3,420 research outputs found
Convergence analysis of the scaled boundary finite element method for the Laplace equation
The scaled boundary finite element method (SBFEM) is a relatively recent
boundary element method that allows the approximation of solutions to PDEs
without the need of a fundamental solution. A theoretical framework for the
convergence analysis of SBFEM is proposed here. This is achieved by defining a
space of semi-discrete functions and constructing an interpolation operator
onto this space. We prove error estimates for this interpolation operator and
show that optimal convergence to the solution can be obtained in SBFEM. These
theoretical results are backed by a numerical example.Comment: 15 pages, 3 figure
Entropy involved in fidelity of DNA replication
Information has an entropic character which can be analyzed within the
Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed
that a logical copy can be carried out in the limit of no dissipation if the
computation is performed sufficiently slowly. Structural and recent
single-molecule assays have provided dynamic details of polymerase machinery
with insight into information processing. We introduce a rigorous
characterization of Shannon Information in biomolecular systems and apply it to
DNA replication in the limit of no dissipation. Specifically, we devise an
equilibrium pathway in DNA replication to determine the entropy generated in
copying the information from a DNA template in the absence of friction. Both
the initial state, the free nucleotides randomly distributed in certain
concentrations, and the final state, a polymerized strand, are mesoscopic
equilibrium states for the nucleotide distribution. We use empirical stacking
free energies to calculate the probabilities of incorporation of the
nucleotides. The copied strand is, to first order of approximation, a state of
independent and non-indentically distributed random variables for which the
nucleotide that is incorporated by the polymerase at each step is dictated by
the template strand, and to second order of approximation, a state of
non-uniformly distributed random variables with nearest-neighbor interactions
for which the recognition of secondary structure by the polymerase in the
resultant double-stranded polymer determines the entropy of the replicated
strand. Two incorporation mechanisms arise naturally and their biological
meanings are explained. It is known that replication occurs far from
equilibrium and therefore the Shannon entropy here derived represents an upper
bound for replication to take place. Likewise, this entropy sets a universal
lower bound for the copying fidelity in replication.Comment: 25 pages, 5 figure
The Rate of Information Transfer of Naturalistic Stimulation by Graded Potentials
We present a method to measure the rate of information transfer for any continuous signals of finite duration without assumptions. After testing the method with simulated responses, we measure the encoding performance of Calliphora photoreceptors. We find that especially for naturalistic stimulation the responses are nonlinear and noise is nonadditive, and show that adaptation mechanisms affect signal and noise differentially depending on the time scale, structure, and speed of the stimulus. Different signaling strategies for short- and long-term and dim and bright light are found for this graded system when stimulated with naturalistic light changes
Effects of an eccentric inner Jupiter on the dynamical evolution of icy body reservoirs in a planetary scattering scenario
Aims. We analyze the dynamics of small body reservoirs under the effects of an eccentric inner giant planet resulting from a planetary scattering event around a 0.5 M⊙ star. Methods. First, we used a semi-analytical model to define the properties of the protoplanetary disk that lead to the formation of three Jupiter-mass planets. Then, we carried out N-body simulations assuming that the planets are close to their stability limit together with an outer planetesimal disk. In particular, the present work focused on the analysis of N-body simulations in which a single Jupiter-mass planet survives after the dynamical instability event. Results. Our simulations produce outer small body reservoirs with particles on prograde and retrograde orbits, and other ones whose orbital plane flips from prograde to retrograde and back again along their evolution (“Type-F particles”). We find strong correlations between the inclination i and the ascending node longitude Ω of Type-F particles. First, Ω librates around 90° or/and 270°. This property represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods of i and Ω are equal and they are out to phase by a quarter period. We also remark that the larger the libration amplitude of i, the larger the libration amplitude of Ω. We analyze the orbital parameters of Type-F particles immediately after the instability event (post IE orbital parameters), when a single Jupiter-mass planet survives in the system. Our results suggest that the orbit of a particle can flip for any value of its post IE eccentricity, although we find only two Type-F particles with post IE inclinations i ≲ 17°. Finally, our study indicates that the minimum value of the inclination of the Type-F particles in a given system decreases with an increase in the eccentricity of the giant planet.Fil: Zanardi, Macarena. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: de Elia, Gonzalo Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Di Sisto, Romina Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Naoz, S.. University of California at Los Angeles; Estados UnidosFil: Li, G.. Harvard-Smithsonian Center for Astrophysics; Estados UnidosFil: Guilera, O. M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Brunini, A.. Universidad Nacional de la Patagonia Austral; Argentin
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