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Sample records for poisson-nernst-planck pnp equations

  1. Application of the Poisson-Nernst-Planck equations to the migration test

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Krabbenhøft, Jørgen

    2008-01-01

    The Poisson-Nernst-Planck (PNP) equations are applied to model the migration test. A detailed analysis of the equations is presented and the effects of a number of common, simplifying assumptions are quantified. In addition, closed-form solutions for the effective chloride diffusivity based...... on the full PNP equations are derived, a number of experiments are analyzed in detail, and a new, truly accelerated migration test is proposed. Finally, we present a finite element procedure for numerical solution of the PNP equations....

  2. Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

    Science.gov (United States)

    Yan, David

    This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and

  3. Development of a Generalized Version of the Poisson-Nernst-Planck Equations Using the Hybrid Mixture Theory: Presentation of 2D Numerical Examples

    DEFF Research Database (Denmark)

    Johannesson, Björn

    2010-01-01

    A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson-Nernst-Planck ......A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson......-Nernst-Planck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst-Planck equations describing the diffusion of the ionic species and the Gauss’ law in used are......, however, coupled in both directions. The governed set of equations is derived from a simplified version of the so-called hybrid mixture theory (HMT). This theory is a special version of the more ‘classical’ continuum mixture theories in the sense that it works with averaged equations at macro...

  4. Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson-Nernst-Planck equations involving ionization in a weak electrolyte

    Science.gov (United States)

    Suzuki, Yohichi; Seki, Kazuhiko

    2018-03-01

    We studied ion concentration profiles and the charge density gradient caused by electrode reactions in weak electrolytes by using the Poisson-Nernst-Planck equations without assuming charge neutrality. In weak electrolytes, only a small fraction of molecules is ionized in bulk. Ion concentration profiles depend on not only ion transport but also the ionization of molecules. We considered the ionization of molecules and ion association in weak electrolytes and obtained analytical expressions for ion densities, electrostatic potential profiles, and ion currents. We found the case that the total ion density gradient was given by the Kuramoto length which characterized the distance over which an ion diffuses before association. The charge density gradient is characterized by the Debye length for 1:1 weak electrolytes. We discuss the role of these length scales for efficient water splitting reactions using photo-electrocatalytic electrodes.

  5. Electroneutral models for dynamic Poisson-Nernst-Planck systems

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    Song, Zilong; Cao, Xiulei; Huang, Huaxiong

    2018-01-01

    The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modeling and computational challenges. In this paper, we derive simplified electroneutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First, it is much cheaper to solve them numerically. Second, EN models are easier to deal with compared to the original PNP system; therefore, it would also be easier to derive macroscopic models for cellular structures using EN models. Even though the approach used here is applicable to higher-dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to the EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher-order contributions into the effective boundary conditions. For Dirichlet boundary conditions, the higher-order terms can be neglected and the classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, higher-order terms account for the accumulation of ions in boundary layer and neglecting them leads to physically incorrect solutions. To validate the EN model, numerical computations are carried out for several examples. Our results show that solving the EN model is much more efficient than the original PNP system. Implemented with the Hodgkin-Huxley model, the computational time for solving the EN model is significantly reduced without sacrificing the accuracy of the solution due to the fact that it allows for relatively large mesh and time-step sizes.

  6. Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.

    Science.gov (United States)

    Liu, Jinn-Liang; Eisenberg, Bob

    2015-07-01

    Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are

  7. Poisson-Nernst-Planck models of nonequilibrium ion electrodiffusion through a protegrin transmembrane pore.

    Directory of Open Access Journals (Sweden)

    Dan S Bolintineanu

    2009-01-01

    Full Text Available Protegrin peptides are potent antimicrobial agents believed to act against a variety of pathogens by forming nonselective transmembrane pores in the bacterial cell membrane. We have employed 3D Poisson-Nernst-Planck (PNP calculations to determine the steady-state ion conduction characteristics of such pores at applied voltages in the range of -100 to +100 mV in 0.1 M KCl bath solutions. We have tested a variety of pore structures extracted from molecular dynamics (MD simulations based on an experimentally proposed octomeric pore structure. The computed single-channel conductance values were in the range of 290-680 pS. Better agreement with the experimental range of 40-360 pS was obtained using structures from the last 40 ns of the MD simulation, where conductance values range from 280 to 430 pS. We observed no significant variation of the conductance with applied voltage in any of the structures that we tested, suggesting that the voltage dependence observed experimentally is a result of voltage-dependent channel formation rather than an inherent feature of the open pore structure. We have found the pore to be highly selective for anions, with anionic to cationic current ratios (I(Cl-/I(K+ on the order of 10(3. This is consistent with the highly cationic nature of the pore but surprisingly in disagreement with the experimental finding of only slight anionic selectivity. We have additionally tested the sensitivity of our PNP model to several parameters and found the ion diffusion coefficients to have a significant influence on conductance characteristics. The best agreement with experimental data was obtained using a diffusion coefficient for each ion set to 10% of the bulk literature value everywhere inside the channel, a scaling used by several other studies employing PNP calculations. Overall, this work presents a useful link between previous work focused on the structure of protegrin pores and experimental efforts aimed at investigating their

  8. Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels.

    Science.gov (United States)

    Singer, A; Gillespie, D; Norbury, J; Eisenberg, R S

    2008-01-01

    Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).

  9. Simulating Electric Double Layer Capacitance by Using Lattice Boltzmann Method

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    Sun, Ning; Gersappe, Dilip

    2015-03-01

    By using the Lattice Boltzmann Method (LBM) we studied diffuse-charge dynamics in electrochemical systems. We use the LBM to solve Poisson-Nernst-Planck equations (PNP) and Modified Poisson-Nernst-Planck equations (MPNP). The isotropic permittivity of electrolyte is modeled using the Booth model. The results show that both steric effect (MPNP) and isotropic permittivity (Booth model) can have large influence on diffuse-charge dynamics, especially when electrolyte concentration or applied potential is high. This model can be applied to simulate electric double layer capacitance of super capacitors with complex geometry and also incorporate other effects such as heat convection in a modular manner.

  10. Comparison of two generation-recombination terms in the Poisson-Nernst-Planck model

    Energy Technology Data Exchange (ETDEWEB)

    Lelidis, I. [Solid State Section, Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece); Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Universite de Picardie Jules Verne, Laboratoire de Physique des Systemes Complexes, 33 rue Saint-Leu 80039, Amiens (France); Barbero, G. [Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Sfarna, A. [Solid State Section, Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)

    2012-10-21

    Two phenomenological forms proposed to take into account the generation-recombination phenomenon of ions are investigated. The first form models the phenomenon as a chemical reaction, containing two coefficients describing the dissociation of neutral particles in ions, and the recombination of ions to give neutral particles. The second form is based on the assumption that in thermodynamical equilibrium, a well-defined density of ions is stable. Any deviation from the equilibrium density gives rise to a source term proportional to the deviation, whose phenomenological coefficient plays the role of a life time. The analysis is performed by evaluating the electrical response of an electrolytic cell to an external stimulus for both forms. For simplicity we assume that the electrodes are blocking, that there is only a group of negative and positive ions, and that the negative ions are immobile. For the second form, two cases are considered: (i) the generation-recombination phenomenon is due to an intrinsic mechanism, and (ii) the production of ions is triggered by an external source of energy, as in a solar cell. We show that the predictions of the two models are different at the impedance as well as at the admittance level. In particular, the first model predicts the existence of two plateaux for the real part of the impedance, whereas the second one predicts just one. It follows that impedance spectroscopy measurements could give information on the model valid for the generation-recombination of ions.

  11. A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

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    Cheung, James; Frischknecht, Amalie L.; Perego, Mauro; Bochev, Pavel

    2017-11-01

    We develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson-Nernst-Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independently on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.

