Complete Range Of Parameters Research Articles

Competition of alliances in a cyclically dominant eight-species population

In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures them stable coexistence against the invasion of an external species. Our principal goal is to identify those general features of a formation which determine its vitality. Therefore, we here study a traditional Lotka–Volterra model of eight-species where two four-species cycles can fight for space. Beside these formations, there are other solutions which may emerge when invasion rates are varied. The complete range of parameters is explored and we find that in most of the cases those alliances prevail which are formed by equally strong members. Interestingly, there are regions where the symmetry is broken and the system is dominated by a solution formed by seven species. Our work also highlights that serious finite-size effects may emerge which prevent observing the valid solution in a small system.

Urn models for stochastic gene expression yield intuitive insights into the probability distributions of single-cell mRNA and protein counts

Fitting the probability mass functions from analytical solutions of stochastic models of gene expression to the single-cell count distributions of mRNA and protein molecules can yield valuable insights into mechanisms underlying gene expression. Solutions of chemical master equations are available for various kinetic schemes but, even for the basic ON–OFF genetic switch, they take complex forms with generating functions given as hypergeometric functions. Interpretation of gene expression dynamics in terms of bursts is not consistent with the complete range of parameters for these functions. Physical insights into the probability mass functions are essential to ensure proper interpretations but are lacking for models considering genetic switches. To fill this gap, we develop urn models for stochastic gene expression. We sample RNA polymerases or ribosomes from a master urn, which represents the cytosol, and assign them to recipient urns of two or more colors, which represent time intervals in which no switching occurs. Colors of the recipient urns represent sub-systems of the promoter states, and the assignments to urns of a specific color represent gene expression. We use elementary principles of discrete probability theory to solve a range of kinetic models without feedback, including the Peccoud–Ycart model, the Shahrezaei–Swain model, and models with an arbitrary number of promoter states. In the last case, we obtain a novel result for the protein distribution. For activated genes, we show that transcriptional lapses, which are events of gene inactivation for short time intervals separated by long active intervals, quantify the transcriptional dynamics better than bursts. We show that the intuition gained from our urn models may also be useful in understanding existing solutions for models with feedback. We contrast our models with urn models for related distributions, discuss a generalization of the Delaporte distribution for single-cell data analysis, and highlight the limitations of our models.

Hydrodynamics of a tandem fish school with asynchronous undulation of individuals

We perform numerical simulations using immersed boundary method for flow over a single and two fish in tandem performing traveling wave like motion for a range of Strouhal numbers. We investigate the hydrodynamic performance of single- and tandem-fish configurations using unsteady profiles of lateral side-force and drag coefficients, their time-averaged values, and wake behind these bodies. We present the spectra of hydrodynamic forces and find that the nature of these forces for a single fish resembles to those of stationary/oscillating bluff bodies and oscillating airfoils. For tandem cases, we vary the phase speed of undulatory motion of the rear fish while keeping the free-stream velocity constant. We show that hydrodynamic forces of the upstream and rear fish contain harmonics which are produced by nonlinear interaction of the oscillation frequencies of both fish. We find that the wake and time-averaged drag of the upstream fish remain almost independent of the undulating frequency of the rear fish at a certain Strouhal number. We also relate this observation with the absence of oscillation frequency of the rear fish in the Fourier spectra of hydrodynamic forces of the upstream fish. For the complete range of parameters, it is inferred that swimming in a tandem configuration seems more beneficial for the upstream fish. It happens due to wake-splitting effect of the rear fish that causes an enhancement of pressure in its wake. For the rear fish, it gains an advantage of drafting under certain conditions and its performance deteriorates at Strouhal numbers greater than 0.40.

Laser Cutting of CFRP with a Fibre Guided High Power Nanosecond Laser Source – Influence of the Optical Fibre Diameter on Quality and Efficiency

For the development of a robot based laser cutting process of automotive 3D parts consisting of carbon fibre reinforced plastics (CFRP), investigations with a newly developed fibre guided nanosecond pulsed laser with an average power of PL = 1.5 kW were conducted. In order to investigate the best combination of quality and process time 2 different optical fibres were used, with diameters of df = 400 μm and df = 600 μm. The main differences between the two setups are the resulting focal diameter and the maximum available pulse energy up to EP = 80 mJ. In a first instance, a comparable investigation was performed with both fibres for a constant pulse overlap. For each fibre the minimum required line energy was investigated and cuts were performed, distributed over the complete parameter range of the laser source. The influences of the fibre diameter on the quality and efficiency of the cutting process are summarized and discussed.

