Poisson Theory Research Articles

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if (2n−1) first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Algebraic structure and Poisson method for a weakly nonholonomic system

The algebraic structure and the Poisson method for a weakly nonholonomic system are studied. The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed. The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system. An example is given to illustrate the application of the result.

Poisson theory and integration method of Birkhoffian systems in the event space

This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by (2n + 1) Birkhoff's variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.

Coulomb Explosion and Energy Loss of Energetic C20 Clusters in Dense Plasmas

The molecular dynamics (MD) method is used to simulate the interactions of energetic C20 clusters with the dense plasma targets within the framework of the linear Vlasov–Poisson theory. The influences of various clusters (H2, N2, C20 and C60 respectively) on stopping power are discussed. The simulation results show that the vicinage effects in the Coulomb explosion dynamics and the stopping power are strongly affected by the variations in the cluster speed and the plasma parameters. Coulomb explosions are found to proceed faster for higher speeds, lower plasma densities and higher electron temperatures. In addition, the cluster stopping power is strongly enhanced in the early stages of Coulomb explosions due to the vicinage effect, but this enhancement eventually diminishes, after the cluster constituent ions are sufficiently separated. For the large and heavy clusters, the stopping power ratio reaches much higher values in the early stage of Coulomb explosion owing to the constructive interferences in the vicinage effect.

Poisson theory of generalized Bikhoff equations

This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.

Integral of differential equations of three-particle Toda lattice

The differential equations of three-particle Toda lattice are a Hamiltonian system. The integrals of the equations can be obtained by using the Noether theory and the Poisson theory.

Algebraic structure and Poisson's theory of mechanico-electrical systems

The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange?Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.

Analysis of errors in Still's equation for macromolecular electrostatic solvation energies

The generalized Born (GB) solvation model is a simple dielectric model for the calculation of molecular electrostatic solvation energies. There are two distinct steps in the model: the calculation of Born radii from self-energies, and the calculation of interaction energies using an interpolation formula, such as Still's equation. The first step, the calculation of the Born radii, has been solved to high-accuracy in recent work by this author and others [M. S. Lee, F. R. Salsbury Jr, and M. A. Olson, J. Comput. Chem. 25, 1967 (2004)], so that the errors in the interpolation formula need to be considered to further improve GB theory. We examine the errors in the interpolation formula by calculating Born radii and atomic interaction energies using Poisson theory, and determining the errors associated with Still's equation. We then verify that a slight modification reduces the error in the interaction energies. We also explore alternative formulations of Still's equation, and the combinations rules for Born radii. We conclude that the Gaussian portion of Still's equation should be modified. Although additional generalizations of Still's equation do not further reduce the errors inherent to generalized Born theory substantially, there is considerable flexibility in the form of the interpolation equations which can be used in GB theory.

Balancing an accurate representation of the molecular surface in generalized born formalisms with integrator stability in molecular dynamics simulations

Different integrator time steps in NVT and NVE simulations of protein and nucleic acid systems are tested with the GBMV (Generalized Born using Molecular Volume) and GBSW (Generalized Born with simple SWitching) methods. The simulation stability and energy conservation is investigated in relation to the agreement with the Poisson theory. It is found that very close agreement between generalized Born methods and the Poisson theory based on the commonly used sharp molecular surface definition results in energy drift and simulation artifacts in molecular dynamics simulation protocols with standard 2-fs time steps. New parameters are proposed for the GBMV method, which maintains very good agreement with the Poisson theory while providing energy conservation and stable simulations at time steps of 1 to 1.5 fs.

Coulomb explosion and energy loss of fast C60 clusters in plasmas

The spherical-shell model and the molecular dynamics (MD) method are used to simulate the interactions of energetic C60 clusters with the high-density plasma targets within the framework of the linearized Vlasov–Poisson theory. While the shell model describes Coulomb explosions of randomly oriented clusters under the assumption of isotropic expansion, the MD simulations capture the role of the wake effect in the interionic forces due to the dynamical polarization of the plasma. We find that the vicinage effects in the cluster self-energy, the Coulomb explosion dynamics, and the stopping power are strongly affected by the variations in the cluster speed and the plasma parameters. For example, Coulomb explosions are found to proceed faster for higher speeds, lower plasma densities, and higher electron temperatures. Both approaches show that the cluster stopping power is strongly enhanced in the early stages of Coulomb explosions due to the vicinage effect, but this enhancement eventually diminishes, after the cluster constituent ions are sufficiently separated. This takes place after a penetration time, which is found to be shorter in the MD simulation than in the shell model, owing to the wake-induced elongation of the cluster structure in the course of Coulomb explosion.

