The rule for a subdiffusive particle in an extremely diverse environment

We consider a subdiffusive continuous time random walker in an inhomogeneous environment. Each microscopic random time is drawn from a waiting time probability density function (WT-PDF) of the form: , 0<β?1. The parameter k is a random quantity also, and is drawn from a PDF, , 0?γ<1, for a cutoff parameter . We show that the effective WT-PDF, ψ(t), obtained by averaging φ(t;k) with p(k), exhibits a transition in the rule that governs the power of ψ(t). ψ(t) obeys, , and μ is given by two different formula. When, 1−γ>β, μ=β, but otherwise, μ=1−γ. The rule for the scaling of ψ(t) reflects the competition between two different mechanisms for subdiffusion: subdiffusion due to the heavily tailed φ(t;k) for individual jumps, and subdiffusion due to the collective effect of an environment made of many slow local regions. These two different mechanisms for subdiffusion are not additive, and compete each other. The reported transition is dimension independent, and disappears when the power β is also distributed, in the range, 0<β?1. Simulations exemplified the transition, and implications are discussed.     

The magnetocaloric effect and low temperature specific heat of SmNi

The magnetocaloric effect (MCE) in a magnetic SmNi sample was evaluated from magnetization and heat capacity measurements. The MCE phenomena in the vicinity of magnetic phase transitions in terms of magnetic entropy change, , and adiabatic temperature change, , are reported. Isothermal magnetization measurements at several temperatures around the transition were carried out and used for versusT calculations. A similar dependence of the magnetic entropy change was evaluated from heat capacity C_p(T) measurements under zero field and 5 T. The SmNi system provides magnetic refrigerants that induce an adiabatic cooling of about during the magnetization process with a field of 5 T in the temperature range of 35-45 K. The temperature dependence of C_p(T) is analyzed in terms of the magnetic and the lattice contributions.     

Equilibrium structure in the presence of internal rotation: A case study of cis-methyl formate

The Born-Oppenheimer (BO) equilibrium molecular structure () of cis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-ζ quality and a core correlation correction. The quadratic, cubic and semi-diagonal quartic force field in normal coordinates has also been computed at the MP2 level employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure () has been derived from experimental ground-state rotational constants and the lowest-order rovibrational interaction parameters calculated from the ab initio cubic force field. To determine structures, it is important to start from accurate ground-state rotational constants. Different spectroscopic methods, applicable in the presence of internal rotation and used in the literature to obtain “unperturbed” rotational constants from the analysis and fitting of the spectrum, are reviewed and compared. They are shown to be compatible though their precision may be different. The and structures are in good agreement showing that, in the particular case of cis-methyl formate, the methyl torsion can still be treated as a small-amplitude vibration. The best equilibrium structure obtained for cis-methyl formate is: r(C_m-O) = 1.434 Å, r(O-C_c) = 1.335 Å, r(C_m-H_s) = 1.083 Å, r(C_m-H_a) = 1.087 Å, r(C_c-H) = 1.093 Å, r(CO) = 1.201 Å, ∠(COC) = 114.4°, ∠(CCH_s) = 105.6°, ∠(CCH_a) = 110.2°, ∠(OCH) = 109.6°, ∠(OCO) = 125.5°, and τ(H_aCOC) = 60.3°. The accuracy is believed to be about 0.001 Å for the bond lengths and 0.1° for the angles.     

Crystallisation progress in Si-rich ultra-soft nanocomposite alloy fabricated by melt spinning

The crystallisation process and the ultras-soft magnetic properties of amorphous/nanocomposite alloy Fe_73.5Si_17.5B₅Nb₃Cu₁ fabricated by conventional melt-spinning technique are systematically investigated in terms of thermal analysis and in-situ measurement of magnetisation dynamics. The thermal analysis using differential scanning calorimetry showed that crystallisation from Fe-based amorphous state to α-Fe(Si) started at . Further heating the sample leads to a transformation from the α-Fe(Si) to Fe-B phases at . Crystallisation activation energies were determined using two models: Kissinger and John-Mehl-Avrami (JMA), which were consistent to each other with a value of . High resolution transmission electron microscopy investigation revealed an ultrafine structure of α-Fe(Si) nanocrystallite with mean size of 12.5 nm embedded in an amorphous matrix. At a volume fraction of 86% of α-Fe(Si) phase, optimum soft magnetic properties were obtained with very high permeability of 110,000 and a very low coercivity of 0.015 Oe by annealing the amorphous alloy at in 40 min.     