  12. Fluctuation-enhanced electric conductivity in electrolyte solutions.

    Science.gov (United States)

    Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

    2017-10-10

    We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

  13. Improvements in continuum modeling for biomolecular systems

    Science.gov (United States)

    Yu, Qiao; Ben-Zhuo, Lu

    2016-01-01

    Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann (PB)/Poisson-Nernst-Planck (PNP) equations has made great contributions towards simulation of these processes. However, the model has shortcomings in its commonly used form and cannot capture (or cannot accurately capture) some important physical properties of the biological systems. Considerable efforts have been made to improve the continuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecular systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress. Project supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation.

  14. Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

    Directory of Open Access Journals (Sweden)

    Xu Shixin

    2014-01-01

    Full Text Available Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP equations that are solved by Finite Element Method (FEM. Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

  15. A Coupled Transport and Chemical Model for Durability Predictions of Cement Based Materials

    DEFF Research Database (Denmark)

    Jensen, Mads Mønster; Johannesson, Björn; Geiker, Mette Rica

    for the multi-physics durability model, established in this work, is an extended version of the Poisson-Nernst-Planck system of equations. The extension of the Poisson-Nernst-Planck system includes a two phase description of the moisture transport as well as chemical interactions. The vapor and liquid contents...... are conducted. The theoretical background for the model is to a large extent based on the hybrid mixture theory, which is a modern continuum approach. The hybrid mixture theory description considers the individual phases and species, building up the whole mixture, with individual differential equations....... The differential equations includes exchange terms between the phases and species accounting for the exchange of physical quantities which are essential for a stringent physical description of concrete. Balance postulates for, mass, momentum and energy, together with an entropy inequality are studied within...

  16. Framework for reactive mass transport

    DEFF Research Database (Denmark)

    Jensen, Mads Mønster; Johannesson, Björn; Geiker, Mette Rica

    2014-01-01

    Reactive transport modeling is applicable for a range of porous materials. Here the modeling framework is focused on cement-based materials, where ion diffusion and migration are described by the Poisson-Nernst-Planck equation system. A two phase vapor/liquid flow model, with a sorption hysteresis...... description is coupled to the system. The mass transport is solved by using the finite element method where the chemical equilibrium is solved explicitly by an operator splitting method. The IPHREEQC library is used as chemical equilibrium solver. The equation system, solved by IPHREEQC, is explained...

  17. Influence of the Chemical Interactions on the Removal Rate of Different Salts in Electrokinetic Desalination Processes

    DEFF Research Database (Denmark)

    Paz-Garcia, Juan Manuel; Johannesson, Björn; Ottosen, Lisbeth M.

    2011-01-01

    Electrokinetic desalination techniques have been successfully applied for the prevention of salt-induced deterioration problems of masonry and other construction materials. A mathematical model for electrochemical desalination treatments is described, based on the Poisson-Nernst-Planck system...... of equations and accounting for the chemical interactions between the species in the pore solution and the solid matrix. Due to their high abundance in the natural environment, chlorides, nitrates and sulfates are considered the main ions responsible to the salt decay processes in buildings materials...

  18. Nanopore density effect of polyacrylamide gel plug on electrokinetic ion enrichment in a micro-nanofluidic chip

    Science.gov (United States)

    Wang, Jun-yao; Xu, Zheng; Li, Yong-kui; Liu, Chong; Liu, Jun-shan; Chen, Li; Du, Li-qun; Wang, Li-ding

    2013-07-01

    In this paper, the nanopore density effect on ion enrichment is quantitatively described with the ratio between electrophoresis flux and electroosmotic flow flux based on the Poisson-Nernst-Planck equations. A polyacrylamide gel plug is integrated into a microchannel to form a micro-nanofluidic chip. With the chip, electrokinetic ion enrichment is relatively stable and enrichment ratio of fluorescein isothiocyanate can increase to 600-fold within 120 s at the electric voltage of 300 V. Both theoretical research and experiments show that enrichment ratio can be improved through increasing nanopore density. The result will be beneficial to the design of micro-nanofluidic chips.

  19. A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

    Science.gov (United States)

    Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

    2013-09-15

    A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can

  20. cDF Theory Software for mesoscopic modeling of equilibrium and transport phenomena

    Energy Technology Data Exchange (ETDEWEB)

    2015-12-01

    The approach is based on classical Density Functional Theory ((cDFT) coupled with the Poisson-Nernst-Planck (PNP) transport kinetics model and quantum mechanical description of short-range interaction and elementary transport processes. The model we proposed and implemented is fully atomistic, taking into account pairwise short-range and manybody long-range interactions. But in contrast to standard molecular dynamics (MD) simulations, where long-range manybody interactions are evaluated as a sum of pair-wise atom-atom contributions, we include them analytically based on wellestablished theories of electrostatic and excluded volume interactions in multicomponent systems. This feature of the PNP/cDFT approach allows us to reach well beyond the length-scales accessible to MD simulations, while retaining the essential physics of interatomic interactions from first principles and in a parameter-free fashion.

  1. Structural bioinformatics study of PNP from Schistosoma mansoni

    International Nuclear Information System (INIS)

    Silveira, Nelson Jose Freitas da; Uchoa, Hugo Brandao; Canduri, Fernanda; Pereira, Jose Henrique; Camera, Joao Carlos; Basso, Luiz Augusto; Palma, Mario Sergio; Santos, Diogenes Santiago; Filgueira de Azevedo, Walter

    2004-01-01

    The parasite Schistosoma mansoni lacks the de novo pathway for purine biosynthesis and depends on salvage pathways for its purine requirements. Schistosomiasis is endemic in 76 countries and territories and amongst the parasitic diseases ranks second after malaria in terms of social and economic impact and public health importance. The PNP is an attractive target for drug design and it has been submitted to extensive structure-based design. The atomic coordinates of the complex of human PNP with inosine were used as template for starting the modeling of PNP from S. mansoni complexed with inosine. Here we describe the model for the complex SmPNP-inosine and correlate the structure with differences in the affinity for inosine presented by human and S. mansoni PNPs

  2. Lateral PNP bipolar transistor with aiding field diffusions

    Science.gov (United States)

    Gallagher, R. C.; Mc Cann, D. H.

    1969-01-01

    Fabrication technique produces field aided lateral PNP transistors compatible with micropower switching circuits. The sub-collector diffusion is performed with phosphorus as the dopant and the epitaxy is grown using the higher temperature silicon tetrachloride process.

  3. Efficient Fludarabine-Activating PNP From Archaea as a Guidance for Redesign the Active Site of E. Coli PNP.

    Science.gov (United States)

    Cacciapuoti, Giovanna; Bagarolo, Maria Libera; Martino, Elisa; Scafuri, Bernardina; Marabotti, Anna; Porcelli, Marina

    2016-05-01

    The combination of the gene of purine nucleoside phosphorylase (PNP) from Escherichia coli and fludarabine represents one of the most promising systems in the gene therapy of solid tumors. The use of fludarabine in gene therapy is limited by the lack of an enzyme that is able to efficiently activate this prodrug which, consequently, has to be administered in high doses that cause serious side effects. In an attempt to identify enzymes with a better catalytic efficiency than E. coli PNP towards fludarabine to be used as a guidance on how to improve the activity of the bacterial enzyme, we have selected 5'-deoxy-5'-methylthioadenosine phosphorylase (SsMTAP) and 5'-deoxy-5'-methylthioadenosine phosphorylase II (SsMTAPII), two PNPs isolated from the hyperthermophilic archaeon Sulfolobus solfataricus. Substrate specificity and catalytic efficiency of SsMTAP and SsMTAPII for fludarabine were analyzed by kinetic studies and compared with E. coli PNP. SsMTAP and SsMTAPII share with E. coli PNP a comparable low affinity for the arabinonucleoside but are better catalysts of fludarabine cleavage with k(cat)/K(m) values that are 12.8-fold and 6-fold higher, respectively, than those reported for the bacterial enzyme. A computational analysis of the interactions of fludarabine in the active sites of E. coli PNP, SsMTAP, and SsMTAPII allowed to identify the crucial residues involved in the binding with this substrate, and provided structural information to improve the catalytic efficiency of E. coli PNP by enzyme redesign. © 2015 Wiley Periodicals, Inc.

