A Lagrangian description of transport associated with a front-eddy interaction: Application to data from the North-Western Mediterranean Sea

We discuss the Lagrangian transport in a time-dependent oceanic system involving a Lagrangian barrier associated with a salinity front which interacts intermittently with a set of Lagrangian eddies — ‘leaky’ coherent structures that entrain and detrain fluid as they move. A theoretical framework, rooted in the dynamical systems theory, is developed in order to describe and analyse this situation. We show that such an analysis can be successfully applied to a realistic ocean model. Here, we use the output of the numerical ocean model DieCAST from Dietrich et al. (2004) [17] and Fernández et al. (2005) [18] studied earlier in Mancho et al. (2008) [15] where a Lagrangian barrier associated with the North Balearic Front in the North-Western Mediterranean Sea was identified. The numerical model provides an Eulerian view of the flow and we employ the dynamical systems approach to identify relevant hyperbolic trajectories and their stable and unstable manifolds. These manifolds are used to understand the Lagrangian geometry of the evolving front-eddy system. Transport in this system is effected by the turnstile mechanism whose spatio-temporal geometry reveals intermittent pathways along which transport occurs. Particular attention is paid to the ‘Lagrangian’ interactions between the front and the eddies, and to transport implications associated with the transition between the one-eddy and two-eddy situation. The analysis of this ‘Lagrangian’ transition is aided by a local kinematic model that provides insight into the nature of the change in hyperbolic trajectories and their stable and unstable manifolds associated with the ‘birth’ and ‘death’ of leaky Lagrangian eddies.     

Are per capita incomes of MENA countries converging or diverging?

This study considers the issue of income convergence among the MENA (Middle East and North African) countries by using real per capita incomes over the period 1950-2006. We employed (Kapetanios et al. 2003) [21] unit root test by incorporating an additive constant and a trend component as Chong et al. (2008) [20] did in their study and found most of the MENA countries diverging during the sample period.     

Chiral decomposition in the non-commutative Landau problem

The decomposition of the non-commutative Landau (NCL) system into two uncoupled one-dimensional chiral components, advocated by Alvarez et al. (2008) [1], is generalized to nonvanishing electric fields. This allows us to discuss the main properties of the NCL problem including its exotic Newton–Hooke symmetry and its relation to the Hall effect. The “phase transition” when the magnetic field crosses a critical value determined by the non-commutative parameter is studied in detail.     

Spectral variations in the optical transition matrix element and their impact on the optical properties associated with hydrogenated amorphous silicon

Using an empirical model for the density of states functions associated with hydrogenated amorphous silicon, in conjunction with an elementary model for the optical transition matrix elements, we aim to explore how variations in the matrix elements impact upon the spectral dependence of the optical properties associated with this material. We also wish to ascertain as to whether or not the hydrogenated amorphous silicon mobility gap result suggested by Jackson et al. [W.B. Jackson, S.M. Kelso, C.C. Tsai, J.W. Allen, S.-J. Oh, Phys. Rev. B 31 (1985) 5187] is consistent with the results of the experiment. We find that the mobility gap value suggested by Jackson et al. is too large. An upper bound on the mobility gap associated with hydrogenated amorphous silicon of 1.68 eV is suggested instead. Electrical measurements performed on undoped hydrogenated amorphous silicon yield a mobility gap value that is consistent with this bound.     

Biquantization of symmetric pairs and the quantum shift

The biquantization of symmetric pairs was studied by Cattaneo et al. (2008)  [1] in terms of Kontsevich-like graphs. This note, also in view of recent results by Calaque et al. (2009)  [3], amends a minor mistake that did not spoil the main results of the paper. The mistake consisted in ignoring a regular term in the boundary contribution of some propagators. On the other hand, its correction brings back the quantum shift, present in the approaches by the orbit method, that was otherwise puzzlingly missing. In addition a detailed comparison of the two, equivalent, ways of defining biquantization working on the upper half plane or on one quadrant is presented, as well as a more conceptual approach to biquantization and the due corrections of some results of Cattaneo et al. (2008)  [1] in view of the aforementioned correction by the quantum shift.     

Global variational calculations of high-resolution rovibrational spectra: isotopic effects,intensity anomalies and experimental confirmations for H2S,HDS, D2S molecules

Variational calculations of high-resolution infrared molecular spectra for isotopically substituted triatomic molecules from potential and dipole moment functions are discussed. A study of intensity anomalies and of their isotopical behavior especially for symmetry-breaking substitutions represents a particularly interesting subject. Extreme manifestations of intensity anomalies present in spectra of the hydrogen sulfide molecule are considered. A first qualitative experimental confirmation of reported theoretical results for deuterium containing species is discussed. To cite this article: Vl.G. Tyuterev et al., C. R. Physique 5 (2004).     

