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].     

The Ho thickness dependence of spin-triplet supercurrents in Nb/Ho/Co/Ho/Nb films

Robinson et al. [J.W.A. Robinson, et al., Science 329 (2010) 59] reported control of spin-triplet supercurrents into ferromagnets by varying the thicknesses of the Ho injector and attributed the voltage peaks to non-integer spiral wavelengths of λ/2 and 5λ/2 in Ho. Here we demonstrate that these peaks correspond to λ/2 and 3λ/2.     

The generalized zero-mode supersymmetry scheme and the confluent algorithm

We show the relationship between the mathematical framework used in recent papers by Rosu et al. (2014) [1–3] and the second-order confluent supersymmetric quantum mechanics. In addition, we point out several immediate generalizations of the approach taken in the latter references. Furthermore, it is shown how to apply the generalized scheme to the Dirac and to the Fokker–Planck equation.     

Local Gromov–Witten invariants of blowups of Fano surfaces

In this paper, using the degeneration formula we obtain a blowup formula of local Gromov–Witten invariants of Fano surfaces. This formula makes it possible to compute the local Gromov–Witten invariants of non-toric Fano surfaces from toric Fano surfaces, such as del Pezzo surfaces. This formula also verified an expectation of Chiang–Klemm–Yau–Zaslow in Section 8.3 of Chiang et al. (1999) [7]     

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.     

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].     

Modeling quantum mechanical double slit interference via anomalous diffusion: Independently variable slit widths

Based on a re-formulation of the classical explanation of quantum mechanical Gaussian dispersion (Grössing et al. (2010) [1]) as well as interference of two Gaussians (Grössing et al. (2012) [6]), we present a new and more practical way of their simulation. The quantum mechanical “decay of the wave packet” can be described by anomalous sub-quantum diffusion with a specific diffusivity varying in time due to a particle’s changing thermal environment. In a simulation of the double-slit experiment with different slit widths, the phase with this new approach can be implemented as a local quantity. We describe the conditions of the diffusivity and, by connecting to wave mechanics, we compute the exact quantum mechanical intensity distributions, as well as the corresponding trajectory distributions according to the velocity field of two Gaussian wave packets emerging from a double-slit. We also calculate probability density current distributions, including situations where phase shifters affect a single slit’s current, and provide computer simulations thereof.     

Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

The inverse of the Faddeev–Popov operator plays a pivotal role within the Gribov–Zwanziger approach to the quantization of Euclidean Yang–Mills theories in Landau gauge. Following a recent proposal (Capri et al., 2014), we show that the inverse of the Faddeev–Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders.     

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.     

Pinkness of the North Atlantic Oscillation signal revisited

The long episode of negative values in the North Atlantic Oscillation (NAO) index during the winter season 2009-2010 has attracted more attention to its predictability. Previous analyses (Fernández et al. (2003) [16] and Caldeira et al. (2007) [25]) by this same author group have established that the NAO signal behaves as a slightly red noise and therefore the prediction of the phenomenon must rely upon a deeper understanding of the underlying Physics. In this paper the authors address a predictability study of the NAO index by applying the “detrended fluctuation analysis” (DFA) to a composite series, completed with a bootstrap spectral analysis. The DFA provides a quantitative measure of predictability by computing several piecewise fits, either linear or higher degree polynomial ones, to a cumulative series of fluctuations associated to the original series. These newer measurements agree with the previous results.     

The discrimination algorithms for overlapped MPSK and MQAM modulations using higher-order cumulants

Automatic Modulation Classification (AMC) is responsible for detecting the correct modulation types in the intelligent receivers. AMC performance degrades when the signal-to-noise ratio (SNR) decreases because of the overlapping among the digital modulation types’ features, and this performance worsens under fading channel conditions. This paper proposes two new algorithms that improve the AMC performance accuracy of the overlapped digital modulations in feature space by improving their discrimination. These algorithms are named temporal Fisher discriminant analysis (TFDA) and supervised Fisher discriminant analysis (SFDA). The simulation results show that TFDA improves AMC performance accuracy up to 19.01% compared with the reference paper (Ge et al., 2021) and up to 38.15% compared with the reference paper (Teng et al., 2018). In contrast, SFDA improves AMC performance accuracy up to 23.12 % compared with the reference paper (Ge et al., 2021) and up to 49.025% compared with the reference paper (Teng et al., 2018).     

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.     

Radial distribution of dose within heavy charged particle tracks – Models and experimental verification using LiF:Mg,Cu,P TL detectors

A new method of experimental verification of radial dose distribution models using solid state thermoluminescent (TL) detectors LiF:Mg,Cu,P has been recently proposed. In this work the method was applied to verify the spatial distribution of energy deposition within a single ¹³¹Xe ion track. Detectors were irradiated at the Department of Physics of the University of Jyväskylä, Finland. The obtained results have been compared with theoretical data, calculated according to the Zhang et al., Cucinotta et al. and Geiss et al. radial dose distribution (RDD) models. At the lowest dose range the Zhang et al. RDD model exhibited the best agreement as compared to experimental data. In the intermediate dose range, up to 10⁴ Gy, the best agreement was found for the RDD model of Cucinotta et al. The probability of occurrence of doses higher than 10⁴ Gy within a single ¹³¹Xe ion track was found to be lower than predicted by all the studied RDD models. This may be a result of diffusion of the charge, which is then captured by TL-related trapping sites, at the distances up to dozens of nanometers from the ionization site.     

