Poisson Theory Research Articles

Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians

Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians

Canonical transformations and Poisson theory for second-order generalized mechanical systems with power-law Lagrangians

The canonical transformation and Poisson theory for the second-order generalized mechanical systems based on non-standard power-law Lagrangians are studied. First, the Euler–Lagrange equations and the Hamilton canonical equations for the second-order generalized mechanics with the power-law Lagrangians are established. Second, the canonical transformation theory of the systems is studied by establishing the relationship between old and new variables. Four basic forms of canonical transformation are given, and the transformation formulas in each case are derived. Third, the algebraic structure of the dynamical equations of the systems is studied, and the corresponding Poisson theory is established. Finally, the corresponding examples are presented to illustrate the application of the results we obtained.

Analytical Physical Model for Organic Metal‐Electrolyte‐Semiconductor Capacitors

AbstractThis work presents the analytical physical modeling of undoped organic metal‐electrolyte‐semiconductor (OMES) capacitors in the framework of the Nernst–Planck–Poisson theory, including the presence of compact interfacial layers. This work derives an exact analytical solution, up to a quadrature, for the stationary electric potential and charge density distributions in both the semiconductor film and the electrolyte solution, and from them the sheet semiconductor charge and the stationary differential capacitance are obtained as a function of the applied voltage. The dependence of these magnitudes on the physical device parameters, like the ionic concentration of the electrolyte, the capacitance of the interfacial compact layers and the injected hole density is then analyzed. This work shows that ionic diffusive effects in the electrolyte can play an important role in the device response, inducing a broadening of the transition from the weak to the strong accumulation regimes. This fact can make that the strong accumulation regime is not achieved in OMES within the usual voltage operation range of these devices. The analytical solution is validated by means of finite element numerical calculations. The implications of the results obtained on the physics of electrolyte gated organic field effect transistors (EGOFETs) are discussed.

Impact of red blood cell lysing on rare event analysis.

The challenges associated with analyzing rare cells are dependent on a series of factors, which usually require large numbers of cells per sample for successful resolution. Among these is determining the minimum number of total events needed to be acquired as defined by the expected frequency of the target cell population. The choice of markers that identify the target population, as well as the event rate and the number of aborted events/second, will also determine the statistically significant detection of rare cell events. Sample preparation is another important but often overlooked factor in rare cell analysis, and in this study we examine Poisson theory and methods to determine the effect of sample manipulation on rare cell detection. After verifying the applicability of this theory, we have evaluated the potential impact of red cell lysis on rare cell analysis, and how cell rarity can be underestimated or overestimated based on erythrolytic sensitivity or resistance of healthy leukocytes and pathological rare cells.

The Sloan Digital Sky Survey Reverberation Mapping Project: the XMM-Newton X-Ray Source Catalog and Multiband Counterparts

The XMM-RM project was designed to provide X-ray coverage of the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) field. Forty-one XMM-Newton exposures, placed surrounding the Chandra AEGIS field, were taken, covering an area of 6.13 deg2 and reaching a nominal exposure depth of ∼15 ks. We present an X-ray catalog of 3553 sources detected in these data, using a PSF-fitting algorithm and a sample selection threshold that produces a ∼5% fraction of spurious sources. In addition to the PSF-fitting likelihood, we calculate a second source reliability measure based on Poisson theory using source and background counts within an aperture. Using the Poissonian likelihood, we select a subsample with a high purity and find that it has number count profiles similar to previous X-ray surveys. The Bayesian method "NWAY" was employed to identify counterparts of the X-ray sources from the optical Legacy and the IR unWISE catalogs, using a two-dimensional unWISE magnitude–color prior created from optical/IR counterparts of Chandra X-ray sources. A significant number of the optical/IR counterparts correspond to sources with low detection likelihoods, proving the value of retaining the low-likelihood detections in the catalog. A total of 932 of the XMM-RM sources are covered by SDSS spectroscopic observations, where 89% of them are classified as active galactic nuclei, and 71% of these active galactic nuclei are in the SDSS-RM quasar catalog. Among the SDSS-RM quasars, 80% are detectable at the depth of the XMM observations.