On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability

In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.     

Room evacuation in the presence of an obstacle

The investigation of human behaviour while trying to escape from a room under panic is an important issue in complex systems research. Several authors have called attention to the fact that placing an obstacle near the exit improves the evacuation time of the room (Helbing et al. (2000, 2005) [2] and [8], Hughes (2003) [6], Johansson and Helbing (2005) [16], Piccoli and Tosin (2009) [5]). We studied this effect in the context of the “social force model” (Helbing et al. (2000) [2]). We show that placing an obstacle does not guarantee, by itself, better chances of survival for all pedestrians. The way they choose to avoid the obstacle is critical for their own performance. We found not only that the faster they try to escape, the slower they get out (“faster is slower” effect), but also, the short cut they might take in order to get to the exit will probably do no better (“clever is not always better” effect).     

Analysis of stock prices of mining business

Stock exchanges have a diversity of so-called business groups and much evidence has been presented by covariance matrix analysis (Laloux et al. (1999) [6], Plerou et al. (2002) [7], Plerou et al. (1999) [8], Mantegna (1999) [9], Utsugi et al. (2004) [21] and Lim et al. (2009) [26]). A market-wide effect plays a crucial role in shifting the correlation structure from random to non-random. In this work, we study the structural properties of stocks related to the mining industry, especially rare earth minerals, listed on two exchanges, namely the TSX (Toronto stock exchange) and the TSX-V (Toronto stock exchange-ventures). In general, raw-material businesses are sensitively affected by the global economy while each firm has its own cycle. We prove that the global crisis during 2006–2009 affected the mineral market considerably. These two aspects compete to control price fluctuations. We show that the internal cycle overwhelms the global economic environment in terms of random matrix theory and overlapping matrices. However, during the period of 2006–2009, the effect of the global economic environment emerges. This result is well explained by the recent global financial/economic crisis. For comparison, we analyze the time stability of business clusters of the KOSPI, that is, the electric/electronic business, using an overlapping matrix. A clear difference in behavior is confirmed. Consequently, rare earth minerals in the raw-material business should be classified not by standard business classifications but by the internal cycle of business.     

Theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen

The 7σ$7\sigma$ discrepancy between the proton rms charge radius from muonic hydrogen and the CODATA-2010 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S–2P transition frequencies measured in muonic hydrogen; see Pohl et al. (2010) [9] and Antognini et al. (2013) [71].     

flatIGW — An inverse algorithm to compute the density of states of lattice self avoiding walks

We show that the Density of States (DoS) for lattice Self Avoiding Walks can be estimated by using an inverse algorithm, called flatIGW, whose step-growth rules are dynamically adjusted by requiring the energy histogram to be locally flat. Here, the (attractive) energy associated with a configuration is taken to be proportional to the number of non-bonded nearest neighbor pairs (contacts). The energy histogram is able to explicitly direct the growth of a walk because the step-growth rule of the Interacting Growth Walk (Narasimhan et al. (2003) [5]) samples the available nearest neighbor sites according to the number of contacts they would make. We have obtained the complex Fisher zeros corresponding to the DoS, estimated for square lattice walks of various lengths, and located the θ temperature by extrapolating the finite size values of the real zeros to their asymptotic value, ∼1.49 (reasonably close to the known value, ∼1.50 (Barkema et al. (1998) [14]).     

Anderson Localization for a Supersymmetric Sigma Model

We study a lattice sigma model which is expected to reflect the Anderson localization and delocalization transition for real symmetric band matrices in 3D. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. The existence of a diffusive phase in 3 dimensions was proved in Disertori et al. (Commun. Math. Phys., doi:, 2009) [2] for low temperatures. Here we prove localization at high temperatures for any dimension d ≥ 1. Our analysis uses Ward identities coming from internal supersymmetry.     

Michaelis-Menten mechanism for single-enzyme and multi-enzyme system under stochastic noise and spatial diffusion

The investigation of enzymatic reaction under stochastic effect and spatial effect is an interesting problem. By virtue of Monte Carlo simulation, the stochastic dynamic of enzyme and the related Michaelis-Menten mechanism with stochastic internal noise and spatial diffusion are explored in this article. (i) For the single-enzyme system, two cases, including the fast phosphorylation case [X. S. Xie, et al., J. Phys. Chem. B 109 (2005) 19068] and slow phosphorylation case [X. S. Xie, et al., Nat. Chem. Biol. 2 (2006) 87] are considered. It is found the micro enzymatic velocity rate shows a rough hyperbolic dependence on the substrate concentration, hence obeys the Michaelis-Menten law qualitatively. In addition, our result reveals that diffusion rate can adjust the Michaelis-Menten curve; especially, it is shown that increasing diffusion rate enhances the micro enzyme rate. (ii) For the multi-enzyme system, a typical example, i.e., MAPK signaling pathway is used. We apply the Michaelis-Menten mechanism to the MAPK cascade and give a simple comparison for the signaling ability between the Michaelis-Menten mechanism and the single collision mechanism [J. W. Locasale et al., PLOS Comput. Biol. 4 (2008) e1000099].     

