Spin switch effect in multiply connected superconductor-ferromagnet hybrid geometry

We consider a superconducting spin valve in multiply connected superconductor-ferromagnet hybrid geometry such as a superconducting ring enclosed a ferromagnetic metal, in the framework of linearized Usadel equations. We simplify our model by considering the presence of the exchange field in the superconducting ring which allows us to manipulate magnetization orientations in parallel or antiparallel configurations by switching the weaker exchange field. In such geometry the superconducting ground state is activated to higher orbital states characterized by the nonvanishing vorticity parameters L which will be the energetically favorable superconducting state in some ranges of the proximity superconductor-ferromagnet region. The competing effects caused by the exchange interactions and the orbital effect, are analyzed through the nonmonotonic dependence of the superconducting critical temperature $T_c$ on the radius $d_f$ of the ferromagnetic core. The analytic $T_c(d_f)$ formula is obtained within the single mode approach and the analysis of the spin switch effect is given.     

Moment of inertia of superconductors

We find that the bulk moment of inertia per unit volume of a metal becoming superconducting increases by the amount $m_e/(\pi r_c)$, with $m_e$ the bare electron mass and $r_c=e^2/m_e{c}^2$ the classical electron radius. This is because superfluid electrons acquire an intrinsic moment of inertia $m_e{(2{\lambda }_L)}^2$, with ${\lambda }_L$ the London penetration depth. As a consequence, we predict that when a rotating long cylinder becomes superconducting its angular velocity does not change, contrary to the prediction of conventional BCS-London theory that it will rotate faster. We explain the dynamics of magnetic field generation when a rotating normal metal becomes superconducting.     

Co-thickness and oxidation states effect on magnetic anisotropy in Co/MgO heterostructure

Interfacial magnetism and magnetic anisotropy constant ($K_i$) in Co/MgO heterostructure have been studied using ab-initio density functional calculations. It is found that interfacial Co spin magnetic moment shows a strong interdependence on Co-O bond lengths and a reasonable spin-polarization of ～80% is established as a function of Co layers. Our results revealed a saturated positive (out-of-plane) $K_i$ of +2.80 mJ/m² at ≥12 Co layers (～1.6 nm Co thickness), which is associated with orbital magnetic moment difference in [100] and [001] direction along with a strong hybridization between $d_{xy}$ and $d_{x^2?y^2}$ orbitals through orbital angular momentum operator $\stackrel{?}{L_z}$. Furthermore, it is shown that the $K_i$ magnitude almost remains constant and weakens in the case of under- and over-oxidations in the interfacial MgO and Co layers, respectively. Interestingly, $K_i$ improved for oxygen migrated interface due to enhanced $d_{xy}$ and $d_{x^2?y^2}$ orbitals coupling. The disordered interfaces stability is checked by analyzing the formation energy. Hence, the present findings disclose that the higher Co thickness in ordered Co/MgO structure supports to out-of-plane [001] (positive) $K_i$, which could be useful for its technological implementation in high-density magnetic data storage devices with high thermal stability.     

Thermodynamic calculation of spin scaling functions

Critical phenomena theory centers on the scaled thermodynamic potential per spin $?(\beta ,h)=|t{|}^{p}Y(h|t{|}^{?q})$, with inverse temperature $\beta =1/T$, $h=?\beta H$, ordering field H, reduced temperature $t=t(\beta )$, critical exponents p and q, and function $Y(z)$ of $z=h|t{|}^{?q}$. I discuss calculating $Y(z)$ with the information geometry of thermodynamics. Scaled solutions are found to obtain with three admissible functions $t(\beta )$: 1) $t=e^{?J\beta }$, 2) $t={\beta }^{?1}$, and 3) $t={\beta }_C?\beta$, where J and ${\beta }_C$ are constants. For $p=q$, information geometry yields $Y(z)=\sqrt{1+z^2}$, consistent with the one-dimensional (1D) ferromagnetic Ising model.     