Wilson loops in warped resolved deformed conifolds

We calculate quark–antiquark potentials using the relationship between the expectation value of the Wilson loop and the action of a probe string in the string dual. We review and categorise the possible forms of the dependence of the energy on the separation between the quarks. In particular, we examine the possibility of there being a minimum separation for probe strings which do not penetrate close to the origin of the bulk space, and derive a condition which determines whether this is the case. We then apply these considerations to the flavoured resolved deformed conifold background of Gaillard et al. (2010) [8]. We suggest that the unusual behaviour that we observe in this solution is likely to be related to the IR singularity which is not present in the unflavoured case.     

A note on fractional linear pure birth and pure death processes in epidemic models

In this note we highlight the role of fractional linear birth and linear death processes, recently studied in Orsingher et al. (2010) [5] and Orsingher and Polito (2010) [6], in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation for self-consistency of the epidemic type aftershock sequences (ETAS) model and the fractional differential equation describing the mean value of fractional linear growth processes, we show some interesting applications of fractional modelling in studying ab initio epidemic processes without the assumption of any empirical distribution. We also show that, in the framework of fractional modelling, subcritical regimes can be linked to linear fractional death processes and supercritical regimes to linear fractional birth processes.Moreover we discuss a simple toy model in order to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth.     

Towards molecular computers that operate in a biological environment

Even though electronic computers are the only computer species we are accustomed to, the mathematical notion of a programmable computer has nothing to do with electronics. In fact, Alan Turing’s notional computer [L.M. Turing, On computable numbers, with an application to the entcheidungsproblem, Proc. Lond. Math. Soc. 42 (1936) 230-265], which marked in 1936 the birth of modern computer science and still stands at its heart, has greater similarity to natural biomolecular machines such as the ribosome and polymerases than to electronic computers. This similarity led to the investigation of DNA-based computers [C.H. Bennett, The thermodynamics of computation — Review, Int. J. Theoret. Phys. 21 (1982) 905-940; A.M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021-1024]. Although parallelism, sequence specific hybridization and storage capacity, inherent to DNA and RNA molecules, can be exploited in molecular computers to solve complex mathematical problems [Q. Ouyang, et al., DNA solution of the maximal clique problem, Science 278 (1997) 446-449; R.J. Lipton, DNA solution of hard computational problems, Science 268 (1995) 542-545; R.S. Braich, et al., Solution of a 20-variable 3-SAT problem on a DNA computer, Science 296 (2002) 499-502; Liu Q., et al., DNA computing on surfaces, Nature 403 (2000) 175-179; D. Faulhammer, et al., Molecular computation: RNA solutions to chess problems, Proc. Natl. Acad. Sci. USA 97 (2000) 1385-1389; C. Mao, et al., Logical computation using algorithmic self-assembly of DNA triple-crossover molecules, Nature 407 (2000) 493-496; A.J. Ruben, et al., The past, present and future of molecular computing, Nat. Rev. Mol. Cell. Biol. 1 (2000) 69-72], we believe that the more significant potential of molecular computers lies in their ability to interact directly with a biochemical environment such as the bloodstream and living cells. From this perspective, even simple molecular computations may have important consequences when performed in a proper context. We envision that molecular computers that operate in a biological environment can be the basis of “smart drugs”, which are potent drugs that activate only if certain environmental conditions hold. These conditions could include abnormalities in the molecular composition of the biological environment that are indicative of a particular disease. Here we review the research direction that set this vision and attempts to realize it.     

Possible existence of wormholes in the central regions of halos

An earlier study (Rahaman, et al., 2014 and Kuhfittig, 2014) has demonstrated the possible existence of wormholes in the outer regions of the galactic halo, based on the Navarro–Frenk–White (NFW) density profile. This paper uses the Universal Rotation Curve (URC) dark matter model to obtain analogous results for the central parts of the halo. This result is an important compliment to the earlier result, thereby confirming the possible existence of wormholes in most of the spiral galaxies.     

Solving Toda field theories and related algebraic and differential properties

Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld–Sokolov gauge is used. The main objective of this paper is to carry out this approach of solving the Toda field theories for the classical Lie algebras, following Balog et al. (1990) [5]. In this process, we discover and prove some algebraic identities for principal minors of special matrices. The known elegant solutions of Leznov (1980) [10] fit in our scheme in the sense that they are the general solutions to our conditions discovered in this solving process. To prove this, we find and prove some differential identities for iterated integrals. It can be said that altogether our paper gives complete mathematical proofs for Leznov’s solutions.     

Continuous distribution of relaxation times during mechanical relaxation of fully-stabilized zirconia

The internal friction (IF) was measured for ZrO₂ doped with 10 mol% Y₂O₃ polycrystals and single crystals before aging. The degree of the temperature shift with the frequency change δ(1/T?) was examined in order to determine if one or both parameters in the Arrhenius's equation contribute to the occurrence of the continuous distribution of relaxation times (τ). A continuous distribution is derived only from the continuous distribution of the pre-exponential factor (τ ₀), while the activation energies (H?) for τ are constant in two peaks. The peak fitting was carried out using some conventional distribution functions, i.e., the RCSI model, and some famous functions for dielectric relaxation. The IF curves can be fitted quite well by the Kohlrousch–Williams–Watts (KWW) equation with reasonable parameters. The orientation factor (Γ) dependence of the relaxation of the reciprocal torsional modulus (δG ^?1) is a linear function relative to Γ in both peaks. When the H for τ of both peaks of the poly- and single crystals was compared, the polycrystalline results should be considered average values of the single-crystalline results. Therefore, the single-crystalline IF peaks also consist of two peaks and the parameters (the relaxation strength and H?) obtained by the peak fitting are valid. A continuous distribution of τ is derived only from the continuous distribution of τ ₀ and the distribution function is the KWW equation.     

The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

This paper studies a reaction–diffusion–chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.