Scaling of the turbulence transition threshold in a pipe

We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in the Reynolds number Re. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as O(Re-1).     

Scaling analysis of phase transition in Hg-based superconductor

With the vibrating-reed technique, the internal friction (IF) Q⁻¹ is measured for sing-phase (Hg_0.66Pb_0.34)Ba₂Ca₂Cu₃O_8+x superconductor as a function of temperature at low applied magnetic field up to 0.5 T and as a function of frequency at normal state temperatures. An IF peak associated with flux motion can be found below T_C. The IF peak becomes higher and shifts towards lower temperature with increasing magnetic field. In addition an IF peak is found near 200 K. By scaling analysis we have demonstrated that the internal friction around the peak temperature can be collapsed into a single curve, indicating that the IF peak below T_C is originated from a phase transition associated with a vortex glass transition and a structural phase transition occurs at around 200 K in the superconductor.     

Deconfined criticality: generic first-order transition in the SU(2) symmetry case

Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first-order transition, similar to the case of U(1) x U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.     

Cassie-Baxter to Wenzel state wetting transition: Scaling of the front velocity

We experimentally study the dynamics of water in the Cassie-Baxter state to Wenzel state transition on surfaces decorated with assemblies of micrometer-size square pillars arranged on a square lattice. The transition on the micro-patterned superhydrophobic polymer surfaces is followed with a high-speed camera. Detailed analysis of the movement of the liquid during this transition reveals the wetting front velocity dependence on the geometry and material properties. We show that a decrease in gap size as well as an increase in pillar height and intrinsic material hydrophobicity result in a lower front velocity. Scaling arguments based on balancing surface forces and viscous dissipation allow us to derive a relation with which we can rescale all experimentally measured front velocities, obtained for various pattern geometries and materials, on one single curve.     

Scaling function near a transition to an insulator state

Analysis of experimental results yields a scaling function of the form β(g)=121/g near the metal-insulator transition in three-dimensional systems. In two-dimensional electronic systems demonstrating a transition to an insulator state, the same relation holds for the function νβ, where ν is the critical exponent characterizing the divergence of the correlation length. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 807–811 (10 December 1998)     

Scaling behavior of the Hall coefficient of Si:P at the metal-insulator transition

Measurements of the Hall coefficient R _H (T, B) of Si:P with P concentration N between 3.54 and 7.0·10¹⁸ cm^?3 are reported for the temperature range 0.04 K ≤ T ≤ 4K and in magnetic fields up to 7 T. Even far above the metal-insulator transition (MIT), a sign change of the temperature coefficient similar to the behavior of the conductivity σ(T) in moderate fields is not observed in R _H (T). Field and temperature dependence of R _H both increase as the MIT (at the critical concentration N _c = 3.52 · 10¹⁸ cm^?3) is approached. A careful extrapolation to T → 0 and B → 0 indicates that R _H ^?1 scales to zero as R _H ^?1 ～| N ? N _c ^μH with μ _H = (0.44 ± 0.04) in agreement with previous results.     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

Scaling analysis of the magnetic field-tuned quantum transition in superconducting amorphous In-O films

We studied the magnetic field-tuned superconductor-insulator transition (SIT) in amorphous In-O films with different oxygen contents and, hence, different electron densities. Whereas the two-dimensional scaling behavior was confirmed for the states of the film near the zero-field SIT, the SIT scenario changed for the deeper states in the superconducting phase; in addition to the scaling function describing the conductivity of the fluctuation-induced Cooper pairs, the temperature-dependent contribution to the film resistance emerged. This contribution can originate from the conductivity of normal electrons.     

Scaling properties of hadron production in the Ising model for quark-hadron phase transition

Earlier study of quark-hadron phase transition in the Ginzberg-Landau theory is reexamined in the Ising model, so that spatial fluctuations during the transition can be taken into account. Although the dimension of the physical system is 2, as will be argued, bothd=2 andd=4 Ising systems are studied, the latter being theoretically closer to the Ginzberg-Landau theory. The normalized factorial momentsF _q are used to quantify multiplicity fluctuations, and the scaling exponentν is used to characterize the scaling properties. It is found by simulation on the Ising lattice thatν becomes a function of the temperatureT nearT _c . The average value ofν over a range ofT<T _c agrees with the value of 1.3 derived analytically from the Ginzberg-Landau theory. Thus the implications of the mean-field theory are not invalidated by either the introduction of spatial fluctuations or the restriction to a 2D system.     

Scaling law for a subcritical transition in plane Poiseuille flow

The scaling law for the threshold amplitude of perturbations to initiate a transition in subcritical plane Poiseuille flow as a function of the Reynolds number is demonstrated experimentally. The disturbances are introduced through an almost streamwise independent slot drilled at the bottom wall of a horizontal air-channel flow. Following the two stages of transition, linear transient growth and nonlinear secondary instability, it is found that the normalized critical injection rate (v0) scales with the Reynolds number (R) as v0 approximately R-3/2. This scaling law agrees with the theoretical predictions of Chapman [J. Fluid Mech. 451, 34 (2002).].     

石墨烯量子霍尔平台与平台之间转变的标度律关系

在2到50 K温度范围内测量了单层石墨烯量子霍尔平台与平台之间转变的标度律关系. 发现石墨烯的标度律指数κ不是普适的,在低温段的κ大约是0.13,在高温段的κ大约是0.33. 这一结果进一步验证了石墨烯中长程散射的主导地位. 关键词： 石墨烯 量子霍尔效应 标度律