Continued Roots, Power Transform and Critical Properties

We consider the problem of calculation of the critical amplitudes at infinity by means of the self-similar continued root approximants. Region of applicability of the continued root approximants is extended from the determinate (convergent) problem with well-defined conditions studied before by Gluzman and Yukalov (Phys. Lett. A 377 2012, 124), to the indeterminate (divergent) problem my means of power transformation. Most challenging indeterminate for the continued roots problems of calculating critical amplitudes, can be successfully attacked by performing proper power transformation to be found from the optimization imposed on the parameters of power transform. The self-similar continued roots were derived by systematically applying the algebraic self-similar renormalization to each and every level of interactions with their strength increasing, while the algebraic renormalization follows from the fundamental symmetry principle of functional self-similarity, realized constructively in the space of approximations. Our approach to the solution of the indeterminate problem is to replace it with the determinate problem, but with some unknown control parameter b in place of the known critical index β. From optimization conditions b is found in the way making the problem determinate and convergent. The index β is hidden under the carpet and replaced by b. The idea is applied to various, mostly quantum-mechanical problems. In particular, the method allows us to solve the problem of Bose-Einstein condensation temperature with good accuracy.

Experimental study of the transport properties of Nd-Fe-B and Sm-Co magnets

The article adduces new reliable experimental data on the thermal conductivity and the thermal diffusivity of hard magnetic materials of brands N35M, N35H, N35SH, as well as YX18, YX24 and YXG22, YXG30 with main components represented by the crystalline phases of Nd2Fe14B, SmCo5 and Sm2Co17 type, respectively. The temperature range from 293 to 773…1273 K has been investigated by laser flash technique with an error of 3—4%. The reference tables of the thermal diffusivity and thermal conductivity coefficients have been developed. The character of the thermal diffusivity changes near the Curie point has been determined. The critical indices and the critical amplitudes have been defined.

Effect of Structure and Cyclic Loading on the Internal Damping Capacity

The damping capacity, which was characterized by dissipating of mechanical energy, was examined in magnesium alloys (AZ31, AZ61 and AZ91). Internal damping is usually divided into three regions, namely the regions in which the internal damping is strain independent, weakly dependent and strongly dependent. The article is focused on the critical amplitudes of deformation which separate the strain independent, weakly dependent and strongly dependent regions. In experimental measurements resonance method was used, which is based on continuous excitation of oscillations of the specimen and the entire apparatus vibrates at a frequency which is near to the resonance.

Unsteady Aerodynamic Characteristics of the Pitched Supersonic Biplane

In this work, supersonic biplanes of the Busemann concept have been analysed, focusing on the unsteady aerodynamic characteristic due to flow disturbance using Computational Fluid Dynamics (CFD) codes in viscous flow. Flow disturbance is modelled by sinusoidal pitch motion simulated by mesh morphing using radial basis functions (RBF) method. The results suggest that there are two flow patterns of the Busemann biplane: oblique wave sequences flow (Pattern A) and choke-flow (Pattern B) with higher wave drag. Unsteady aerodynamic disturbance represented by pitch motion may cause flow pattern transformation. We have also obtained that Pattern B is more stable than Pattern A and choke-flow cannot be eliminated even after returning to the initial flight attitude. Moreover, amplitudes and frequencies of sinusoidal pitch motion play important roles in flow pattern transformation and there exist critical amplitudes and frequencies.

A PROPERTY OF THE SATURATED VAPOR PRESSURE: RESULTS FROM EQUATIONS OF STATE

Experimentally, a maximum point in the curve of the saturated property ψ=(1-Tr)Pr versus the saturated temperature was postulated (High Temp.-High Press.26 (1994) 427). Here, Tr is the saturated temperature reduced by the critical temperature and Pr is the saturated pressure reduced by the critical pressure. Later, this behavior was applied to assure the saturated vapor pressure critical amplitudes (Appl. Phys. Lett.90 (2007) 141905). In this paper, we indicate that theory of equation of state (EOS) can predict this maximum point. The EOSs we study are the combinations of the hard sphere repulsions and some normally used attractions such as the Redlich–Kwong attraction. We find the EOSs with Redlich–Kwong attractive terms give out the results in the experimental range.

Critical threshold in pipe flow transition

This study provides a numerical characterization of the basin of attraction of the laminar Hagen–Poiseuille flow by measuring the minimal amplitude of a perturbation required to trigger transition. For pressure-driven pipe flow, the analysis presented here covers autonomous and impulsive scenarios where either the flow is perturbed with an initial disturbance with a well-defined norm or perturbed by means of local impulsive forcing that mimics injections through the pipe wall. In both the cases, the exploration is carried out for a wide range of Reynolds numbers by means of a computational method that numerically resolves the transitional dynamics. For , the present work provides critical amplitudes that decay as Re −3/2 and Re −1 for the autonomous and impulsive scenarios, respectively. For Re =2875, accurate threshold amplitudes are found for constant mass-flux pipe by means of a shooting method that provides critical trajectories that never relaminarize or trigger transition. These transient states are used as initial guesses in a damped Newton–Krylov method formulated to find periodic travelling wave solutions that either travel downstream or exhibit a helicoidal advection.