Influence of strong laser fields on Coulomb explosions energy losses of correlated-ion clusters in plasmas

Interactions of correlated-ion clusters with classical plasma targets are studied in the presence of a strong laser field. General expressions of the dynamic interaction potential are derived within the framework of the linearized Vlasov–Poisson theory. Coulomb explosions and the energy losses of the cluster moving in the plasma target are simulated by solving the equations of motion for the constituent ions. Numerical results show that the laser field affects the correlation between the two ions and contributes to decrease of the plasma stopping power, as compared to the laser-free case. In addition, the Coulomb explosions and the energy losses are discussed for a range of laser parameters.

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times Δt between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail ∼(Δt)γ for large waiting times (Δt>10 hours). It is shown that the power-law index γ varies with the solar cycle. For the minimum phase of the cycle the index is γ=−1.4±0.1, and for the maximum phase of the cycle the index is −3.2±0.2. For all years 1975–2001, the index is −2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate λ(t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(λ), the time distribution of the rate λ. If f(λ) has a power-law form ∼λα for low rates, the waiting time-distribution is predicted to have a power-law tail ∼(Δt)−(3+α) (α>−3). Distributions f(λ) are constructed from the GOES data. For the entire catalog a power-law index α=−0.9±0.1 is found in the time distribution of rates for low rates (λ<0.1 hours −1). For the maximum and minimum phases power-law indices α=−0.1±0.5 and α=−1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices −2.2±0.1 (1975–2001), −2.9±0.5 (maximum phase) and −1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.

Simulation approaches to ion channel structure-function relationships.

1. Introduction 4751.1 Ion channels 4751.1.1 Gramicidin 4761.1.2 Helix bundle channels 4771.1.3 K channels 4801.1.4 Porins 4831.1.5 Nicotinic acetylcholine receptor 4831.1.6 Physiological properties 4831.2 Simulations 4841.2.1 Atomistic versus mean-field simulations 4842. Atomistic simulations 4852.1 Modelling of ion-interaction parameters 4852.1.1 Interatomic distances and the problem of ionic radii 4862.1.2 Solvation energy 4872.1.3 Hydration shells and coordination numbers 4892.1.4 Parameters in common use and transferability 4912.1.5 Summary 4912.2 Water in pores versus bulk 4912.2.1 Simple pore models 4942.2.2 gA 4952.2.3 Alm 4962.2.4 LS36 (and LS24) 4962.2.5 Nicotinic receptor M2δ5 4972.2.6 Influenza A M2 4972.2.7 K channels 4972.2.8 nAChR 4982.2.9 Porins 4982.2.10 Relevance 4992.2.11 Problems with simulations 5012.3 Dynamics of ions in pores 5032.3.1 Simple pore models 5032.3.2 Helix bundles 5042.3.3 gA and KcsA 5052.4 Energetics of permeation and ion selectivity 5092.4.1 Potential and free energy profiles 5092.4.2 gA 5102.4.3 α-Helix bundles 5112.4.4 KcsA 5122.4.5 Ion selectivity 5142.4.6 Problems of estimating energetic profiles 5152.5 Conformational changes 5162.5.1 gA 5162.5.2 Alm and LS3 5162.5.3 KcsA 5172.6 Protonation states 5233. Coarse-grained simulations 5243.1 Introduction 5243.1.1 Predicting conductance magnitudes 5253.2 Electro-diffusion: the Nernst–Planck approach 5263.2.1 Calculating the potential profile from Poisson and PB theory 5283.2.2 Calculating the potential profile from BD simulations 5303.2.3 Combining Nernst–Planck and Poisson: PNP 5303.3 Beyond PNP 5323.4 BD simulations 5323.4.1 Basic theory in ion channels 5323.4.2 Incorporating the environment 5333.5 Applications 5353.5.1 Model systems 5353.5.1.1 Solving the Poisson and PB equation for channel-like geometries 5353.5.1.2 Comparing PB, PNP and BD 5363.5.2 Applications to known structures 5373.5.2.1 gA 5373.5.2.2 Porin 5393.5.2.3 LS3 5403.5.2.4 Alm 5423.5.2.5 nAChR 5423.5.2.6 KcsA 5433.6 pKa calculations 5433.7 Selectivity 5443.7.1 Anion/cation selectivity 5453.7.2 Monovalent/divalent ion selectivity 5454. Problems 5464.1 Atomistic simulations 5464.1.1 Problems 5464.1.2 Parameters 5484.2 BD 5494.3 Mean-field simulations 5495. Conclusions 5505.1 Progress 5505.2 The future 5506. Acknowledgements 5517. References 551Ion channels are proteins that form ‘holes’ in membranes through which selected ions move passively down their electrochemical gradients. The ions move quickly, at (nearly) diffusion limited rates (ca. 107 ions s−1 per channel). Ion channels are central to many properties of cell membranes. Traditionally they have been the concern of neuroscientists, as they control the electrical properties of the membranes of excitable cells (neurones, muscle; Hille, 1992). However, it is evident that ion channels are present in many types of cell, not all of which are electrically excitable, from diverse organisms, including plants, bacteria and viruses (where they are involved in functions such as cell homeostasis) in addition to animals. Thus ion channels are of general cell biological importance. They are also of biomedical interest, as several dizeases (‘channelopathies’) have been described which are caused by changes in properties of a specific ion channel (Ashcroft, 2000). Moreover, passive diffusion channels for substances other than ions are common (porins, aquaporins), as are active membrane transport processes coupled to ion gradients or ATP hydrolysis. An understanding of ion channels may also provide a gateway to understanding these processes.