  4. Towards understanding the E. coli PNP binding mechanism and FRET absence between E. coli PNP and formycin A.

    Science.gov (United States)

    Prokopowicz, Małgorzata; Greń, Bartosz; Cieśla, Joanna; Kierdaszuk, Borys

    2017-11-01

    The aim of this study is threefold: (1) augmentation of the knowledge of the E. coli PNP binding mechanism; (2) explanation of the previously observed 'lack of FRET' phenomenon and (3) an introduction of the correction (modified method) for FRET efficiency calculation in the PNP-FA complexes. We present fluorescence studies of the two E. coli PNP mutants (F159Y and F159A) with formycin A (FA), that indicate that the aromatic amino acid is indispensable in the nucleotide binding, additional hydroxyl group at position 159 probably enhances the strength of binding and that the amino acids pair 159-160 has a great impact on the spectroscopic properties of the enzyme. The experiments were carried out in hepes and phosphate buffers, at pH7 and 8.3. Two methods, a conventional and a modified one, that utilizes the dissociation constant, for calculations of the energy transfer efficiency (E) and the acceptor-to-donor distance (r) between FA and the Tyr (energy donor) were employed. Total difference spectra were calculated for emission spectra (λ ex 280nm, 295nm, 305nm and 313nm) for all studied systems. Time-resolved techniques allowed to conclude the existence of a specific structure formed by amino acids at positions 159 and 160. The results showed an unexpected pattern change of FRET in the mutants, when compared to the wild type enzyme and a probable presence of a structure created between 159 and 160 residue, that might influence the binding efficiency. Additionally, we confirmed the indispensable role of the modification of the FRET efficiency (E) calculation on the fraction of enzyme saturation in PNP-FA systems. Copyright © 2017 Elsevier B.V. All rights reserved.

  5. On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

    Directory of Open Access Journals (Sweden)

    Luisa Consiglieri

    2011-01-01

    Full Text Available We deal with the transmembrane sodium diffusion in a nerve. We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions. This system of partial differential equations can be understood as a reduced three-dimensional Poisson-Nernst-Planck model of the sodium concentration. The representation of the membrane includes a jump boundary condition describing the mechanisms involved in the excitation-contraction couple. Our first novelty comes from this general dynamical boundary condition. The second one is the three-dimensional behaviour of the extracellular stimulus. An analytical solution to the mathematical model is proposed depending on the morphology of the excitation.

  6. Modeling electrokinetics in ionic liquids: General

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chao [Physical and Computational Science Directorate, Pacific Northwest National Laboratory, Richland WA USA; Bao, Jie [Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland WA USA; Pan, Wenxiao [Department of Mechanical Engineering, University of Wisconsin-Madison, Madison WI USA; Sun, Xin [Physical and Computational Science Directorate, Pacific Northwest National Laboratory, Richland WA USA

    2017-04-07

    Using direct numerical simulations we provide a thorough study on the electrokinetics of ionic liquids. In particular, the modfied Poisson-Nernst-Planck (MPNP) equations are solved to capture the crowding and overscreening effects that are the characteristics of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the MPNP equations are coupled with the Navier-Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel plates, charging dynamics in a 2D straight-walled pore, electro-osmotic ow in a nano-channel, electroconvective instability on a plane ion-selective surface, and electroconvective ow on a curved ion-selective surface. We discuss how the crowding and overscreening effects and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.

  7. Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology

    Science.gov (United States)

    Cartailler, J.; Schuss, Z.; Holcman, D.

    2017-12-01

    We report here new electrical laws, derived from nonlinear electrodiffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck equations for charge concentration and electric potential as a model of electrodiffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nanopipettes and help to understand the local voltage changes inside dendrites and axons with heterogeneous local geometry.

  8. Elucidation of the Signal Transduction Pathways Activated by the Plant Natriuretic Peptide AtPNP-A

    KAUST Repository

    Turek, Ilona

    2014-11-01

    Plant natriuretic peptides (PNPs) comprise a novel class of hormones that share some sequence similarity in the active site with their animal analogues that function as regulators of salt and water balance. A PNP present in Arabidopsis thaliana (AtPNP-A) has been assigned a role in abiotic and biotic stress responses, and the recombinant protein has been demonstrated to elicit cyclic guanosine monophosphate (cGMP)-dependent stomatal guard cell opening, regulate ion movements, and induce osmoticum-dependent water uptake. Although the importance of the hormone in maintaining ion and fluid homeostasis has been established, key components of the AtPNP-A-dependent signal transduction pathway remain unknown. Since identification of the binding partners of AtPNP-A, including its receptor(s), is fundamental to understanding the mode of its action at the molecular level, comprehensive protein-protein interaction studies, involving yeast two-hybrid screening, affinity-based assays, protein cross-linking and co-immunoprecipitation followed by mass spectrometric (MS) analyses have been performed. Several candidate binding partners of AtPNP-A identified with at least two independent methods were subsequently expressed as recombinant proteins, purified, and the specificity of their interactions with the recombinant AtPNP-A was verified using surface plasmon resonance. Several specific binary interactants of AtPNP-A were subjected to functional assays aimed at unraveling the consequences of the interactions in planta. These experiments have revealed that reactive oxygen species (ROS) are novel secondary messengers involved in the transduction of AtPNP-A signal in suspension-cultured cells of A. thaliana (Col-0). Further insight into the AtPNP-A dependent signalling events occurring in suspension-cultured cells in ROS-dependent or ROS-independent manner have been obtained from the large-scale proteomics study employing tandem mass tag (TMT) labelling followed by MS analysis to

  9. Impact of pore size variability and network coupling on electrokinetic transport in porous media

    Science.gov (United States)

    Alizadeh, Shima; Bazant, Martin Z.; Mani, Ali

    2016-11-01

    We have developed and validated an efficient and robust computational model to study the coupled fluid and ion transport through electrokinetic porous media, which are exposed to external gradients of pressure, electric potential, and concentration. In our approach a porous media is modeled as a network of many pores through which the transport is described by the coupled Poisson-Nernst-Planck-Stokes equations. When the pore sizes are random, the interactions between various modes of transport may provoke complexities such as concentration polarization shocks and internal flow circulations. These phenomena impact mixing and transport in various systems including deionization and filtration systems, supercapacitors, and lab-on-a-chip devices. In this work, we present simulations of massive networks of pores and we demonstrate the impact of pore size variation, and pore-pore coupling on the overall electrokinetic transport in porous media.

  10. [99mTcN(PNP5)(NOEt)]+. A novel potential myocardial perfusion imaging agent

    International Nuclear Information System (INIS)

    Jinfeng Chu; Bin Li; Dejing Kong; Xuebin Wang; Junbo Zhang

    2006-01-01

    The asymmetrical [ 99m TcN(PNP5)(NOEt)] + heterocomplex containing a terminal technetium-nitrogen multiple bond coordinated to the diphosphine ligand (PNP5) and the dithiocarbamate ligand (NOEt), was prepared through ligand exchange reaction. Its radiochemical purity was over 90% as measured by TLC and HPLC. Biodistribution in mice and SPECT imaging in dog were studied. The results showed that [ 99m TcN(PNP5)(NOEt)] + possessed high myocardial uptake and good retention, and high target to non-target ratios, suggesting that it may be a potential myocardial perfusion imaging agent. (author)

  11. The effects of gamma irradiation on neutron displacement sensitivity of lateral PNP bipolar transistors

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chenhui, E-mail: wangchenhui@nint.ac.cn; Chen, Wei; Liu, Yan; Jin, Xiaoming; Yang, Shanchao; Qi, Chao

    2016-09-21

    The effects of gamma irradiation on neutron displacement sensitivity of four types of lateral PNP bipolar transistors (LPNPs) with different neutral base widths, emitter widths and the doping concentrations of the epitaxial base region are studied. The physical mechanisms of the effects are explored by defect analysis using deep level transient spectroscopy (DLTS) techniques and numerical simulations of recombination process in the base region of the lateral PNP bipolar transistors, and are verified by the experiments on gate-controlled lateral PNP bipolar transistors (GCLPNPs) manufactured in the identical commercial bipolar process with different gate bias voltage. The results indicate that gamma irradiation increases neutron displacement damage sensitivity of lateral PNP bipolar transistors and the mechanism of this phenomenon is that positive charge induced by gamma irradiation enhances the recombination process in the defects induced by neutrons in the base region, leading to larger recombination component of base current and greater gain degradation.