Simulation of Fractional-Order Low-Pass Filters

The attenuation of standard analog low-pass filters corresponds to a multiple value of -6 decibels per octave. This quantified value is related to the order of the filter. The issue addressed here is concerned with the extension of integer orders to non integer orders, such that the attenuation of a low-pass filter can be continuously adjusted. Fractional differential systems are known to provide such asymptotic behaviors and many results about their simulation are available. But even for a fixed cutoff frequency, their combination does not generate an additive group with respect to the order and they involve stability problems. In this paper, a class of low-pass filters with orders between 0 (the filter is a unit gain) and 1 (standard one-pole filter) is defined to restore these properties. These infinite dimensional filters are not fractional differential but admit some well-posed representations into weighted integrals of standard one-pole filters. Based on this, finite dimensional approximations are proposed and recast into the framework of statespace representations-space representations. A special care is given to reduce the computational complexity, through the dimension of the state. In practice, this objective is reached for the complete family, without damaging the perceptive quality, with dimension 13. Then, an accurate low-cost digital version of this family is built in the time-domain. The accuracy of the digital filters is verified on the complete range of parameters (cutoff frequencies and fractional orders). Moreover, the stability is guaranteed, even for time-varying parameters. As an application, a plugin has been implemented which provides a new audio tool for tuning the cutoff frequency and the asymptotic slope in a continuous way. As a very special application, choosing a one-half order combined with a low cutoff frequency (20 Hz or less), the filter fed with a white noise provides a pink noise generator.

Lattice density-functional theory of the attractive Hubbard model

The attractive Hubbard model is investigated in the framework of lattice density-functional theory (LDFT). The ground-state energy $E=T+W$ is regarded as a functional of the single-particle density matrix ${\ensuremath{\gamma}}_{ij}$ with respect to the lattice sites, where $T[\ensuremath{\gamma}]$ represents the kinetic and crystal-field energies and $W[\ensuremath{\gamma}]$ the interaction energy. Aside from the exactly known functional $T[\ensuremath{\gamma}]$, we propose a simple scaling approximation to $W[\ensuremath{\gamma}]$, which is based on exact analytic results for the attractive Hubbard dimer and on a scaling hypothesis within the domain of representability of $\ensuremath{\gamma}$. As applications, we consider one-, two-, and three-dimensional finite and extended bipartite lattices having homogeneous or alternating onsite energy levels. In addition, the Bethe lattice is investigated as a function of coordination number. Results are given for the kinetic, Coulomb, and total energies, as well as for the density distribution ${\ensuremath{\gamma}}_{ii}$, nearest-neighbor bond order ${\ensuremath{\gamma}}_{ij}$, and pairing energy $\ensuremath{\Delta}{E}_{p}$, as a function of the interaction strength $|U|/t$, onsite potential $\ensuremath{\varepsilon}/t$, and band filling $n={N}_{e}/{N}_{a}$. Remarkable even-odd and super-even oscillations of $\ensuremath{\Delta}{E}_{p}$ are observed in finite rings as a function of band filling. Comparison with exact Lanczos diagonalizations and density-matrix renormalization-group calculations shows that LDFT yields a very good quantitative description of the properties of the model in the complete parameter range, thus providing a significant improvement over the mean-field approaches. Goals and limitations of the method are discussed.

Viral Blips May Not Need a Trigger: How Transient Viremia Can Arise in Deterministic In-Host Models

Recurrent infection is characterized by short episodes of high viral reproduction, separated by long periods of relative quiescence. This recurrent pattern is observed in many persistent infections, including the “viral blips” observed during chronic infection with the human immunodeficiency virus (HIV). Although in-host models which incorporate forcing functions or stochastic elements have been shown to display viral blips, simple deterministic models also exhibit this phenomenon. We describe an analytical study of a 4-dimensional HIV antioxidant-therapy model which exhibits viral blips, showing that an increasing, saturating infectivity function contributes to the recurrent behavior of the model. Using dynamical systems theory, we hypothesize four conditions for the existence of viral blips in a deterministic in-host infection model. In particular, we explain how the blips are generated, which is not due to homoclinic bifurcation since no homoclinic orbits exist. These conditions allow us to develop very simple (2- and 3-dimensional) infection models which produce viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability analysis. We also use these conditions to demonstrate that low-dimensional in-host models with linear or constant infectivity functions cannot generate viral blips. Finally, we demonstrate that a 5-dimensional immunological model satisfies the conditions and exhibits recurrent infection even with constant infectivity; thus, an increasing, saturating infectivity function is not necessary if the model is sufficiently complex.