High-resolution infrared and subterahertz spectroscopy of the v2 = 1, v5 = 1, and v3 = 2 levels of CH3Cl

High-resolution Fourier-transform infrared spectra between 1235 and 1680 cm⁻¹ and subterahertz spectra between 250 and 630 GHz of monoisotopic ¹³CH₃³⁵Cl have been recorded and analyzed simultaneously, with all Coriolis, α-resonance, and l-type interactions in the polyad of the v₂ = 1, v₅ = 1, and v₃ = 2 levels taken into account. Several α-resonances (Δk = ±2, Δl = ?1) generating perturbation-allowed transitions have been assigned in the rovibrational spectra. These resonances enabled us to determine accurately and independently the ground state rotational and centrifugal distortion parameters A₀ = 5.205 746 9 (55) cm⁻¹ and . Even , which is, however, correlated to higher-order α-resonance terms, was determined. With 51 upper state parameters varied, about 5800 rovibrational wavenumbers and more than 550 rotational frequencies pertaining to the excited vibrational states were fitted within their experimental accuracy.     

The 2ν4 overtone bands of FClO3

The high resolution infrared spectrum of the mono-isotopic species F³⁵Cl¹⁶O₃ has been studied in the region of the 2ν₄ overtone, from 2560 to 2680 cm⁻¹. The perpendicular component is strong and clearly observed while the parallel component is very weak and almost completely hidden by the perpendicular one. Their origins differ by 12.6 cm⁻¹, the being located at higher wavenumbers. The band is perturbed by the anharmonic interaction between the v₄ = 2, l₄ = ?2 and v₂ = v₄ = v₅ = 1, l₄ = l₅ = ±1 excited states, both of E symmetry. In total 3157 transitions have been assigned, 83% of these to , 12% to , and 5% to . The three bands have been analyzed simultaneously, taking into account the Fermi resonance effective between the excited states of E symmetry. The ro-vibration parameters of the excited states have been obtained, including the deperturbed band origins of and , at 2628.5890(4) and 2619.3342(5) cm⁻¹, respectively. The W₂₄₅ anharmonic constant is equal to 4.0161(4) cm⁻¹. The x₄₄+g₄₄ and x₂₄+x₄₅+g₄₅ anharmonicity constants have been derived from the obtained band origins and those of ν₄ and ν₂ + ν₅.     

Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing

This work focuses on one-dimensional (1D) quasi-periodically forced nonlinear wave equations. This means studying with Dirichlet boundary conditions, where ε is a small positive parameter, (t) is a real analytic quasi-periodic function in t with frequency vector ω=(ω₁,ω₂…,ω_m) and the nonlinearity h is a real analytic odd function of the form It is shown that, under a suitable hypothesis on (t) and h, there are many quasi-periodic solutions for the above equation via KAM theory.     

Exact solutions for a forced Burgers equation with a linear external force

We investigate the solutions of the Burgers equation , where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F(x,t)=k₁(t)−k₂(t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein-Uhlenbeck process and depending on the choice of k₁(t) and k₂(t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x,t)=Φ₁(t)+Φ₂(t)x and Φ(x,t)=Φ₃x−Φ₄/x³ are incorporated in the previous analysis and exact solutions are obtained for both cases.     

The millimetre-wave rotational spectrum of phenylacetylene

The room-temperature rotational spectrum of phenylacetylene (C₆H₅CCH), was studied at frequencies up to 340 GHz. Extensive new measurements, covering rotational transitions with quantum number values up to J=140 and K_a=59, allowed determination of precise spectroscopic constants for the ground state and for the lowest two excited vibrational states, v₂₄=1 and v₃₆=1. The two excited states belong to the lowest B₁ and B₂ symmetry normal modes and their rotational transitions are very strongly perturbed by a-axis Coriolis resonance. A successful fit of the resonance is reported, resulting in and , in good agreement with results of ab initio computations.     

Ac magnetotransport in La0.7Sr0.3Mn0.95Fe0.05O3 at low dc magnetic fields

We report the ac electrical response of La_0.7Sr_0.3Mn_1−xFe_xO₃(x=0.05) as a function of temperature, magnetic field (H) and frequency of radio frequency (rf) current (). The ac impedance (Z) was measured while rf current directly passes through the sample as well as in a coil surrounding the sample. It is found that with increasing frequency of the rf current, Z(T) shows an abrupt increase accompanied by a peak at the ferromagnetic Curie temperature. The peak decreases in magnitude and shifts down with increasing value of H. We find a magnetoimpedance of for at around room temperature when the rf current flows directly through the sample and when the rf current flows through a coil surrounding the sample. It is suggested that the magnetoimpedance observed is a consequence of suppression of transverse permeability which enhances skin depth for current flow. Our results indicate that the magnetic field control of high frequency impedance of manganites is more useful than direct current magnetoresistance for low-field applications.     

