Polarized beams and final state heavy fermion polarization

The final state τ longitudinal polarization is discussed in e⁺e⁻ collisions with polarized electron beams. Explicit formulae are given in the context of the standard model, taking into account mass effects and energy dependence. In particular dips in the cross section and zeros in the longitudinal polarization are examined.     

Violation of scaling in annihilation and electroproduction

It is speculated that there may be large violation of scaling in electroproduction, in the kinematic region of large ω. It reflects the large violation of scaling in e⁺e^?-annihilation.     

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ? Q² ? 16 GeV². Excellent agreement is obtained using $\text{g}{}^2\text{(2}\text{GeV}\text{)}\text{4π}{}^2\text{= 0.17}$ for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of $\text{M}{}_0{}^2\text{Q}{}^2$. We use data from the resonance region to show $\text{M}{}_0\text{? 400}\text{MeV}$, in agreement with theoretical expectations. Our fit to νW₂ in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of $\text{R =}\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ at large x and Q² are systematically higher than our predictions.     

Confinement scaling laws for the conventional reversed-field pinch

Mechanical behavior of the Si(111)/Si(3)N4(0001) interface is studied using million atom molecular dynamics simulations. At a critical value of applied strain parallel to the interface, a crack forms on the silicon nitride surface and moves toward the interface. The crack does not propagate into the silicon substrate; instead, dislocations are emitted when the crack reaches the interface. The dislocation loop propagates in the (1; 1;1) plane of the silicon substrate with a speed of 500 (+/-100) m/s. Time evolution of the dislocation emission and nature of defects is studied.     

Ion source scaling laws

Simple theory and basic plasma physics experiments are used to deduce scaling laws for ion source discharges.     

Allometric scaling laws of metabolism

One of the most pervasive laws in biology is the allometric scaling, whereby a biological variable Y is related to the mass M of the organism by a power law, Y=Y₀M^b, where b is the so-called allometric exponent. The origin of these power laws is still a matter of dispute mainly because biological laws, in general, do not follow from physical ones in a simple manner. In this work, we review the interspecific allometry of metabolic rates, where recent progress in the understanding of the interplay between geometrical, physical and biological constraints has been achieved.

For many years, it was a universal belief that the basal metabolic rate (BMR) of all organisms is described by Kleiber's law (allometric exponent b=3/4). A few years ago, a theoretical basis for this law was proposed, based on a resource distribution network common to all organisms. Nevertheless, the 3/4-law has been questioned recently. First, there is an ongoing debate as to whether the empirical value of b is 3/4 or 2/3, or even nonuniversal. Second, some mathematical and conceptual errors were found these network models, weakening the proposed theoretical arguments. Another pertinent observation is that the maximal aerobically sustained metabolic rate of endotherms scales with an exponent larger than that of BMR. Here we present a critical discussion of the theoretical models proposed to explain the scaling of metabolic rates, and compare the predicted exponents with a review of the experimental literature. Our main conclusion is that although there is not a universal exponent, it should be possible to develop a unified theory for the common origin of the allometric scaling laws of metabolism.     

Scattering length scaling laws for ultracold three-body collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.     

Some more universal scaling laws for critical mappings

We study such nonlinear mappingsx _n +1=F(x _n ;b _cr) of an intervalI into itself for which the Feigenbaum scaling laws hold (i.e., for which b_cr is an accumulation point of bifurcation points). Letx ₀ be a random variable with some absolutely continuous distribution inI. We show in particular that (i) the geometric average distance ofx _n from the nearest point of the attractor decreases liken ^–1.93387; (ii) the geometric average of ¦x _n /x ₀¦ increases liken ^0.60; (iii) the geometric mean distance ¦x _n –y _n ¦ between the iterates of two close-by pointsx ₀,y ₀ asymptotically tends towards a value ¦x ₀–y ₀¦^0.77. These-and other-properties are also borne out from a simple probabilistic model which depicts the evolution as a random walklike process.     

Asymptotic scaling laws for imploding thin fluid shells

Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the (A,M) parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A,M >1. It is shown that there exists a critical value gamma(cr) = 1+2/nu (nu = 1,2 for, respectively, cylindrical and spherical flows) of the adiabatic index gamma, which separates two qualitatively different patterns of the density buildup in the last phase of implosion. The scaling of the stagnation density rho(s) and pressure P(s) with the peak value M(0) of the Mach number is obtained.     

New scaling laws for trapped-particle anomalous transport in tokamaks

An improved formula for anomalous transport caused by the dissipative trapped-ion instability (without shear effect) is derived numerically and by two independent analytical methods. The new shearless result is also used to derive the anomalous diffusion with shear effect by a general method already published.     

Stiffness scaling laws and vibration isolators

The variation in dynamic stiffness due to a geometrical shift of a cylindrical vibration isolator is predicted by a scaling law and compared to the results of a waveguide solution. The simple scaling law fails to model satisfactorily the stiffness variation due to a single length or radius shift, while predicting successfully the results of an isolator shape invariant shift. The small deviations arise from a disregarded material property shift.     

Two-threshold model for scaling laws of noninteracting snow avalanches

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity-driven systems, we introduce a two-threshold 2D cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceding the lattice system breakdown are power-law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power-law exponents observed for land, rock, or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.     

Range,light-cone dominance and scaling at low Q2 in electroproduction

The analysis of light cone singularities is used to connect the y · P, or range, dependence of the current correlation function with the Q² dependence of the inelastic electroproduction structure functions. We study for what regions of the Q², ν plane and for what y · P dependence the leading light-cone singularity dominates contributions from less singular terms with the same y · P dependence. When the leading singularity can be shown to dominate for a particular region of Q² and ν, we study whether this implies scaling for νW₂ in that kinematic region. It is shown that a division of the current correlation function into short and long range contributions is fundamentally ambiguous and not related to scaling at low Q². Short range terms which are shown to be light-cone dominated for all Q² so long as ν → ∞, are found but are shown not to scale at low Q² and to be indistinguishable from corrections to long range terms which produce the leading Regge behavior. We show that leading Regge terms may receive contributions far away from the light cone for small virtual photon mass, but that light-cone dominance and scaling are recovered when the photon mass is taken very large.     

Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model

We establish a relation between several entanglement properties in the Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins embedded in a magnetic field. We provide analytical proofs that the single-copy entanglement and the global geometric entanglement of the ground state close to and at criticality behave as the entanglement entropy. These results are in deep contrast to what is found in one- dimensional spin systems where these three entanglement measures behave differently.     

General entanglement scaling laws from time evolution

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.