Conditions for Transient Viremia in Deterministic in-Host Models: Viral Blips Need No Exogenous Trigger

This paper presents an analytical study of the phenomenon of recurrent infection, that is, transient episodes of high viral reproduction, separated by long periods of relative quiescence, which are observed in many persistent infections; the “viral blips” observed during chronic infection with human immunodeficiency virus (HIV) are a well-known example. Although in-host models which incorporate forcing functions or stochastic elements have been proposed to generate viral blips, simple deterministic models also exhibit this phenomenon. Analyzing a 4-dimensional HIV antioxidant-therapy model which exhibits viral blips, we show that an increasing, saturating infectivity function may contribute to the recurrent behavior of the model. We then propose four conditions for the existence of viral blips in a deterministic in-host infection model. We use these conditions to derive the simplest (2- and 3-dimensional) infection model which produces viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability analysis. We also use these conditions to demonstrate that low-dimensional in-host models with linear or constant infectivity functions cannot generate viral blips. Further, we find that a 5-dimensional immunological model satisfies the conditions and exhibits recurrent infection even with constant infectivity; thus, an increasing, saturating infectivity is not necessary if the model is sufficiently complex.

On standard and optimal designs of industrial-scale 2-D seismic surveys

SUMMARY The principal aim of performing a survey or experiment is to maximize the desired information within a data set by minimizing the post-survey uncertainty on the ranges of the model parameter values. Using Bayesian, non-linear, statistical experimental design (SED) methods we show how industrial scale amplitude variations with offset (AVO) surveys can be constructed to maximize the information content contained in AVO crossplots, the principal source of petrophysical information from seismic surveys. The design method allows offset dependent errors, previously not allowed in non-linear geoscientific SED methods. The method is applied to a single common-midpoint gather. The results show that the optimal design is highly dependent on the ranges of the model parameter values when a low number of receivers is being used, but that a single optimal design exists for the complete range of parameters once the number of receivers is increased above a threshold value. However, when acquisition and processing costs are considered we find that a design with constant spatial receiver separation survey becomes close to optimal. This explains why regularly-spaced, 2-D seismic surveys have performed so well historically, not only from the point of view of noise attenuation and imaging in which homogeneous data coverage confers distinct advantages, but also to provide data to constrain subsurface petrophysical information.

Measurement of Complex Permittivity using Artificial Neural Networks

In this paper, a neural-network-based methodology is presented to measure the complex permittivity of materials using monopole probes. A multilayered artificial neural network, using the Levenberg Marquardt back-propagation algorithm, is used to back solve the complex permittivity of the medium. The proposed network can be trained using an analytical model, numerical model, or measurement data spread over the complete range of parameters of interest. The input training data for the nonlinear inverse problem of reconstructing the complex permittivity comprises the complex reflection coefficient of the monopole probe. For the results presented in this paper, the network was trained using the analytical model for impedances of monopole antennas in a half space by Gooch et al. In addition to computational efficiency, the proposed approach gave 990/0 accurate results in the frequency range of 2.5-5 GHz, with the values of permittivity varying across a range of 3-10 for the real part, and 0-0.5 for the imaginary part. The accuracy and the effective range of real and imaginary components of the complex permittivity that can be reconstructed using this approach depend upon the accuracy and robustness of the model/system used to generate the training data. The analytical model used in this paper had a limited range for the values of loss tangent that it can model accurately. However, the performance of the back-solving algorithm remains independent from any specific model, and the scheme can be successfully applied using any reliable analytical or numerical model, or reflection-coefficient training data generated through a series of measurements. The methodology is likely to be employed for experimental measurements of complex permittivity of dissipative media.

Quantum critical dynamics of anS=12antiferromagnetic Heisenberg chain studied byC13NMR spectroscopy

We present a $^{13}\text{C}$ NMR study of the magnetic field driven transition to complete polarization of the $S=\frac{1}{2}$ antiferromagnetic Heisenberg chain system copper pyrazine dinitrate $\text{Cu}({\text{C}}_{4}{\text{H}}_{4}{\text{N}}_{2}){({\text{NO}}_{3})}_{2}$ (CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, were explored from the low to the high field limit and at temperatures from the quantum regime $({k}_{B}T⪡J)$ up to the classical regime $({k}_{B}T⪢J)$. The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in ${T}_{1}^{\ensuremath{-}1}$ is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.