  12. Mechanisms of ionizing-radiation-induced gain degradation in lateral PNP BJTs

    International Nuclear Information System (INIS)

    Schmidt, D.M.; Wu, A.; Schrimpf, R.D.; Pease, R.L.; Combs, W.E.

    1996-01-01

    The physical mechanisms for gain degradation in laterals PNP bipolar transistors are examined experimentally and through simulation. The effect of increased surface recombination velocity at the base surface is moderated by positive oxide charge

  13. The effects of emitter-tied field plates on lateral PNP ionizing radiation response

    International Nuclear Information System (INIS)

    Barnaby, H.J.; Schrimpf, R.D.; Cirba, C.R.; Pease, R.L.; Fleetwood, D.M.; Kosier, S.L.

    1998-03-01

    Radiation response comparisons of lateral PNP bipolar technologies reveal that device hardening may be achieved by extending the emitter contact over the active base. The emitter-tied field plate suppresses recombination of carriers with interface traps

  14. Unjuk Kerja Catu Daya 12 Volt 2a Dengan Pass Element Transistor Npn Dan Pnp

    OpenAIRE

    Fathoni, Fathoni

    2010-01-01

    Transistor pelewat (pass element transistor) yang dipasang pada rangkain catu daya yang menggunakan IC regulator 3 terminal adalah untuk booster arus output. Ada dua cara pemasangan transistor pelewat yang umum digunakan, yaitu dengan transistor pnp dan npn. Transistor pnp dipasang dengan basis transistor yang terhubung pada input IC regulator sedangkan transistor npn dipasang dengan basis transistor yang terhubung pada output IC regulator.Untuk mengetahui unjuk kerja dari kedua ...

  15. Ionic PN and PNP junctions -- Diodes and Transistors

    Science.gov (United States)

    Kalman, Eric; Vlassiouk, Ivan; Apel, Pavel; Siwy, Zuzanna

    2008-03-01

    There are well-known devices for controlling the transport of electrons, but very few control ions in a solution. We have prepared ionic diodes and transistors that function in a similar manner to their semiconductor analogues. Ionic PN junctions were created by surface patterning single conical nanopores in polymer films, so that the pore walls are split into two sections: one with positive charge, and the other with negative. These diodes can achieve rectification degrees of several hundreds. Ionic PNP junctions were created by surface patterning single double-conical nanopores in polymer films with tip diameter between 2 and 6 nm, so that the pore walls are split into three sections: the two areas near the large pore openings which are positively charged, while the center of the pore, near the pore tip, is negatively charged. This device works in a similar fashion to a semiconducting BJT transistor, and we show that we can control the electric potential chemically in a manner sufficient to gate the ion current through the device.

  16. Evidence for purine nucleoside phosphorylase (PNP) release from rat C6 glioma cells.

    Science.gov (United States)

    Giuliani, Patricia; Zuccarini, Mariachiara; Buccella, Silvana; Peña-Altamira, Luis Emiliano; Polazzi, Elisabetta; Virgili, Marco; Monti, Barbara; Poli, Alessandro; Rathbone, Michel P; Di Iorio, Patrizia; Ciccarelli, Renata; Caciagli, Francesco

    2017-04-01

    Intracellular purine turnover is mainly oriented to preserving the level of triphosphate nucleotides, fundamental molecules in vital cell functions that, when released outside cells, act as receptor signals. Conversely, high levels of purine bases and uric acid are found in the extracellular milieu, even in resting conditions. These compounds could derive from nucleosides/bases that, having escaped to cell reuptake, are metabolized by extracellular enzymes similar to the cytosolic ones. Focusing on purine nucleoside phosphorylase (PNP) that catalyzes the reversible phosphorolysis of purine (deoxy)-nucleosides/bases, we found that it is constitutively released from cultured rat C6 glioma cells into the medium, and has a molecular weight and enzyme activity similar to the cytosolic enzyme. Cell exposure to 10 μM ATP or guanosine triphosphate (GTP) increased the extracellular amount of all corresponding purines without modifying the levels/activity of released PNP, whereas selective activation of ATP P2Y 1 or adenosine A 2A metabotropic receptors increased PNP release and purine base formation. The reduction to 1% in oxygen supply (2 h) to cells decreased the levels of released PNP, leading to an increased presence of extracellular nucleosides and to a reduced formation of xanthine and uric acid. Conversely, 2 h cell re-oxygenation enhanced the extracellular amounts of both PNP and purine bases. Thus, hypoxia and re-oxygenation modulated in opposite manner the PNP release/activity and, thereby, the extracellular formation of purine metabolism end-products. In conclusion, extracellular PNP and likely other enzymes deputed to purine base metabolism are released from cells, contributing to the purinergic system homeostasis and exhibiting an important pathophysiological role. © 2017 International Society for Neurochemistry.

  17. A comparative study on electrical characteristics of 1-kV pnp and npn SiC bipolar junction transistors

    Science.gov (United States)

    Okuda, Takafumi; Kimoto, Tsunenobu; Suda, Jun

    2018-04-01

    We investigate the electrical characteristics of 1-kV pnp SiC bipolar junction transistors (BJTs) and compare them with those of npn SiC BJTs. The base resistance, current gain, and blocking capability are characterized. It is found that the base resistance of pnp SiC BJTs is two orders of magnitude lower than that of npn SiC BJTs. However, the obtained current gains are low below unity in pnp SiC BJTs, whereas npn SiC BJTs exhibit a current gain of 14 without surface passivation. The reason for the poor current gain of pnp SiC BJTs is discussed.

  18. 2D device-level simulation study of strained-Si pnp heterojunction bipolar transistors on virtual substrates

    Science.gov (United States)

    Jankovic, N. D.; O'Neill, A.

    2004-02-01

    A novel strained-Si pnp heterojunction bipolar transistor (HBT) design, suitable for virtual substrate technology, is proposed that is inherently free from the detrimental valence band barrier effects usually encountered in conventional SiGe pnp HBTs on silicon. It takes advantage of the heterojunction formed between a strained-Si layer and a relaxed SiGe buffer (virtual substrate), whose associated valence band offset appears favorable for minority hole transport at the base/collector junction. From two-dimensional (2D) numerical simulation, it is found that the newly proposed strained-Si pnp HBT substantially outperforms the equivalent BJT on a silicon substrate in terms of DC and high-frequency characteristics. A threefold increase in maximum current gain β, a fourfold improvement in peak ft and a 2.5 times increase in peak fmax are predicted for strained-Si pnp HBTs on a 50% Ge virtual substrate in comparison with identical conventional silicon pnp BJTs.

  19. De-embedding and Modelling of pnp SiGe HBTs

    DEFF Research Database (Denmark)

    Hadziabdic, Dzenan; Jiang, Chenhui; Johansen, Tom Keinicke

    2007-01-01

    In this work we present a direct parameter extraction procedure for SiGe pnp heterojunction bipolar transistor (HBT) large-signal and small-signal models. Test structure parasitics are removed from the measured small-signal parameters using an open-short de-embedding technique, improved to account...

