations for the cosmological perturbations at early times and determine their solutions. In addition, we discuss also some implications of adding higher spatial-derivative terms.     

Universal fractal scaling of self-organized networks

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes.     

Energy decay laws in strongly anisotropic magnetohydrodynamic turbulence

We investigate the influence of a uniform magnetic field B(0)=B(0)e( parallel) on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along B(0) is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology of Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong B(0), with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.     

Effective masses in a strongly anisotropic fermi liquid

Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_{q}. Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor 1/Z_{q}, while the effective Hall mass is proportional to Z_{q}/Z_{q};{2}, where cdots, three dots, centered implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.     

Exact scaling relations in relativistic hydrodynamic turbulence

We consider the steady state statistics of turbulence in general classes of dissipative hydrodynamic equations, where the fluctuations are sustained by a random source concentrated at large scales. It is well known that in some particular cases, such as non-relativistic incompressible turbulence, a Kolmogorov-type exact scaling relation for a correlation function holds. We show that all such scaling relations follow from a general relation on the current-density correlation function. The derivation does not require an energy cascade picture and suggests that this traditional interpretation of the Kolmogorov relation for incompressible turbulence may be misleading. Using this we derive exact scaling results for compressible turbulence in relativistic hydrodynamics, which reduce in the slow motion limit to the Kolmogorov relation. We discuss the experimental implications of the results.     

Universal scaling in highly doped conducting polymer films

Electrical transport of a highly doped disordered conducting polymer, viz. poly-3,4-ethylenedioxythiophene stabilized with poly-4-styrenesulphonic acid, is investigated as a function of bias and temperature. The transport shows universal power-law scaling with both bias and temperature. All measurements constitute a single universal curve, and the complete J(V,T) characteristics are described by a single equation. We relate this scaling to dissipative tunneling processes, such as Coulomb blockade.