Dispersion of graphene using surfactant mixtures: Experimental and molecular dynamics simulation studies

The capability of sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide (CTAB), cationic-rich and anionic-rich mixtures for dispersion of graphene nanosheets in an aqueous medium was assessed through both experimental and molecular dynamics (MD) simulation methods. The experimental results, especially measurements of ζ-potential showed that the dispersing power of pure SDS and the anionic-rich mixture is more than that of pure CTAB and cationic-rich mixture due to the smaller size of the SDS and more adsorption of it on the surface of graphene compared with CTAB. Nonetheless, stable dispersed graphene nanosheets were obtained at a lower total surfactant mixture concentration compared to when used alone, suggest the synergistic effect of catanionic mixtures. Regarding environmental impacts and costs, using surfactant mixtures for dispersing graphene nanosheets is promising. Moreover, MD simulations were used to examine surfactant mixture assemblies’ structure on graphene and explain the experimental results, which showed that the random adsorption model first changes to the monolayer model and then the hemispherical model with an increased surfactant concentration. The ζ-potential about surfactant mixture-graphene assemblies was estimated using the results of MD simulation and Poisson's theory, and the results conformed to the experimental results favorably. Eventually, interactions between two surfactant mixture-graphene assemblies were evaluated through calculating the potential of mean force (PMF), and it was found that increasing surfactant surface coverage would lead to an enhanced repulsive barrier of PMF. Understanding the mechanism of interactions will help the design and selection of appropriate surfactants, the optimization of the process and the improvement of graphene dispersion in aqueous solutions of surfactants.

Algebraic structure and Poisson brackets of single degree of freedom non-material volumes

This paper investigates an algebraic structure and Poisson theory of single degree of freedom non-material volumes. The equations of motion are proposed in a contravariant algebraic form, and an algebraic product is determined. A consistent algebraic structure and a Lie algebra structure are proposed, and a proposition is obtained. The Poisson theory of the non-material volume is established, and five theorems are derived. Three examples are given to illustrate the application of the method.

Nonlatching positive feedback enables robust bimodality by decoupling expression noise from the mean

Fundamental to biological decision-making is the ability to generate bimodal expression patterns where 2 alternate expression states simultaneously exist. Here, we use a combination of single-cell analysis and mathematical modeling to examine the sources of bimodality in the transcriptional program controlling HIV’s fate decision between active replication and viral latency. We find that the HIV transactivator of transcription (Tat) protein manipulates the intrinsic toggling of HIV’s promoter, the long terminal repeat (LTR), to generate bimodal ON-OFF expression and that transcriptional positive feedback from Tat shifts and expands the regime of LTR bimodality. This result holds for both minimal synthetic viral circuits and full-length virus. Strikingly, computational analysis indicates that the Tat circuit’s noncooperative “nonlatching” feedback architecture is optimized to slow the promoter’s toggling and generate bimodality by stochastic extinction of Tat. In contrast to the standard Poisson model, theory and experiment show that nonlatching positive feedback substantially dampens the inverse noise-mean relationship to maintain stochastic bimodality despite increasing mean expression levels. Given the rapid evolution of HIV, the presence of a circuit optimized to robustly generate bimodal expression appears consistent with the hypothesis that HIV’s decision between active replication and latency provides a viral fitness advantage. More broadly, the results suggest that positive-feedback circuits may have evolved not only for signal amplification but also for robustly generating bimodality by decoupling expression fluctuations (noise) from mean expression levels.

A Stochastic Emergency Response Location Model Considering Secondary Incidents on Freeways

Location and allocation of emergency response units are assumed to be interdependent in the incident management system. System costs will be excessive if delay regarding allocating decisions is ignored when locating response units. This paper presents an integrated method to solve location and allocation problem of emergency vehicles on freeways. The principle is to begin with a location phase for managing initial incidents and to progress through an allocation phase for managing the stochastic occurrence of next incidents. Previous studies used the frequency of independent incidents and ignored scenarios in which two incidents occurred within proximal regions and intervals. The proposed analytical model relaxes the structural assumptions of Poisson process (independent increments) and incorporates evolution of primary and secondary incident probabilities over time. Interdependent ERUs location-allocation problem is solved by taking stochastic information of future incidents explicitly into account with lookahead. The mathematical model overcomes several limiting assumptions of the previous models, such as no waiting time, returning rule to original depot, and fixed depot. The initial nonlinear stochastic model is linearized. The temporal locations flexible with lookahead are compared with current practice that locates units in depots based on Poisson theory. An efficient heuristic algorithm is implemented to deal with time-consuming process of a large-scale problem in real time.

Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

AbstractOutlier detection algorithms are intimately connected with robust statistics that down‐weight some observations to zero. We define a number of outlier detection algorithms related to the Huber‐skip and least trimmed squares estimators, including the one‐step Huber‐skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.