  20. Impact of pnpR, a LysR-type regulator-encoding gene, on the cellular processes of Pseudomonas putida DLL-E4.

    Science.gov (United States)

    Chen, Qiongzhen; Tu, Hui; Huang, Fei; Wang, Yicheng; Dong, Weiliang; Wang, Wenhui; Li, Zhoukun; Wang, Fei; Cui, Zhongli

    2016-06-01

    LysR-type transcriptional regulators (LTTRs) regulate various cellular processes in bacteria. pnpR is an LTTR-encoding gene involved in the regulation of hydroquinone (HQ) degradation, and its effects on the cellular processes of Pseudomonas putida DLL-E4 were investigated at the physiological, biochemical and molecular levels. Reverse transcription polymerase chain reaction revealed that pnpR positively regulated its own expression and that of the pnpC1C2DECX1X2 operon; additionally, pnpR partially regulated the expression of pnpA when P. putida was grown on para-nitrophenol (PNP) or HQ. Strains DLL-E4 and DLL-ΔpnpR exhibited similar cellular morphologies and growth rates. Transcriptome analysis revealed that pnpR regulated the expression of genes in addition to those involved in PNP degradation. A total of 20 genes were upregulated and 19 genes were downregulated by at least 2-fold in strain DLL-ΔpnpR relative to strain DLL-E4. Bioinformatic analysis revealed putative PnpR-binding sites located in the upstream regions of genes involved in PNP degradation, carbon catabolite repression and other cellular processes. The utilization of L-aspartic acid, L-histidine, L-pyroglutamic acid, L-serine, γ-aminobutyric acid, D,L-lactic acid, D-saccharic acid, succinic acid and L-alaninamide was increased at least 1.3-fold in strain DLL-ΔpnpR as shown by BIOLOG assays, indicating that pnpR plays a potential negative regulation role in the utilization of carbon sources. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  1. What a difference a 5f element makes: trivalent and tetravalent uranium halide complexes supported by one and two bis[2-(diisopropylphosphino)-4-methylphenyl]amido (PNP) ligands.

    Science.gov (United States)

    Cantat, Thibault; Scott, Brian L; Morris, David E; Kiplinger, Jaqueline L

    2009-03-02

    The coordination behavior of the bis[2-(diisopropylphosphino)-4-methylphenyl]amido ligand (PNP) toward UI3(THF)4 and UCl4 has been investigated to access new uranium(III) and uranium(IV) halide complexes supported by one and two PNP ligands. The reaction between (PNP)K (6) and 1 equiv of UI3(THF)4 afforded the trivalent halide complex (PNP)UI2(4-tBu-pyridine)2 (7) in the presence of 4-tert-butylpyridine. The same reaction carried out with UCl4 and no donor ligand gave [(PNP)UCl3]2 (8), in which the uranium coordination sphere in the (PNP)UCl3 unit is completed by a bridging chloride ligand. When UCl4 is reacted with 1 equiv (PNP)K (6) in the presence of THF, trimethylphosphine oxide (TMPO), or triphenylphosphineoxide (TPPO), the tetravalent halide complexes (PNP)UCl3(THF) (9), (PNP)UCl3(TMPO)2 (10), and (PNP)UCl3(TPPO) (11), respectively, are formed in excellent yields. The bis(PNP) complexes of uranium(III), (PNP)2UI (12), and uranium(IV), (PNP)2UCl2 (13), were easily isolated from the analogous reactions between 2 equiv of 6 and UI3(THF)4 or UCl4, respectively. Complexes 12 and 13 represent the first examples of complexes featuring two PNP ligands coordinated to a single metal center. Complexes 7-13 have been characterized by single-crystal X-ray diffraction and 1H and 31P NMR spectroscopy. The X-ray structures demonstrate the ability of the PNP ligand to adopt new coordination modes upon coordination to uranium. The PNP ligand can adopt both pseudo-meridional and pseudo-facial geometries when it is kappa3-(P,N,P) coordinated, depending on the steric demand at the uranium metal center. Additionally, its hemilabile character was demonstrated with an unusual kappa2-(P,N) coordination mode that is maintained in both the solid-state and in solution. Comparison of the structures of the mono(PNP) and bis(PNP) complexes 7, 9, 11-13 with their respective C5Me5 analogues 1-4 undoubtedly show that a more sterically congested environment is provided by the PNP ligand. The

  2. Correlator receiver architecture with PnpN optical thyristor operating as optical hard-limiter

    Science.gov (United States)

    Kang, Tae-Gu; Ho Lee, Su; Park, Soonchul

    2011-07-01

    We propose novel correlator receiver architecture with a PnpN optical thyristor operating as optical hard-limiter, and demonstrate a multiple-access interference rejection of the proposed correlator receiver. The proposed correlator receiver is composed of the 1×2 splitter, optical delay line, 2×1 combiner, and fabricated PnpN optical thyristor. The proposed correlator receiver enhances the system performance because it excludes some combinations of multiple-access interference patterns from causing errors as in optical code-division multiple access systems with conventional optical receiver shown in all previous works. It is found that the proposed correlator receiver can fully reject the interference signals generated by decoding processing and multiple access for two simultaneous users.

  3. Floating-gate controlled programmable non-volatile black phosphorus PNP junction memory.

    Science.gov (United States)

    Zhang, Pengfei; Li, Dong; Chen, Mingyuan; Zong, Qijun; Shen, Jun; Wan, Dongyun; Zhu, Jingtao; Zhang, Zengxing

    2018-02-15

    To meet the increasing requirements of minimizing circuits, the development of novel device architectures that use ultra-thin two-dimensional materials is encouraged. Here, we demonstrate a non-volatile black phosphorus (BP) PNP junction in a BP/h-BN/graphene heterostructure in which BP acts as a transport channel layer, hexagonal boron nitride (h-BN) serves as a tunnel barrier layer and graphene is the charge-trapping layer. The device architecture is designed such that only the middle part of the BP is aligned over the graphene flake, enabling the flexible tuning of the charge carriers in the BP over the graphene charge-trapping layer. Thus, the device exhibits the ability to work in two different operating modes (PNP and PP + P). Each operating mode can be retained well and demonstrates non-volatile behavior, and each can be programmed by using the control-gate.

  4. Isomerization of Allylic Alcohols to Ketones Catalyzed by Well-Defined Iron PNP Pincer Catalysts.

    Science.gov (United States)

    Xia, Tian; Wei, Zhihong; Spiegelberg, Brian; Jiao, Haijun; Hinze, Sandra; de Vries, Johannes G

    2018-03-15

    [Fe(PNP)(CO)HCl] (PNP=di-(2-diisopropylphosphanyl-ethyl)amine), activated in situ with KOtBu, is a highly active catalyst for the isomerization of allylic alcohols to ketones without an external hydrogen supply. High reaction rates were obtained at 80 °C, but the catalyst is also sufficiently active at room temperature with most substrates. The reaction follows a self-hydrogen-borrowing mechanism, as verified by DFT calculations. An alternative isomerization through alkene insertion and β-hydride elimination could be excluded on the basis of a much higher barrier. In alcoholic solvents, the ketone product is further reduced to the saturated alcohol. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  5. Mechanistic Studies of Ethylene and α-Olefin Co-Oligomerization Catalyzed by Chromium−PNP Complexes

    OpenAIRE

    Do, Loi H.; Labinger, Jay A.; Bercaw, John E.

    2012-01-01

    To explore the possibility of producing a narrow distribution of mid- to long-chain hydrocarbons from ethylene as a chemical feedstock, co-oligomerization of ethylene and linear α-olefins (LAOs) was investigated, using a previously reported chromium complex, [CrCl_3(PNP^(OMe))] (1, where PNP^(OMe) = N,N-bis(bis(o-methoxyphenyl)- phosphino)methylamine). Activation of 1 by treatment with modified methylaluminoxane (MMAO) in the presence of ethylene and 1-hexene afforded mos...