Two-Dimensional Optical Analysis of Small Pixels in Reflective Silicon Microdisplay

We present a two-dimensional optical analysis of small pixels in reflective liquid-crystal-on-silicon microdisplay. The optical analysis is divided into two parts. In the first part, the two-dimensional (2D) director configuration of the liquid crystal display (LCD) in rectangular mesh was calculated by simultaneously solving the 2D Poisson and continuum theory equations. In the second part, generalized Jones matrix was used to simulate for optical reflectance through the LCD with the 2D director configuration obtained from the first part. This optical modeling was applied to analyze optical reflectance of small pixels in reflective mixed-mode twisted nematic and birefrigence (MTB) cells on silicon substrate. Both the simulated and experimental data of the MTB cells under frame and column inversions were presented. It was found that the frame inversion could give rise to a higher contrast ratio than the column inversion at the same driving voltage. It was also found that the optical reflectance decreased as the pixel size decreased due to the lateral electric field between the small pixels.

Examination of the performance exhibited by a single detector double focusing magnetic sector ICP-MS instrument for uranium isotope abundance ratio measurements over almost three orders of magnitude and down to pg g−1 concentration levels

Calibration experiments were performed on a commercially available double focusing magnetic sector single detector ICP-MS instrument to evaluate its potential for accurate isotope abundance ratio measurements down to the 1 pg g−1 isotope concentration level (without involving any preconcentration step). Its performance, for isotope abundance ratios varying over almost three orders of magnitude from ≈1∶1 to ≈1∶500, was checked using the IRMM-072 series of Isotopic Reference Materials. Routine experimental settings were applied and remained unchanged for the entire series of experiments. It is shown that all the certified ratios (certified to within 0.03% expanded combined uncertainty, k = 2) could be matched experimentally within the expanded (k = 2) combined uncertainty of the measurements (from ±0.11 to ±0.33% for 233U/235U, and from ±0.16 to ±0.31% for 233U/238U). For 1∶1 ratios (235U/238U) a 0.05% precision could be reproducibly obtained of which only 33% could be accounted for by Poisson statistics, whereas for 1∶500 ratios a 0.16% precision was obtained which could be completely explained by the same Poisson theory. In addition to the experimental precision other possible sources of uncertainty were investigated. The way isotope abundance ratios are measured (acceleration voltage is varied while the magnetic field is kept constant) is discussed as a potential extra source of mass discrimination. The crucial importance of a proper correction for dead-time effects is demonstrated. Finally, the hypothesis of a contamination with natural uranium that would have biased the results could be ruled out for all samples.