Composition law for the Cole-Cole relaxation and ensuing evolution equations

Physically natural assumption says that any relaxation process taking place in the time interval $[t_0,t_2]$, $t_2>t_0\ge 0$ may be represented as a composition of processes taking place during time intervals $[t_0,t_1]$ and $[t_1,t_2]$ where $t_1$ is an arbitrary instant of time such that $t_0\le t_1\le t_2$. For the Debye relaxation such a composition is realized by usual multiplication which claim is not valid any longer for more advanced models of relaxation processes. We investigate the composition law required to be satisfied by the Cole-Cole relaxation and find its explicit form given by an integro-differential relation playing the role of the time evolution equation. The latter leads to differential equations involving fractional derivatives, either of the Caputo or the Riemann-Liouville senses, which are equivalent to the special case of the fractional Fokker-Planck equation satisfied by the Mittag-Leffler function known to describe the Cole-Cole relaxation in the time domain.     

Time-periodic quantum states of weakly interacting bosons in a harmonic trap

We consider quantum bosons with contact interactions at the Lowest Landau Level (LLL) of a two-dimensional isotropic harmonic trap. At linear order in the coupling parameter g, we construct a large, explicit family of quantum states with energies of the form $E_0+g{E}_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. Any superposition of these states evolves periodically with a period of $8\pi /g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ may become relevant. These quantum states provide a counterpart to the known time-periodic behaviors of the corresponding classical (mean field) theory.     

An existence of universality in the dynamics of two types of glass-forming liquids - fragile liquids and strong liquids

By employing a simplified nonlinear memory function proposed recently by the present author, a universal equation for a collective-intermediate scattering function derived based on the time-convolutionless mode-coupling theory is numerically solved to study the dynamics of glass-forming liquids. The numerical calculation is done based on the simulation results performed on two types of liquids, fragile liquids and strong liquids. Those are then shown to be uniquely determined by the long-time collective diffusion coefficient $D(q_m)$, where $q_m$ is a first peak position of a static structure factor for a whole system. Thus, there exists such a universality that there is only one solution for different liquids of a same type at a given value of D. This may be consistent with the fact that strong liquids are structurally quite different from fragile liquids. Finally, it is emphasized that such a universality must be helpful to predict $q_m$ from experimental data.     

Multi-objective optimization of the cavitation generation unit structure of an advanced rotational hydrodynamic cavitation reactor

Hydrodynamic cavitation (HC) has been widely considered a promising technique for industrial-scale process intensifications. The effectiveness of HC is determined by the performance of hydrodynamic cavitation reactors (HCRs). The advanced rotational HCRs (ARHCRs) proposed recently have shown superior performance in various applications, while the research on the structural optimization is still absent. The present study, for the first time, identifies optimal structures of the cavitation generation units of a representative ARHCR by combining genetic algorithm (GA) and computational fluid dynamics, with the objectives of maximizing the total vapor volume, $V_{\mathit{vapor}}$ , and minimizing the total torque of the rotor wall, ${\overrightarrow{M}}_z$ . Four important geometrical factors, namely, diameter (D), interaction distance (s), height (h), and inclination angle (θ), were specified as the design variables. Two high-performance fitness functions for $V_{\mathit{vapor}}$ and ${\overrightarrow{M}}_z$ were established from a central composite design with 25 cases. After performing 10,001 simulations of GA, a Pareto front with 1630 non-dominated points was obtained. The results reveal that the values of s and θ of the Pareto front concentrated on their lower (i.e., 1.5 mm) and upper limits (i.e., 18.75°), respectively, while the values of D and h were scattered in their variation regions. In comparison to the original model, a representative global optimal point increased the $V_{\mathit{vapor}}$ by 156% and decreased the ${\overrightarrow{M}}_z$ by 14%. The corresponding improved mechanism was revealed by analyzing the flow field. The findings of this work can strongly support the fundamental understanding, design, and application of ARHCRs for process intensifications.