  6. Implemented Crime Prevention Strategies of PNP in Salug Valley, Zamboanga Del Sur, Philippines

    Directory of Open Access Journals (Sweden)

    Mark E. Patalinghug

    2017-05-01

    Full Text Available This study aimed primarily to determine the effectiveness of crime prevention strategies implemented by the Salug Valley Philippine National Police (PNP in terms of Police Integrated Patrol System, Barangay Peacekeeping Operation, Anti - Criminality Operation, Integrated Area Community Public Safety services, Bantay Turista and Scho ol Safety Project as evaluated by 120 inhabitants and 138 PNP officers from four Municipalities of Salug Valley Zamboanga del Sur. Stratified random sampling was utilized in determining the respondents. Index crime rate were correlated with the crime preve ntion strategies of the PNP in town of Salug Valley. A descriptive method of research was applied in this study utilizing self - made questionnaire. The data collected were analyzed using the main statistical tools like frequency count, percentage, mean com putation, Kruskal Wallis Analysis of Variance and simple correlation. Findings of the study revealed that the crime prevention strategies in four (4 municipalities were “much effective” to include Integrated Patrol System, Barangay Peace Keeping Operation s, Anti - Criminality Operations, Integrated Area Community Public Safety Services, Bantay Turista and School Safety Project in connection to the responses of 158 participants. There is a significant relationship between crime prevention strategies employed and index crime rate.

  7. PNPase autocontrols its expression by degrading a double-stranded structure in the pnp mRNA leader

    Science.gov (United States)

    Jarrige, Anne-Charlotte; Mathy, Nathalie; Portier, Claude

    2001-01-01

    Polynucleotide phosphorylase synthesis is autocontrolled at a post-transcriptional level in an RNase III-dependent mechanism. RNase III cleaves a long stem–loop in the pnp leader, which triggers pnp mRNA instability, resulting in a decrease in the synthesis of polynucleotide phosphorylase. The staggered cleavage by RNase III removes the upper part of the stem–loop structure, creating a duplex with a short 3′ extension. Mutations or high temperatures, which destabilize the cleaved stem–loop, decrease expression of pnp, while mutations that stabilize the stem increase expression. We propose that the dangling 3′ end of the duplex created by RNase III constitutes a target for polynucleotide phosphorylase, which binds to and degrades the upstream half of this duplex, hence inducing pnp mRNA instability. Consistent with this interpretation, a pnp mRNA starting at the downstream RNase III processing site exhibits a very low level of expression, regardless of the presence of polynucleotide phosphorylase. Moreover, using an in vitro synthesized pnp leader transcript, it is shown that polynucleotide phosphorylase is able to digest the duplex formed after RNase III cleavage. PMID:11726520

  8. Characterizations of cross-bridges in the presence of saturating concentrations of MgAMP-PNP in rabbit permeabilized psoas muscle.

    Science.gov (United States)

    Frisbie, S M; Xu, S; Chalovich, J M; Yu, L C

    1998-06-01

    Several earlier studies have led to different conclusions about the complex of myosin with MgAMP-PNP. It has been suggested that subfragment 1 of myosin (S1)-MgAMP-PNP forms an S1-MgADP-like state, an intermediate between the myosin S1-MgATP and myosin S1-MgADP states or a mixture of cross-bridge states. We suggest that the different states observed result from the failure to saturate S1 with MgAMP-PNP. At saturating MgAMP-PNP, the interaction of myosin S1 with actin is very similar to that which occurs in the presence of MgATP. 1) At 1 degrees C and 170 mM ionic strength the equatorial x-ray diffraction intensity ratio I11/I10 decreased with an increasing MgAMP-PNP concentration and leveled off by approximately 20 mM MgAMP-PNP. The resulting ratio was the same for MgATP-relaxed fibers. 2) The two dimensional x-ray diffraction patterns from MgATP-relaxed and MgAMP-PNP-relaxed bundles are similar. 3) The affinity of S1-MgAMP-PNP for the actin-tropomyosin-troponin complex in solution in the absence of free calcium is comparable with that of S1-MgATP. 4) In the presence of calcium, I11/I10 decreased toward the relaxed value with increasing MgAMP-PNP, signifying that the affinity between cross-bridge and actin is weakened by MgAMP-PNP. 5) The degree to which the equatorial intensity ratio decreases as the ionic strength increases is similar in MgAMP-PNP and MgATP. Therefore, results from both fiber and solution studies suggest that MgAMP-PNP acts as a non hydrolyzable MgATP analogue for myosin.

  9. Separation of ionization and displacement damage using gate-controlled lateral PNP bipolar transistors

    Science.gov (United States)

    Ball, D. R.; Schrimpf, R. D.; Barnaby, H. J.

    2002-12-01

    Proton irradiation produces both ionization and displacement damage in semiconductor devices. In this paper, a technique for separating the effects of these two types of damage using a lateral PNP bipolar transistor with a gate contact over the active base region is described. By biasing the gate appropriately, the effects of ionization-induced damage are minimized and the effects of displacement damage can be measured independently. Experiments and simulations are used to validate this approach and provide insight into proton-induced BJT degradation.

  10. The Aluminum-Free P-n-P InGaAsN Double Heterojunction Bipolar Transistors

    Energy Technology Data Exchange (ETDEWEB)

    CHANG,PING-CHIH; LI,N.Y.; BACA,ALBERT G.; MONIER,C.; LAROCHE,J.R.; HOU,H.Q.; REN,F.; PEARTON,S.J.

    2000-08-01

    The authors have demonstrated an aluminum-free P-n-P GaAs/InGaAsN/GaAs double heterojunction bipolar transistor (DHBT). The device has a low turn-on voltage (V{sub ON}) that is 0.27 V lower than in a comparable P-n-p AlGaAs/GaAs HBT. The device shows near-ideal D. C. characteristics with a current gain ({beta}) greater than 45. The high-speed performance of the device are comparable to a similar P-n-p AlGaAs/GaAs HBT, with f{sub T} and f{sub MAX} values of 12 GHz and 10 GHz, respectively. This device is very suitable for low-power complementary HBT circuit applications, while the aluminum-free emitter structure eliminates issues typically associated with AlGaAs.

  11. Singlet-to-triplet ratio in the deuteron breakup reaction pd → pnp at 585 MeV

    International Nuclear Information System (INIS)

    Uzikov, Yu.N.; Komarov, V.I.; Rathmann, F.; Seyfarth, H.

    2001-01-01

    Available experimental data on the exclusive pd → pnp reaction at 585 MeV show a narrow peak in the proton-neutron final-state interaction region. It was supposed previously, on the basis of a phenomenological analysis of the shape of this peak, that the final spin-singlet pn state provided about one third of the observed cross section. By comparing the absolute value of the measured cross section with that of pd elastic scattering using the Faeldt-Wilkin extrapolation theorem, it is shown here that the pd → pnp data can be explained mainly by the spin-triplet final state with a singlet admixture of a few percent. The smallness of the singlet contribution is compatible with existing pN → pNπ data and the one-pion exchange mechanism of the pd → pnp reaction

  12. Crystal structures of carbamate kinase from Giardia lamblia bound with citric acid and AMP-PNP.

    Directory of Open Access Journals (Sweden)

    Kap Lim

    Full Text Available The parasite Giardia lamblia utilizes the L-arginine dihydrolase pathway to generate ATP from L-arginine. Carbamate kinase (CK catalyzes the last step in this pathway, converting ADP and carbamoyl phosphate to ATP and ammonium carbamate. Because the L-arginine pathway is essential for G. lamblia survival and absent in high eukaryotes including humans, the enzyme is a potential target for drug development. We have determined two crystal structures of G. lamblia CK (glCK with bound ligands. One structure, in complex with a nonhydrolyzable ATP analog, adenosine 5'-adenylyl-β,γ-imidodiphosphate (AMP-PNP, was determined at 2.6 Å resolution. The second structure, in complex with citric acid bound in the postulated carbamoyl phosphate binding site, was determined in two slightly different states at 2.1 and 2.4 Å resolution. These structures reveal conformational flexibility of an auxiliary domain (amino acid residues 123-170, which exhibits open or closed conformations or structural disorder, depending on the bound ligand. The structures also reveal a smaller conformational change in a region associated the AMP-PNP adenine binding site. The protein residues involved in binding, together with a model of the transition state, suggest that catalysis follows an in-line, predominantly dissociative, phosphotransfer reaction mechanism, and that closure of the flexible auxiliary domain is required to protect the transition state from bulk solvent.

  13. Differential development of sex-related characters of chickens from the GSP and PNP/DO inbred lines after left ovariectomy.