On the integration methods of non-holonomic dynamics

Some generalizations of the integration methods of the holonomic systems to the non-holonomic systems are given. The generalizations include that of the Whittaker method, the Poisson theory, the field method, the Noether symmetry and the Lie symmetry.

Optical Modeling of Small Pixels in Reflective Mixed‐Mode Twisted Nematic Cells

AbstractWe present optical modeling of small pixels in reflective liquid crystal display (LCD). The optical analysis is divided into two parts. In the first part, the two‐dimensional (2D) director configuration of the LCD in rectangular mesh was calculated by simultaneously solving the 2D Poisson and continuum theory equations. In the second part, the generalized Jones matrix was used to simulate for the optical reflectance through the LCD with the 2D director configuration obtained from the first part. This optical modeling was applied to analyze the optical reflectance of small pixels in reflective mixed‐mode twisted nematic and birefergence (MTB) cells on silicon substrate. Both the simulated and experimental data of the MTB cells under frame and column inversions of polarity are presented.

The algebraic structure and poisson's theory for the equations of motion of non-holonomic systems

Poisson's theory for holonomic conservative systems is shown to apply partially to non-holonomic systems.

What is the optimal time window in symptom analysis of 24-hour esophageal pressure and pH data?

Since noncardiac chest pain is the only well-established indication for 24-hr esophageal pH and pressure recording, the analysis of the association between chest pain episodes and esophageal motility abnormalities or reflux is the most important part of data analysis in 24-hr monitoring. Until now, different time windows have arbitrarily been used by various research groups. The aim of this study was to determine the optimal time window for symptom analysis in 24-hr esophageal pH and pressure monitoring. For this purpose repetitive symptom association analysis was carried out, using time windows of various onsets and durations. For each time window, the symptom indices for reflux and dysmotility were calculated. The symptom index for both reflux and dysmotility showed a gradual increase for windows with increasingly early onset, following a pattern that would be predicted on the basis of Poisson's theory. However, both indices had a relatively sharp cutoff point at 2 min before the onset of pain. Both indices only showed a predictable gradual increase when the time window starting at -2 min was extended beyond the moment of pain onset. It is concluded that the optimal time window for symptom analysis in 24-hr esophageal pH and pressure recording begins at 2 min before the onset of pain and ends at the onset of pain.

Multilocus models of inbreeding depression with synergistic selection and partial self-fertilization

SummaryMean fitness and inbreeding depression values in multi-locus models of the control of fitness were studied, using both a model of mutation to deleterious alleles, and a model of heterozygote advantage. Synergistic fitness interactions between loci were assumed, to find out if this more biologically plausible model altered the conclusions we obtained previously using a model of multiplicative interactions. Systems of unlinked loci were assumed. We used deterministic computer calculations, and approximations based on normal or Poisson theory. These approximations gave good agreement with the exact results for some regions of the parameter space. In the mutational model, we found that the effect of synergism was to lower the number of mutant alleles per individual, and thus to increase the mean fitness, compared with the multiplicative case. Inbreeding depression, however, was increased. Similar effects on mean fitness and inbreeding depression were found for the case of heterozygote advantage. For that model, the results were qualitatively similar to those previously obtained assuming multiplicativity. With the mutational load model, however, the mean fitness sometimes decreased, and the inbreeding depression increased, at high selfing rates, after declining as the selfing rate increased from zero. We also studied the behaviour of modifier alleles that changed the selfing rate, introduced into equilibrium populations. In general, the results were similar to those with the multiplicative model, but in some cases an ESS selfing rate, with selfing slightly below one, existed. Finally, we derive an approximate expression for the inbreeding depression in completely selfing populations. This depends only on the mutation rate and the dominance coefficient and can therefore be used to obtain estimates of the mutation rate to mildly deleterious alleles for plant species.