Monte Carlo calculations of the magnetocaloric effect in gadolinium

In this work we discuss the magnetocaloric effect in metallic gadolinium. We use a model Hamiltonian of interacting 4f spins and treat the 4f spin–spin interaction both in the mean field approximation and in the Monte Carlo simulation. The calculations show that the mean field approximation yields reasonable results for the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but it fails in explaining the experimental data of specific heat at the magnetic ordering temperature. On the other hand, our theoretical results show that the Monte Carlo calculation describes well not only the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but also the specific heat capacity.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Investigation of heat capacities of proteins by statistical mechanical methods

In this study additional heat capacity of the proteins in water dissociation have been investigated by statistical mechanical methods. For this purpose, taking electric field E$E$ and total dipole moment M$M$ as thermodynamical variables and starting with the first law of thermodynamics, an expression which reveals the thermodynamical relation between additional heat capacity in effective electric field Δ_CE$\mathrm{\Delta }{C}_E$ and additional heat capacity at the constant total dipole moment Δ_CM$\mathrm{\Delta }{C}_M$, has been obtained. It is found that, difference between the heat capacities depends linearly on temperature. To establish the hydration effect during the folding and unfolding of the proteins, physical properties of the apolar dissociation have been used [G. Oylumluoglu, et al., Physica A 361 (2006) 255–262]. In the thermodynamical investigation of the protein system, in order to introduce the chemical potential μ$\mu$ (here it takes place of pH), one has to consider the system as a macro-canonical ensemble. In this study, the macro-canonical ensemble is obtained from the canonical ensemble. In this approach the proteins are taken in a heat bath, and also it is supposed that the system is in a particle reservoir. When this reservoir reaches to an equilibrium the number of particles take an average value. In this study, with the purpose of revealing the additional effect to the heat capacity, the partition functions of the proteins obtained in single protein molecule approach are taken. In this way, additional free energy has been related to heat capacities. Calculating the heat capacity Δ_CE$\mathrm{\Delta }{C}_E$ and taking the heat capacity at constant total dipole moment Δ_CM$\mathrm{\Delta }{C}_M$ from the experimental data, the outcomes of the performed calculations have been investigated for Myoglobin and other proteins.     

Coupled caloric effects in multiferroics

We propose a conception – coupled caloric effect   where the enhanced caloric effects originate from the coupling among magnetic, ferroelectric, and structural degrees of freedom. Specifically, as the magneto-electric case, the magnitude of the coupled caloric effect was evaluated for a ferromagnetic–ferroelectric system using a phenomenological calculation based on Landau phase transition theory. The isothermal entropy change is greatly enhanced by increasing the magneto-electric coupling strength. This work indicates that the caloric effect in a ferromagnetic–ferroelectric coupled system consists of pure magnetic entropy change (Δ_SM$\mathrm{\Delta }{S}_M$), pure ferroelectric one (Δ_SE$\mathrm{\Delta }{S}_E$), and coupled one (Δ_SME$\mathrm{\Delta }{S}_{\mathit{ME}}$) that plays a significant part. The counterpart of the last one in magneto-structural coupled system was usually neglected. Our study provides a route to energy-efficient refrigeration via realization of coupling among various ferroic orders.     

On the parallel transport of the Ricci curvatures

Geometrical characterizations are given for the tensor R⋅S$R\cdot S$, where S$S$ is the Ricci tensor   of a (semi-)Riemannian manifold (M,g)$(M,g)$ and R$R$ denotes the curvature operator   acting on S$S$ as a derivation, and of the Ricci Tachibana tensor  _∧g⋅S${\wedge }_g\cdot S$, where the natural metrical operator  _∧g${\wedge }_g$ also acts as a derivation on S$S$. As a combination, the Ricci curvatures   associated with directions on M$M$, of which the isotropy determines that M$M$ is Einstein, are extended to the Ricci curvatures of Deszcz   associated with directions and planes on M$M$, and of which the isotropy determines that M$M$ is Ricci pseudo-symmetric in the sense of Deszcz.     

Force free projective motions of the sphere

Suppose that the sphere Sⁿ$S^n$ has initially a homogeneous distribution of mass and let G$G$ be the Lie group of orientation preserving projective diffeomorphisms of Sⁿ$S^n$. A projective motion of the sphere, that is, a smooth curve in G$G$, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sⁿ$S^n$ and, more generally, examples of subgroups H$H$ of G$G$ such that a force free motion initially tangent to H$H$ remains in H$H$ for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=S_On+1$H=S{O}_{n+1}$). The main tool is a Riemannian metric on G$G$, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy.     

On leafwise conformal diffeomorphisms

For every diffeomorphism φ:M→N$\phi :M\to N$ between 3-dimensional Riemannian manifolds M$M$ and N$N$, there are locally two 2-dimensional distributions _D±$D_{\pm }$ such that φ$\phi$ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of _D±$D_{\pm }$. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator induced from _φ∗${\phi }_{\ast }$. We investigate the integrability condition of _D+$D_{+}$ and _D−$D_{-}$. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves.     

Solubility and diffusion of H in ordered (L12) and disordered Pd3Mn

Hydrogen isotherms have been measured from 423 to 573 K for the disordered and L1₂ ordered forms of Pd₃Mn and, from these equilibrium isotherms, Δ_HH$\mathrm{\Delta }{H}_{\mathrm{H}}$ and Δ_SH$\mathrm{\Delta }{S}_{\mathrm{H}}$ have been determined over a range of r values where r  =H-to-metal, atom ratio. Δ_HH$\mathrm{\Delta }{H}_{\mathrm{H}}$ values are significantly more negative for the L1₂ ordered form than for the disordered form. H diffusion constants have been determined for the L1₂ and disordered forms of Pd₃Mn from gas phase H permeation measurements through Pd₃Mn membranes (423–573 K). The activation energy for diffusion of H in the L1₂ form is 35.2 kJ/mol H which is more reasonable than the value of 76.3 kJ/mol H previously reported. The diffusion constant is greater for the disordered than for the L1₂ form.     