Lie–Poisson theory for direct limit Lie algebras

In the first half of this paper, we develop the fundamentals of Lie–Poisson theory for direct limits G=lim→Gn of complex algebraic groups and their Lie algebras g=lim→gn. We describe the Poisson pro- and ind-variety structures on g⁎=lim←gn⁎ and the coadjoint orbits of G, respectively. While the existence of symplectic foliations remains an open question for most infinite-dimensional Poisson manifolds, we show that for direct limit algebras, the coadjoint orbits give a weak symplectic foliation of the Poisson provariety g⁎.The second half of the paper applies our general results to the concrete setting of G=GL(∞) and g⁎=M(∞), the space of infinite-by-infinite complex matrices with arbitrary entries. We use the Poisson structure of g⁎ to construct an integrable system on M(∞) that generalizes the Gelfand–Zeitlin system on gl(n,C) to the infinite-dimensional setting. We further show that this integrable system integrates to a global action of a direct limit group on M(∞), whose generic orbits are Lagrangian ind-subvarieties of the coadjoint orbits of GL(∞) on M(∞).

Magnetic susceptibility as a tool for mineral exploration (Case study: Southern of Zagros Mountains)

Magnetic susceptibility has been extensively used to determine the magnetic properties of rocks for different applications, such as hydrocarbon or mineral explorations. This magnetic quantity can be directly measured in an accurate but time-consuming operation, or it can be mathematically approximated using a reliable procedure to achieve a desired accuracy. The Poisson theory is one of the most well-known approaches which provide a meaningful relationship between the earth’s gravity and magnetic fields to derive the magnetic susceptibility. In this approach, the reliability and efficiency of the derived magnetic susceptibility depends on the method of computation of the gravity gradient tensor. We investigated two different methods of determination of gradient tensor; different distance method and Fourier transform technique. From the investigation, the Fourier transform method was more consistent with the geological features which led to more reliable information required for mineral explorations. The performance of the Poisson theory, the different distance method, and the Fourier transform was investigated in the coastal Fars, in Iran. This was highly disposing for geological and mineral features. Salt domes in the study area were detected and results compared with the available geological map.

Abstract P4-02-08: Global quantitative measures using next-generation sequencing for breast cancer presence outperform individual tumor markers in plasma

Abstract Background: Analytically and clinically validated non-invasive blood tests that quantify breast cancer burden and clinical drug response/resistance are greatly needed. Many groups have successfully detected tumor markers in blood using a variety of technologies, including next generation sequencing (NGS). We performed a comprehensive NGS study on a small number of patients to evaluate the value of global versus individual markers for the quantitation of tumor-derived cell free DNA (cfDNA) in plasma. Methods: DNA isolated from formalin-fixed primary tumor, buffy coat cells, and plasma from 2 patients with metastatic breast cancer were characterized simultaneously for copy number aberrations (CNAs) and differentially methylated regions (DMRs) using whole genome bisulfite sequencing (WBGS), and targeted sequencing-based genotyping of 346 cancer-associated single nucleotide variations (SNVs). CNA and DMR regions were identified from log normalized, GC content corrected counts and DMR data using Poisson and binomial distribution theory and false discovery rate controlling methods. Percent tumor in cfDNA was estimated from the normalized ratio (plasma: primary tumor) of CNA or DMR compared to buffy coat, aggregating over genomic regions. Sample sets from 8 non-metastatic patients were also profiled using the targeted SNV panel in order to compare SNVs between samples and estimate percent tumor cfDNA. Results: WGBS detected tumor specific alterations in each primary tumor compared to buffy coat. By analyzing the genome using 100 Kb bins, we observed over 1000 bins with detectable CNA signal and, among 56 million CpG sites, over 30,000 DMRs. As expected, 5 or fewer informative somatic SNVs were detected in each patient. Analysis of these somatic changes in plasma revealed that the tumor fraction estimated from SNV detected in cfDNA varied widely between sites originally discovered in the patient’s primary tumor. In contrast, similar estimates of tumor fraction in cfDNA were obtained using CNA and DMR profiles within each patient; both methods yielded similar estimates of over 50% in one patient and less than 10% in the other. For the patient with high tumor fraction, both CNA and DMR profiles contained examples of individual large genomic regions that displayed additional clear aberrations in the plasma compared to the original tumor, such as a striking loss of a >25 Mb region of chromosome 4. Conclusions: Although individual somatic SNV in cfDNA can be detected in metastatic disease, calculated allelic fraction based on individual SNVs varies greatly within the same patient. Measuring and integrating CNA or DMR across the genome provided more consistent and reliable estimates of tumor DNA fraction in plasma, and also revealed alterations in plasma from patients with metastatic disease that were not prominent in the primary tumor. Citation Format: Ellen M Beasley, Richard D Abramson, Gregory E Alexander, David Chan, Kristen Bradley, Francois Collin, Michael Crager, Andrew Dei Rossi, Joseph Dorado, Adam Friedman, William J Gibb, Jennie Jeong, Col Jones, C J Ku, Yan Ma, John Morlan, Kunbin Qu, Aibing Rao, Aaron Scott, Haluk Tezcan. Global quantitative measures using next-generation sequencing for breast cancer presence outperform individual tumor markers in plasma [abstract]. In: Proceedings of the Thirty-Seventh Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2014 Dec 9-13; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2015;75(9 Suppl):Abstract nr P4-02-08.

Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions.

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

S0 Lamb Wave Scattering from a Cylindrical Inhomogeneity in a Transversely Isotropic Composite Plate

An analytical model using the Poisson theory is proposed to predict the S0 Lamb wave scattering from a cylindrical inhomogeneity in a transversely isotropic composite plate. Due to the anisotropic elastic properties of the plate, the suitability of the model is first examined by the dispersion curve of an S0 wave by using approximate Poisson theory compared to the exact Lamb solution. It is found that the Poisson theory can accurately describe the behavior of the S0 wave at low frequency when the incident S0 wave is parallel or perpendicular to the fiber direction of the transversely isotropic composite plate. On this basis, making use of the wave function expansion technique and coupling conditions at the inhomogeneity defect boundary, the far field scattered patterns of various inhomogeneity sizes and properties are then explored. The present results reveal that the scattering patterns are strongly dependent on the size and stiffness of the cylindrical inhomogeneity.

Stopping Power for Ions Moving in Magnetized Plasma

Stopping power of test ions in magnetized plasmas is investigated by means of linearized Vlasov Poisson theory. The influences of the magnetized field, the angle between the test particle velocity and magnetized field, and certain plasma densities and temperatures on the stopping power are studied. Simulation results show that the stopping power emerges a peak around the plasma thermal velocity due to the electron excitation. When the magnetized field is strong, the stopping power is strengthened; while when the magnetized field is weak, the stopping power is weakened.

Influence of a strong laser field on Coulomb explosion and stopping power of energetic H3+ clusters in plasmas

The influence of a high-intensity laser field on the Coulomb explosion and stopping power for a swift H3+ cluster ion in a plasma target is studied by means of the molecular dynamic (MD) method based on the linearized Vlasov–Poisson theory. Excitations of the plasma are described by the classical plasma dielectric function. In the presence of the laser field, the general expressions for the induced potential in the target and the interaction force among the ions within the cluster are derived. Based on the numerical solution of the equations of motion for the constituent ions, the Coulomb explosion patterns and the cluster's stopping power are discussed for a range of laser parameters. Numerical results show that the laser field affects the correlation between the ions and contributes to weaken the wake effect and the stopping power as compared to the laser-free case. On the other hand, the stopping power ratio of H3+ cluster is higher than the situation of dicluster of H2+ due to the vicinage effect in the cluster.

Nonlinear Poisson Equation for Heterogeneous Media

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects.

Bombardment Induced Potassium Ion Transport Through a Sodium Ion Conductor: Conductivities and Diffusion Profiles

Abstract Ion transport through a Ca30 glass, a sodium ion (Na + ) conductor, has been induced by bombardment with a potassium ion (K + ) beam. The measurement of back side ion currents as a function of the ion beam kinetic energy by means of the recently developed BIIT (bombardment induced ion transport) approach allows determining the conductivity of the material. Measurement of this conductivity as a function of the temperature allows deriving the activation energy for ion transport as 0.99 eV ± 0.01 eV in perfect agreement with impedance spectroscopy. While the conductivity as well as the activation energy clearly correspond to the bulk property, i.e. the transport of Na + , depth profiling of the glass sample after the BIIT experiment exhibits K + profiles reaching up to 100 nm into the glass. Ultimately, modeling of the experimental data by means of the Nernst–Planck–Poisson theory provides access to a quantitative understanding of the conductivities and the diffusion profiles under the condition of competing Na + /K + ion transport.

Poisson Theory and Inverse Problem in a Controllable Mechanical System

The Poisson theory and inverse problem are studied in a controllable mechanical system. Equations of motion of the controllable mechanical system in phase space are given. Poisson's integral theory of the system is established. The potential force field is constructed by solving the inverse problem in a controllable mechanical system. Finally, an example is given to illustrate the application of the results.