Kinetics of Particles Adsorption Processes Driven by Diffusion

The kinetics of the deposition of colloidal particles onto a solid surface is analytically studied. We take into account both the diffusion of particles from the bulk as well as the geometrical aspects of the layer of adsorbed particles. We derive the first kinetic equation for the coverage of the surface (a generalized Langmuir equation) whose predictions are in agreement with recent simulation results where diffusion of particles from the bulk is explicitly considered.Comment: 4 page

A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator

Dissipative Particle Dynamics with Energy Conservation

The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the evolution of the probability distribution for the system is deduced together with the corresponding fluctuation-dissipation theorems ensuring that the ab initio chosen equilibrium probability distribution for the relevant variables is a stationary solution. When energy conservation is included, the system can sustain temperature gradients and heat flow can be modeled.Comment: 7 pages, submitted to Europhys. Let

Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces

[EN] Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.J. Bonet was partially supported by the research projects MTM2016-76647-P and GV Prometeo 2017/102 (Spain). M. Worku is supported by ISP project, Addis Ababa University, Ethiopia.Bonet Solves, JA.; Mengestie, T.; Worku, M. (2019). Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces. Results in Mathematics. 74(4):1-15. https://doi.org/10.1007/s00025-019-1123-7S115744Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017)Atzmon, A., Brive, B.: Surjectivity and invariant subspaces of differential operators on weighted Bergman spaces of entire functions, Bergman spaces and related topics in complex analysis, Contemp. Math., vol. 404, Amer. Math. Soc., Providence, RI, pp. 27–39 (2006)Bayart, F., Matheron, E.: Dynamics of Linear Operators, Cambridge Tracts in Math, vol. 179. Cambridge Univ. Press, Cambridge (2009)Bermúdez, T., Bonilla, A., Peris, A.: On hypercyclicity and supercyclicity criteria. Bull. Austral. Math. Soc. 70, 45–54 (2004)Beltrán, M.J.: Dynamics of differentiation and integration operators on weighted space of entire functions. Studia Math. 221, 35–60 (2014)Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141, 4293–4303 (2013)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonet, J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 26, 649–657 (2009)Bonet, J.: The spectrum of Volterra operators on weighted Banach spaces of entire functions. Q. J. Math. 66, 799–807 (2015)Bonet, J., Bonilla, A.: Chaos of the differentiation operator on weighted Banach spaces of entire functions. Complex Anal. Oper. Theory 7, 33–42 (2013)Bonet, J., Taskinen, J.: A note about Volterra operators on weighted Banach spaces of entire functions. Math. Nachr. 288, 1216–1225 (2015)Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. Lond. Math. Soc. 47, 958–963 (2015)Constantin, O., Peláez, J.-Á.: Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2016)De La Rosa, M., Read, C.: A hypercyclic operator whose direct sum is not hypercyclic. J. Oper. Theory 61, 369–380 (2009)Dunford, N.: Spectral theory. I. Convergence to projections. Trans. Am. Math. Soc. 54, 185–217 (1943)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear Chaos. Springer, New York (2011)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008)Krengel, U.: Ergodic Theorems. Walter de Gruyter, Berlin (1985)Lyubich, Yu.: Spectral localization, power boundedness and invariant subspaces under Ritt’s type condition. Studia Mathematica 143(2), 153–167 (1999)Mengestie, T.: A note on the differential operator on generalized Fock spaces. J. Math. Anal. Appl. 458(2), 937–948 (2018)Mengestie, T.: Spectral properties of Volterra-type integral operators on Fock–Sobolev spaces. J. Kor. Math. Soc. 54(6), 1801–1816 (2017)Mengestie, T.: On the spectrum of volterra-type integral operators on Fock–Sobolev spaces. Complex Anal. Oper. Theory 11(6), 1451–1461 (2017)Mengestie, T., Ueki, S.: Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal. Oper. Theory 13, 935–95 (2019)Mengestie, T., Worku, M.: Isolated and essentially isolated Volterra-type integral operators on generalized Fock spaces. Integr. Transf. Spec. Funct. 30, 41–54 (2019)Nagy, B., Zemanek, J.A.: A resolvent condition implying power boundedness. Studia Math. 134, 143–151 (1999)Nevanlinna, O.: Convergence of iterations for linear equations. Lecture Notes in Mathematics. ETH Zürich, Birkhäuser, Basel (1993)Ritt, R.K.: A condition that $$\lim _{n\rightarrow \infty } n^{-1}T^n =0$$. Proc. Am. Math. Soc. 4, 898–899 (1953)Ueki, S.: Characterization for Fock-type space via higher order derivatives and its application. Complex Anal. Oper. Theory 8, 1475–1486 (2014)Yosida, K.: Functional Analysis. Springer, Berlin (1978)Yosida, K., Kakutani, S.: Operator-theoretical treatment of Marko’s process and mean ergodic theorem. Ann. Math. 42(1), 188–228 (1941