Bertrand curves in the three-dimensional sphere

A curve α$\alpha$ immersed in the three-dimensional sphere S³${\mathbb{S}}^3$ is said to be a Bertrand curve if there exists another curve β$\beta$ and a one-to-one correspondence between α$\alpha$ and β$\beta$ such that both curves have common principal normal geodesics at corresponding points. The curves α$\alpha$ and β$\beta$ are said to be a pair of Bertrand curves in S³${\mathbb{S}}^3$. One of our main results is a sort of theorem for Bertrand curves in S³${\mathbb{S}}^3$ which formally agrees with the classical one: “Bertrand curves in S³${\mathbb{S}}^3$ correspond to curves for which there exist two constants λ≠0$\lambda \ne 0$ and μ$\mu$ such that λκ+μτ=1$\lambda \kappa +\mu \tau =1$”, where κ$\kappa$ and τ$\tau$ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S³${\mathbb{S}}^3$ as the only twisted curves in S³${\mathbb{S}}^3$ having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S³${\mathbb{S}}^3$ and (1,3)-Bertrand curves in R⁴${\mathbb{R}}^4$.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

The role of dipolar interaction in nanocomposite permanent magnets

The effects of dipolar interactions on the magnetization behaviors and magnetic properties of the nanocomposite magnets have been studied by micromagnetic simulations. Numerical results show that the dipolar interaction plays an important role during the demagnetization process, especially in the magnets with large soft-phase content _vs$v_{\mathrm{s}}$. For the isotropic nanocomposites, the remanence enhancement can be controlled through adjustments of the grain size D   and _vs$v_{\mathrm{s}}$. However, the appearance of magnetic vortex state leads to a very low remanence in the magnets with large D   and _vs$v_{\mathrm{s}}$. The dependence of coercivity on D   and _vs$v_{\mathrm{s}}$ can be attributed to the exchange-induced magnetization reversal near the grain boundaries and the low nucleation field of soft phase, respectively. For the anisotropic nanocomposites, the reduced remanence _mr$m_{\mathrm{r}}$ is equal to 1.0$1.0$ for the magnets with small D   or with low _vs$v_{\mathrm{s}}$. However, _mr$m_{\mathrm{r}}$ decreases with increasing _vs$v_{\mathrm{s}}$ for the magnet with large D   due to the influence of dipolar interactions. The difference between the calculated coercivity _Hc$H_{\mathrm{c}}$ with and without considering dipolar interaction shows that the dipolar interaction plays a more important role during the magnetization reversal in the soft phase than that in the hard phase. The maximum calculated energy product of the isotropic nanocomposites is only about 40 MGOe due to the conflicting relation between remanence and coercivity, while that of the anisotropic nanocomposites is 112 MGOe. This reminds us that the alignment of hard grain is important to obtain high performance.     

Empirical constraints on parton energy loss in nucleus–nucleus collisions at RHIC

We present empirical features of parton energy loss in nucleus–nucleus collisions at RHIC through studies of the spectra and nuclear modification factors (R_AA$R_{AA}$) for charged hadrons, neutral pions (π⁰${\pi }^0$) and non-photonic electrons. The flat distribution of R_AA$R_{AA}$ at high transverse momentum (pT$p_T$) for a given collision centrality is consistent with a scenario where parton energy loss ΔpT$\mathrm{\Delta }{p}_T$ is proportional to pT$p_T$. The centrality dependence of the parton energy loss indicates the absence of path length dependence in the magnitude of energy loss. The lack of strong path length dependence suggests a dynamical picture where the dense partonic medium undergoes rapid expansion and the density of the medium falls rapidly in the first a few Fermi interval, which may be much shorter than the full path length. Implications of the empirical constraints on the parton energy loss will also be discussed.     

A new entropy based on a group-theoretical structure

A multi-parametric version of the nonadditive entropy S_q$S_q$ is introduced. This new entropic form, denoted by S_a,b,r$S_{a,b,r}$, possesses many interesting statistical properties, and it reduces to the entropy S_q$S_q$ for b=0$b=0$, a=r:=1−q$a=r:=1-q$ (hence Boltzmann–Gibbs entropy S_BG$S_{BG}$ for b=0$b=0$, a=r→0$a=r\to 0$). The construction of the entropy S_a,b,r$S_{a,b,r}$ is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of S_a,b,r$S_{a,b,r}$ with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy S_a,b,r$S_{a,b,r}$ can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles N$N$ of the system, or even stabilizes, by increasing N$N$, to a limiting value.     

Study of magnetization process in ordered Fe nanowire arrays

Fe polycrystalline nanowires were electrodeposited in nanoporous anodized alumina membranes. Their magnetic properties were studied at 10 K. The behavior of the isothermal remanence _Mr$M_{\mathrm{r}}$ and the demagnetization remanence _Md$M_{\mathrm{d}}$ was determined. The corresponding ΔM$\mathrm{\Delta }M$ plot revealed the character demagnetizing of the dominant interactions. A simple analysis suggests that curling is the reversal magnetization mode in these samples. The forms of the _Mrev(_Mirr)Hi$M_{\mathrm{rev}}(M_{\mathrm{irr}}{)}_{H_{\mathrm{i}}}$ curves were different from those encountered until now, and it seems that these forms are associated with the curling reversal mode.