Jahn-Teller effect versus Hund’s rule coupling inC60N−

We propose variational states for the ground state and the low-energy collective rotator excitations in negatively charged ${\mathrm{C}}_{60}^{N\ensuremath{-}}$ ions $(N=1,\dots{},5)$. The approach includes the linear electron-phonon coupling and the Coulomb interaction on the same level. The electron-phonon coupling is treated within the effective mode approximation which yields the linear ${t}_{1u}\ensuremath{\bigotimes}{H}_{g}$ Jahn-Teller problem whereas the Coulomb interaction gives rise to Hund's rule coupling for $N=2,3,4$. The Hamiltonian has accidental SO(3) symmetry which allows an elegant formulation in terms of angular momenta. Trial states are constructed from coherent states and using projection operators onto angular momentum subspaces which results in good variational states for the complete parameter range. The evaluation of the corresponding energies is to a large extent analytical. We use the approach for a detailed analysis of the competition between Jahn-Teller effect and Hund's rule coupling, which determines the spin state for $N=2,3,4$. We calculate the low-spin--high-spin gap for $N=2,3,4$ as a function of the Hund's rule coupling constant $J$. We find that the experimentally measured gaps suggest a coupling constant in the range $J=60--80\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. Using a finite value for $J$, we recalculate the ground state energies of the ${\mathrm{C}}_{60}^{N\ensuremath{-}}$ ions and find that the Jahn-Teller energy gain is partly counterbalanced by the Hund's rule coupling. In particular, the ground state energies for $N=2,3,4$ are almost equal.

Strong versus weak coupling duality and coupling dependence of the Kondo temperature in the two-channel Kondo model

We perform numerical renormalization group (NRG) as well as analytical calculations for the two-channel Kondo model to obtain the dependence of the Kondo temperature $T_K$ on the dimensionless (bare) spin exchange coupling $g$ over the complete parameter range from $g\ll 1$ to $g\gg 1$. We show that there exists a duality between the regimes of small and large coupling. It is unique for the two-channel model and enables a mapping between the strong and the weak coupling cases via the identification $g\leftrightarrow 3/(2g)$, implying an exponential dependence of $T_K$ on $1/g$ and $g$, respectively, in the two regimes. This agrees quantitatively with our NRG calculations where we extract $T_K(g)$ over the complete parameter range and obtain a non-monotonous $T_K(g)$ dependence, strongly peaked at the 2CK fixed point coupling $g^*$. These results may be relevant for resolving the long-standing puzzle within the 2CK interpretation of certain random defect systems, why no broad distribution of $T_K$ is observed in those systems.

Relaxation induced radical pair recombination in micelles

We have derived accurate, analytic expressions for the quantum yield and the decay constants of a geminate radical pair reaction in a micelle. The relative diffusive motion of the radicals, intraradical relaxation (both transverse and longitudinal), and homogeneous scavenging are included. The general expression is exact for the assumed diffusion model, but we have also introduced two approximation schemes, called slow and fast mixing, which cover the complete parameter range. The high accuracy of these approximations is demonstrated by comparison with numerically exact results. A simple expression, derived for the limiting case of diffusion controlled recombination through the singlet channel, is compared with the previously introduced semi-phenomenological exponential, two-positional, and supercage models as well as with approximations based on a level population description. This comparison gives insight into the applicability of the approximate models and the physical meaning of the model parameters. The work is based on the general Green's function results derived in our previous paper [Chem. Phys. 260 (2000) 125].

VISCOTHERMAL WAVE PROPAGATION INCLUDING ACOUSTO-ELASTIC INTERACTION, PART I: THEORY

This research deals with pressure waves in a gas trapped in thin layers or narrow tubes. In these cases viscous and thermal effects can have a significant effect on the propagation of waves. This so-called viscothermal wave propagation is governed by a number of dimensionless parameters. The two most important parameters are the shear wave number and the reduced frequency. These parameters were used to put into perspective the models that were presented in the literature. The analysis shows that the complete parameter range is covered by three classes of models: the standard wave equation model, the low reduced frequency model and the full linearized Navier–Stokes model. For the majority of practical situations, the low reduced frequency model is sufficient and the most efficient to describe viscothermal wave propagation. The full linearized Navier–Stokes model should only be used under extreme conditions.