Magnetic Anisotropy Variations and Non-Equilibrium Tunneling in a Cobalt Nanoparticle

We present detailed measurements of the discrete electron-tunneling level spectrum within nanometer-scale cobalt particles as a function of magnetic field and gate voltage, in this way probing individual quantum many-body eigenstates inside ferromagnetic samples. Variations among the observed levels indicate that different quantum states within one particle are subject to different magnetic anisotropy energies. Gate-voltage studies demonstrate that the low-energy tunneling spectrum is affected dramatically by the presence of non-equilibrium spin excitations

Characterization of horizontal flows around solar pores from high-resolution time series of images

Though there is increasing evidence linking the moat flow and the Evershed flow along the penumbral filaments, there is not a clear consensus regarding the existence of a moat flow around umbral cores and pores, and the debate is still open. Solar pores appear to be a suitable scenario to test the moat-penumbra relation as evidencing the direct interaction between the umbra and the convective plasma in the surrounding photosphere, without any intermediate structure in between. The present work studies solar pores based on high resolution ground-based and satellite observations. Local correlation tracking techniques have been applied to different-duration time series to analyze the horizontal flows around several solar pores. Our results establish that the flows calculated from different solar pore observations are coherent among each other and show the determinant and overall influence of exploding events in the granulation around the pores. We do not find any sign of moat-like flows surrounding solar pores but a clearly defined region of inflows surrounding them. The connection between moat flows and flows associated to penumbral filaments is hereby reinforced by this work.Comment: 10 pages, 10 figures, Accepted for publication in Astronomy and Astrophysics

Orbital Kondo effect in carbon nanotubes

Progress in the fabrication of nanometer-scale electronic devices is opening new opportunities to uncover the deepest aspects of the Kondo effect, one of the paradigmatic phenomena in the physics of strongly correlated electrons. Artificial single-impurity Kondo systems have been realized in various nanostructures, including semiconductor quantum dots, carbon nanotubes and individual molecules. The Kondo effect is usually regarded as a spin-related phenomenon, namely the coherent exchange of the spin between a localized state and a Fermi sea of electrons. In principle, however, the role of the spin could be replaced by other degrees of freedom, such as an orbital quantum number. Here we demonstrate that the unique electronic structure of carbon nanotubes enables the observation of a purely orbital Kondo effect. We use a magnetic field to tune spin-polarized states into orbital degeneracy and conclude that the orbital quantum number is conserved during tunneling. When orbital and spin degeneracies are simultaneously present, we observe a strongly enhanced Kondo effect, with a multiple splitting of the Kondo resonance at finite field and predicted to obey a so-called SU(4) symmetry.Comment: 26 pages, including 4+2 figure

An analysis of the local optima storage capacity of Hopfield network based fitness function models

A Hopfield Neural Network (HNN) with a new weight update rule can be treated as a second order Estimation of Distribution Algorithm (EDA) or Fitness Function Model (FFM) for solving optimisation problems. The HNN models promising solutions and has a capacity for storing a certain number of local optima as low energy attractors. Solutions are generated by sampling the patterns stored in the attractors. The number of attractors a network can store (its capacity) has an impact on solution diversity and, consequently solution quality. This paper introduces two new HNN learning rules and presents the Hopfield EDA (HEDA), which learns weight values from samples of the fitness function. It investigates the attractor storage capacity of the HEDA and shows it to be equal to that known in the literature for a standard HNN. The relationship between HEDA capacity and linkage order is also investigated

Tracking magnetic bright point motions through the solar atmosphere

High-cadence, multiwavelength observations and simulations are employed for the analysis of solar photospheric magnetic bright points (MBPs) in the quiet Sun. The observations were obtained with the Rapid Oscillations in the Solar Atmosphere (ROSA) imager and the Interferometric Bidimensional Spectrometer at the Dunn Solar Telescope. Our analysis reveals that photospheric MBPs have an average transverse velocity of approximately 1 km s−1, whereas their chromospheric counterparts have a slightly higher average velocity of 1.4 km s−1. Additionally, chromospheric MBPs were found to be around 63 per cent larger than the equivalent photospheric MBPs. These velocity values were compared with the output of numerical simulations generated using the MURAM code. The simulated results were similar, but slightly elevated, when compared to the observed data. An average velocity of 1.3 km s−1 was found in the simulated G-band images and an average of 1.8 km s−1 seen in the velocity domain at a height of 500 km above the continuum formation layer. Delays in the change of velocities were also analysed. Average delays of ∼4 s between layers of the simulated data set were established and values of ∼29 s observed between G-band and Ca II K ROSA observations. The delays in the simulations are likely to be the result of oblique granular shock waves, whereas those found in the observations are possibly the result of a semi-rigid flux tube