    Science.gov (United States)

    Valdez, Marcos B; Mizutani, Makoto; Kinoshita, Keiji; Fujiwara, Akira; Yazawa, Hajime; Shimada, Kiyoshi; Namikawa, Takao; Yamagata, Takahiro

    2010-02-01

    To elucidate strain differences in the sex reversal of genetic females to phenotypic males, GSP and PNP/DO females were left ovariectomized (ovx) between one to three days after hatching, and the degree of masculinization based on sex-related characters, histological analysis of the right gonad and hormone assay were assessed at one year of age. The GSP and PNP/DO inbred lines were both derived from the Fayoumi breed and are only differentiated based on the red blood cell antigen type carried by each inbred line. Combs and wattles were found to be significantly bigger (PGSP ovx compared with the PNP/DO ovx chickens, although male plumage patterns were more pronounced in the PNP/DO ovx. Spurs were observed both in the GSP and PNP/DO ovx chickens with no significant difference (P>0.05) in length compared with the respective male controls, and body weight was not significantly different (P>0.05) compared with the female controls. The weight of the right gonad was significantly heavier (PGSP ovx than in the PNP/DO ovx. Positive correlations were found in the sex-related characters as well as the plasma testosterone level and right gonad weight in both the GSP and PNP/DO ovx chickens, but not in the spur length, which showed a negative correlation in the PNP/DO ovx chickens. Histological analysis revealed that the right gonads of the PNP/DO ovx chickens were morphologically developed compared with the GSP ovx chickens, which showed more advance stages of spermatogenesis. It could be inferred that PNP/DO females that exhibit a hereditary persistent right oviduct are more responsive to the masculinizing effect of ovariectomy compared with GSP females, suggesting that genetic background may have a possible contribution to the degree of masculinization and subsequent development of sex related characters.

  14. The impact of Metal-Ligand Cooperation in Hydrogenation of Carbon Dioxide Catalyzed by Ruthenium PNP Pincer

    NARCIS (Netherlands)

    Filonenko, G.A.; Conley, M.P.; Copéret, C.; Lutz, M.; Hensen, E.J.M.; Pidko, E.A.

    2013-01-01

    The metal–ligand cooperative activation of CO2 with pyridine-based ruthenium PNP pincer catalysts leads to pronounced inhibition of the activity in the catalytic CO2 hydrogenation to formic acid. The addition of water restores catalytic performance by activating alternative reaction pathways and

  15. Purine Nucleoside Phosphorylase (PNP) Activity of Lymphocytes and T Cell Subsets in Peripheral Blood in Thyroid Tumors

    International Nuclear Information System (INIS)

    Kim, Dong Soo

    1992-01-01

    To elucidate alteration of purine nucleoside phosphorylase (PNP) activity of peripheral lymphocytes and helper/inducer and suppressor/cytototxic T cells in patients with thyroid tumors, the author examined PNP activity, and CD4 + and CD8 + cells of peripheral blood in 20 cases of simple goiter, 9 cases of thyroid adenoma and 20 cases of thyroid cancer as well as 11 cases of adult healthy subjects as control. Diagnoses were established on the basis of commonly accepted clinical and biochemical criteria in simple goiter and were confirmed histopathologically in thyroid adenoma and cancer. All blood was obtained from veins of the patients and control subjects in Pusan National University Hospital during the period of January to August, 1991. The results obtained were summarized as follows: 1) The PNP activity was significantly decreased or tended to be decreased in thyroid adenomas and cancers as compared with control subjects and simple goiters. 2) The percentage of CD8 cells was significantly decreased or tended to be decreased in thyroid cancers as compared with simple goiters, thyroid adenomas and control subjects. 3) The CD4/CD8 ratio was significantly increased or tended to be increased in thyroid cancer as compared with simple goiters, thyroid adenomas and control subjects. On the basis of the results, it can be suggested that the immunodysfunction in thyroid cancer may be due to decreased suppressor/cytotoxic T cells, and the estimation of PNP activity of peripheral lymphocyte is a helpful test in detecting the immune status in thyroid tumors.

  16. Dependence of Ideality Factor in Lateral PNP Transistors on Surface Carrier Concentration

    Science.gov (United States)

    Li, Xingji; Yang, Jianqun; Barnaby, Hugh J.; Galloway, Kenneth F.; Schrimpf, Ronald D.; Fleetwood, Daniel M.; Liu, Chaoming

    2017-06-01

    The influence of surface carrier concentration on the ideality factor of excess base current (ΔIB) in gated lateral PNP (GLPNP) bipolar junction transistors (BJTs) induced by 1-MeV electrons is investigated. ΔIB in LPNP BJTs is impacted by the surface carrier density and radiation-induced interface traps. In GLPNP BJTs, the surface carrier concentration can be controlled by the voltage applied to a gate over the base region. The ideality factor changes after irradiation, and its dependence on emitter-base voltage (VEB) is a function of gate voltage. For the irradiated devices, as the gate voltage decreases from +20 to -5 V, the ideality factor for excess base current changes from a single slope to two-slope behavior. The majority carrier concentration at the surface of the base, controlled by the gate voltage, impacts the excess base current and its ideality factor.

  17. Final state interaction in the pd → pnp reaction at 1 GeV

    International Nuclear Information System (INIS)

    Deloff, A.

    1992-09-01

    The pd → pnp reaction at 1 GeV in both the direct and charge exchange channel has been investigated. The experimental data come from a line reversed beam-target experiment with 3.3 GeV/c deuterons incident on a proton target. In the direct channel data exhibit narrow structures in the np effective mass spectra: at threshold, at 2.02 GeV and at 2.12 GeV which have been seen before and we report on a new narrow enhancement at 1.95 GeV. In charge exchange channel the data show somewhat broader peak at 2.18 GeV. The data are explained by using a conventional approach, i.e. without sub-nucleonic degrees of freedom, but including the ΔN channel in NN scattering. 29 figs., 1 tab., 36 refs. (author)

  18. Streaming current magnetic fields in a charged nanopore

    Science.gov (United States)

    Mansouri, Abraham; Taheri, Peyman; Kostiuk, Larry W.

    2016-01-01

    Magnetic fields induced by currents created in pressure driven flows inside a solid-state charged nanopore were modeled by numerically solving a system of steady state continuum partial differential equations, i.e., Poisson, Nernst-Planck, Ampere and Navier-Stokes equations (PNPANS). This analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale, and applied to a finite length cylindrical nano-channel. The comparison of numerical and analytical studies shows an excellent agreement and verified the magnetic fields density both inside and outside the nanopore. The radially non-uniform currents resulted in highly non-uniform magnetic fields within the nanopore that decay as 1/r outside the nanopore. It is worth noting that for either streaming currents or streaming potential cases, the maximum magnetic field occurred inside the pore in the vicinity of nanopore wall, as opposed to a cylindrical conductor that carries a steady electric current where the maximum magnetic fields occur at the perimeter of conductor. Based on these results, it is suggested and envisaged that non-invasive external magnetic fields readouts generated by streaming/ionic currents may be viewed as secondary electronic signatures of biomolecules to complement and enhance current DNA nanopore sequencing techniques. PMID:27833119

  19. Preparation, characterization and simulation studies of carbon nanotube electrodes for electrochemical energy storage

    Energy Technology Data Exchange (ETDEWEB)

    Meissner, Frank; Endler, Ingolf [Fraunhofer-Institut fuer Keramische Technologien und Systeme (IKTS), Dresden (Germany); Lorrmann, Henning [Fraunhofer-Institut fuer Silicatforschung (ISC), Wuerzburg (Germany); Pastewka, Lars [Fraunhofer-Institut fuer Werkstoffmechanik (IWM), Freiburg im Breisgau (Germany)

    2010-07-01

    Chemical Vapor Deposition (CVD) was employed to synthesize multiwalled carbon nanotubes (MWCNT) on different carrier materials for electrode applications. In the field of electrochemical energy storage it is essential to grow MWCNT on conducting substrates. For this reason titanium nitride (TiN) layers as well as a copper foil were used as substrates. The MWCNT grown on TiN layers show diameters of about 20 nm and lengths up to 13 {mu}m. In the case of copper foil substrates a remarkably higher nanotube diameter of several tens of nanometers was found. First electrochemical characterization via cyclic voltammetry shows the potential of MWCNT as electrodes for energy storage applications. The CNT were measured in an organic carbonate electrolyte vs. a lithium counter electrode with various scan rates. Until now the preliminary investigations by cyclic voltammetry for electrodes consisting of aligned MWCNT on TiN showed a capacity of around 130 F g{sup -1} in the range of 1 - 3 V vs. Li/Li{sup +}. In support of the experiments we construct a one dimensional Poisson-Nernst-Planck (PNP) continuum model that has been shown to yield agreement with corresponding molecular dynamics simulations to model ion transport into these types of electrodes. Our simulations show that first the ions accumulate at the tips of the tubes because the inner volume of the electrodes is initially field-free. A homogeneous charge distribution is then established through diffusion. The PNP model is used to compute cyclic voltammograms which show qualitative agreement with the experiments. (orig.)