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.     

Arc rotation characteristics of a plasma centrifuge with a counter-rotating electrical discharge

Arc rotation velocities of a plasma centrifuge with a counter-rotating electrical discharge were measured by using double probes placed perpendicular to each other. The measurement results were compared with the results calculated from the analytic solutions suggested by Hong et al. The comparison revealed that the arc column near the electrodes can be rotated much faster by increasing the arc currents and magnetic fields. For example, the rotational velocity of the are column near the electrodes was increased from 75 to 150 m/s with the increase of magnetic flux density from 15 to 45 mT at the fixed arc current of 50 A. On the other hand, the rotational velocity of the arc column showed only negligible changes at the plane of symmetry, where the radial component of the arc current was designed to become zero due to the symmetry of the counter-rotating electrical discharge. From these measurement results and analytic solutions, gaseous mixtures of different masses can be separated effectively near the electrode regions of a plasma centrifuge with a counter-rotating electrical discharge.     

Quantum-like dynamics of decision-making

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the “rational strategy” provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect (“irrationality” of players) Asano et al. (2010, 2011) [23] and [24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011) [55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker.     

Phase-field model for multiphase systems with different thermodynamic factors

A modified phase-field model for quantitative simulations of low-speed phase transitions in multiphase systems is proposed, which takes into account the difference between thermodynamic factors in all the phases. The presented model is based on the quantitative phase-field concept developed by Steinbach et al. [I. Steinbach, F. Pezolla, B. Nestler, M. Seeelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135] for multiphase systems allowing to consider the multiphase transition as a superposition of pairwise interactions between two phases. We complete this approach and develop a model, which uses parameters derived from chemical free energy functions of individual phases evaluated from experimental data by the CALPHAD method Lukas et al. (2007) [17]. Because the thermodynamic factors are different in various phases we need to evaluate a special form of total chemical free energy function of a multiphase mixture and use it in the phase-field model. It is shown, that for the developed model the thin-interface asymptotic and the anti-trapping term developed previously for the solidification of pure substances can be applied. The model is verified by an example of the Al-Ni system whose peritectic structural morphology during the directional solidification is investigated. The suggested model can be also extended to multicomponent systems.     

Rare transition event with self-consistent theory of large-amplitude collective motion

A numerical simulation method, based on Dang et al.’s self-consistent theory of large-amplitude collective motion, for rare transition events is presented. The method provides a one-dimensional pathway without knowledge of the final configuration, which includes a dynamical effect caused by not only a potential but also kinetic term. Although it is difficult to apply the molecular dynamics simulation to a narrow-gate potential, the method presented is applicable to the case. A toy model with a high-energy barrier and/or the narrow gate shows that while the Dang et al. treatment is unstable for a changing of model parameters, our method stable for it.     

A first-principles study on phase transition induced by charge ordering of Mn3+/Mn4+ in spinel LiMn2O4

A first-order transition at 290 K in LiMn₂O₄ with a cubic spinel-type structure is known to degrade the electrochemical performance of the positive electrode of rechargeable lithium-ion batteries. Using first-principles density functional theory (DFT), we confirm that the phase transition is induced by charge-ordering of Mn³⁺/Mn⁴⁺ accompanied by orbital-ordering due to Jahn–Teller distortion, which is in agreement with the previous experimental results of Rodríguez-Carvajal et al. [J. Rodríguez-Carvajal, G. Rousse, C. Masquelier, M. Hervieu, Phys. Rev. Lett. 81 (1998) 4660]. The optimized structure of the low-temperature (LT) phase has orthorhombic symmetry with five distinct crystallographic sites for Mn. The spin integration at each Mn site shows that Mn³⁺ resides at three Mn sites and the remaining two sites are occupied by Mn⁴⁺ ions. Total energy calculations indicate that the LT phase is about 0.23 eV/ LiMn₂O₄ more stable than cubic LiMn₂O₄ (high-temperature phase). The electrochemical Li extraction reaction from the LT phase is also investigated using DFT calculations. The results indicate that the reaction is initially divided into two voltage regions. Electrostatic interactions in the LT phase are calculated using a point charge model, accounting for the features of the electronic configurations and electrochemical reactions.