Study of an Ising model with competing long- and short-range interactions.

A classical spin-one lattice gas model is used to study the competition between short-range ferromagnetic coupling and long-range antiferromagnetic Coulomb interactions. The model is a coarse-grained representation of frustrated phase separation in high-temperature superconductors. The ground states are determined for the complete range of parameters by using a combination of numerical and analytical techniques. The crossover between ferromagnetic and antiferromagnetic states proceeds via a rich structure of highly symmetric striped and checkerboard phases. There is no devil's staircase behavior because mixtures of stripes with different period phase separate.

Binary-single-star scattering. III - Numerical experiments for equal-mass hard binaries

view Abstract Citations (55) References (73) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Binary--Single-Star Scattering. III. Numerical Experiments for Equal-Mass Hard Binaries Hut, Piet Abstract Results of scattering experiments involving hard binaries with binding energies up to a few hundred times larger than the kinetic energy of the incoming field star are reported in the form of total and differential cross sections for a variety of processes. An accurate description of equal mass binary-single star scattering over a complete range of parameters is provided. The heating of star clusters through three-body processes, when stellar collisions can be ignored, as is the case for encounters involving degenerate stars, is illustrated by plotting the average amount of energy exchange between binaries and field stars as a function of binary hardness. Publication: The Astrophysical Journal Pub Date: January 1993 DOI: 10.1086/172199 Bibcode: 1993ApJ...403..256H Keywords: Binary Stars; Computational Astrophysics; Star Clusters; Stellar Mass; Stellar Physics; Computerized Simulation; Resonance Scattering; Scattering Cross Sections; Stellar Models; Stellar Systems; Triple Stars; Astrophysics; STARS: BINARIES: GENERAL; CELESTIAL MECHANICS; STELLAR DYNAMICS full text sources ADS | data products SIMBAD (2) Related Materials (6) Part 1: 1983ApJ...268..319H Part 2: 1983ApJ...268..342H Part 4: 1993ApJS...85..347H Part 5: 1993ApJ...403..271G Part 6: 1996ApJ...467..348M Part 7: 1996ApJ...467..359H

The equivalence of the top quark condensate and the elementary Higgs field

Several recent works suggested to replace the fundamental Higgs boson by a top quark condensate in analogy with the Nambu-Jona-Lasinio (NJL) mechanism. We show that the field theoretically correct replacement is a generalized NJL model with the minimal choice of three independent interaction terms in the lagrangian. We demonstrate in the large- N color limit that the physics of this model is fully equivalent to the corresponding simplified Standard Model where the Higgs boson is represented by an elementary scalar field with the usual Yukawa- and self-interactions. The generalized NJL mechanism does not lead to new physical predictions or constraints and the complete parameter range of the simplified Standard Model is recovered. Since there exists a simple mapping between the couplings of these two models, it is difficult to give physical significance to notions like composite versus fundamental, or dynamical symmetry breaking in this scheme. We also present some new numerical results on the relevant phase diagrams.

Transition rates of a non-Markovian Brownian particle in a double well potential

The transition rate of a non-Markovian Brownian particle in a double well potential is determined analytically by means of asymptotic methods and compared with both current theories and numerical simulations by Straub, Borkovec, and Berne [J. Chem. Phys. 83, 3172 (1985)]. We obtain good agreement with these simulations. The ranges of validity for the different current theories which we find do, however, not exhaust the complete parameter range. In particular, for large static friction we identify a region of bath correlation times in which the rate differs grossly from the value predicted by either Grote–Hynes theory or non-Markovian energy diffusion. Additionally, corrections to the Grote–Hynes rate are determined and an analytical expression for the non-Markovian energy diffusion rate is obtained.

Global bifurcations of a periodically forced nonlinear oscillator.

The effects of periodic pulsatile stimulation on a simple mathematical model of biological oscillations, called the radial isochron clock (RIC), are investigated as a function of stimulus frequency and amplitude. This system can be reduced to a two parameter, one-dimensional circle map. Numerical and topological methods are used to give a very detailed picture of the observed bifurcations over the complete range of parameters. The bifurcations are generic for a class of models which generalize the RIC.