Non-Abelian duality from vortex moduli: A dual model of color-confinement

It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G→H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v₁v₂) , under an unbroken, exact color-flavor diagonal symmetry . The transformation property among the regular monopoles characterized by π₂(G/H), follows from that among the non-Abelian vortices with flux quantized according to π₁(H), via the isomorphism π₁(G)π₁(H)/π₂(G/H). Our idea is tested against the concrete models—softly-broken supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v₁v₂Λ) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v₁,v₂Λ).     

Finite and infinite dynamical systems of identical interacting particles

A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S_∞=limS_k, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions p_i(t₀), where p_i(t)=n_i(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution p_i is given by the equation −lnp_i+a+e_ib=0 common to S_k and S_∞ systems with the same value of a and b. The term a=β⁻¹a_e, where a_e is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.     

What is a complex graph?

Many papers published in recent years show that real-world graphs G(n,m) (n nodes, m edges) are more or less “complex” in the sense that different topological features deviate from random graphs. Here we narrow the definition of graph complexity and argue that a complex graph contains many different subgraphs. We present different measures that quantify this complexity, for instance C_1e, the relative number of non-isomorphic one-edge-deleted subgraphs (i.e. DECK size). However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined “product measures”, the products of two quantities which are zero in the extreme cases of a path and clique, and “entropy measures” quantifying the diversity of different topological features. The previously defined network/graph complexity measures Medium Articulation and Offdiagonal complexity (OdC) belong to these two classes. We study OdC measures in some detail and compare it with our new measures. For all measures, the most complex graph has a medium number of edges, between the edge numbers of the minimum and the maximum connected graph . Interestingly, for some measures this number scales exactly with the geometric mean of the extremes: . All graph complexity measures are characterized with the help of different example graphs. For all measures the corresponding time complexity is given.Finally, we discuss the complexity of 33 real-world graphs of different biological, social and economic systems with the six computationally most simple measures (including OdC). The complexities of the real graphs are compared with average complexities of two different random graph versions: complete random graphs (just fixed n,m) and rewired graphs with fixed node degrees.     

Field suppression of the modulated phase of Ce2Pd2Sn

Low temperature magnetic (M) and thermal (C_P) properties of the intermetallic compound Ce₂Pd₂Sn have been investigated at zero and different magnetic fields. Two transitions were recognized at and , with latter nearly coinciding with the extrapolated Curie-Weiss temperature . The Curie factor evaluated from T≥T_M, is ≈2μ_B. The positive value of θ_P, the triangular coordination of the magnetic (Ce) atoms and the weak effect of applied magnetic field, reveal that T_M cannot be considered as a canonic antiferromagnetic transition like claimed in the literature. M(T) measurements under moderate magnetic fields () show T_C(B) increasing while T_M(B) is practically not affected. Both transition merge in a critical point at for , where the intermediate phase is suppressed. At , the cusp of a first order transition is observed in C_P(T). According to the proposed ferromagnetic ground state, it is followed by a C_P(T)∝T^3/2exp(-E_g/T) dependence, with a gap of anisotropy .     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

Pressure cycle of superconducting Cs0.8Fe2Se2 : A transport study

We report measurements of the temperature and pressure dependence of the electrical resistivity (ρ) of single-crystalline iron-based chalcogenide Cs_0.8Fe₂Se₂. In this material, superconductivity with a transition temperature develops from a normal state with extremely large resistivity. At ambient pressure, a large “hump” in the resistivity is observed around 200 K. Under pressure, the resistivity decreases by two orders of magnitude, concomitant with a sudden T_c suppression around . Even at 9 GPa a metallic resistivity state is not recovered, and the ρ(T) “hump” is still detected. A comparison of the data measured upon increasing and decreasing the external pressure leads us to suggest that the superconductivity is not related to this hump.     

Minimal position-velocity uncertainty wave packets in relativistic and non-relativistic quantum mechanics

We consider wave packets of free particles with a general energy-momentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v=∂_pE. The position-velocity uncertainty relation is saturated by minimal uncertainty wave packets Φ(p)=Aexp(-αE(p)+βp). In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation E(p)=p²/2m, analytic calculations are presented for the spreading of wave packets with minimal position-velocity uncertainty product for the lattice dispersion relation E(p)=-cos(pa)/ma² as well as for the relativistic dispersion relation . The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.