  20. Ion current rectification, limiting and overlimiting conductances in nanopores.

    Science.gov (United States)

    van Oeffelen, Liesbeth; Van Roy, Willem; Idrissi, Hosni; Charlier, Daniel; Lagae, Liesbet; Borghs, Gustaaf

    2015-01-01

    Previous reports on Poisson-Nernst-Planck (PNP) simulations of solid-state nanopores have focused on steady state behaviour under simplified boundary conditions. These are Neumann boundary conditions for the voltage at the pore walls, and in some cases also Donnan equilibrium boundary conditions for concentrations and voltages at both entrances of the nanopore. In this paper, we report time-dependent and steady state PNP simulations under less restrictive boundary conditions, including Neumann boundary conditions applied throughout the membrane relatively far away from the nanopore. We simulated ion currents through cylindrical and conical nanopores with several surface charge configurations, studying the spatial and temporal dependence of the currents contributed by each ion species. This revealed that, due to slow co-diffusion of oppositely charged ions, steady state is generally not reached in simulations or in practice. Furthermore, it is shown that ion concentration polarization is responsible for the observed limiting conductances and ion current rectification in nanopores with asymmetric surface charges or shapes. Hence, after more than a decade of collective research attempting to understand the nature of ion current rectification in solid-state nanopores, a relatively intuitive model is retrieved. Moreover, we measured and simulated current-voltage characteristics of rectifying silicon nitride nanopores presenting overlimiting conductances. The similarity between measurement and simulation shows that overlimiting conductances can result from the increased conductance of the electric double-layer at the membrane surface at the depletion side due to voltage-induced polarization charges. The MATLAB source code of the simulation software is available via the website http://micr.vub.ac.be.

  1. Ion current rectification, limiting and overlimiting conductances in nanopores.

    Directory of Open Access Journals (Sweden)

    Liesbeth van Oeffelen

    Full Text Available Previous reports on Poisson-Nernst-Planck (PNP simulations of solid-state nanopores have focused on steady state behaviour under simplified boundary conditions. These are Neumann boundary conditions for the voltage at the pore walls, and in some cases also Donnan equilibrium boundary conditions for concentrations and voltages at both entrances of the nanopore. In this paper, we report time-dependent and steady state PNP simulations under less restrictive boundary conditions, including Neumann boundary conditions applied throughout the membrane relatively far away from the nanopore. We simulated ion currents through cylindrical and conical nanopores with several surface charge configurations, studying the spatial and temporal dependence of the currents contributed by each ion species. This revealed that, due to slow co-diffusion of oppositely charged ions, steady state is generally not reached in simulations or in practice. Furthermore, it is shown that ion concentration polarization is responsible for the observed limiting conductances and ion current rectification in nanopores with asymmetric surface charges or shapes. Hence, after more than a decade of collective research attempting to understand the nature of ion current rectification in solid-state nanopores, a relatively intuitive model is retrieved. Moreover, we measured and simulated current-voltage characteristics of rectifying silicon nitride nanopores presenting overlimiting conductances. The similarity between measurement and simulation shows that overlimiting conductances can result from the increased conductance of the electric double-layer at the membrane surface at the depletion side due to voltage-induced polarization charges. The MATLAB source code of the simulation software is available via the website http://micr.vub.ac.be.

  2. Catalytic mechanisms of direct pyrrole synthesis via dehydrogenative coupling mediated by PNP-Ir or PNN-Ru pincer complexes: Crucial role of proton-transfer shuttles in the PNP-Ir system

    KAUST Repository

    Qu, Shuanglin

    2014-04-02

    Kempe et al. and Milstein et al. have recently advanced the dehydrogenative coupling methodology to synthesize pyrroles from secondary alcohols (e.g., 3) and β-amino alcohols (e.g., 4), using PNP-Ir (1) and PNN-Ru (2) pincer complexes, respectively. We herein present a DFT study to characterize the catalytic mechanism of these reactions. After precatalyst activation to give active 1A/2A, the transformation proceeds via four stages: 1A/2A-catalyzed alcohol (3) dehydrogenation to give ketone (11), base-facilitated C-N coupling of 11 and 4 to form an imine-alcohol intermediate (18), base-promoted cyclization of 18, and catalyst regeneration via H2 release from 1R/2R. For alcohol dehydrogenations, the bifunctional double hydrogen-transfer pathway is more favorable than that via β-hydride elimination. Generally, proton-transfer (H-transfer) shuttles facilitate various H-transfer processes in both systems. Notwithstanding, H-transfer shuttles play a much more crucial role in the PNP-Ir system than in the PNN-Ru system. Without H-transfer shuttles, the key barriers up to 45.9 kcal/mol in PNP-Ir system are too high to be accessible, while the corresponding barriers (<32.0 kcal/mol) in PNN-Ru system are not unreachable. Another significant difference between the two systems is that the addition of alcohol to 1A giving an alkoxo complex is endergonic by 8.1 kcal/mol, whereas the addition to 2A is exergonic by 8.9 kcal/mol. The thermodynamic difference could be the main reason for PNP-Ir system requiring lower catalyst loading than the PNN-Ru system. We discuss how the differences are resulted in terms of electronic and geometric structures of the catalysts and how to use the features in catalyst development. © 2014 American Chemical Society.

  3. Concentration polarization and desalination in nanochannels: Effect of surface charge dynamics

    Science.gov (United States)

    Andersen, Mathias B.; Bruus, Henrik; Mani, Ali; Bazant, Martin Z.

    2011-11-01

    Mani, Zangle, and Santiago (Langmuir, 25, 3898-3916) have shown that at microchannel-nanochannel junctions the coupled effect of concentration polarization and surface conduction can lead to long range propagation of bulk ion-depletion shocks. Essential for this phenomena is the surface charge which for many materials depends on both the concentration and the pH of the local bulk electrolyte. Standard models predict that the surface charge decreases with decreasing concentration leading to the contradictory expectation that there is little or no surface charge in the depleted region and hence no mechanism to sustain long range propagation of desalination shocks. We show that this simple prediction fails to take into account axial transport terms. As such, we couple a surface charge model with the Poisson-Nernst-Planck equations for electric potential and ionic species combined with the Navier-Stokes and continuity equations for fluid velocity. Motivated by experimental work we consider steady-state solutions at the dead end of a nanochannel against a membrane, a scenario where especially space charge and electroosmotic flow are important. Our results suggest that the surface charge density remains finite and does not vanish, and even grows, as the depletion front propagates through the channel.

  4. Diffuse layer effects on the current in galvanic cells containing supporting electrolyte

    International Nuclear Information System (INIS)

    Soestbergen, M. van

    2010-01-01

    We study the effect of an inert supporting electrolyte on the steady-state ionic current through galvanic cells by solving the full Poisson-Nernst-Planck transport equation coupled to the generalized Frumkin-Butler-Volmer boundary equation for the electrochemical charge transfer at the electrodes. Consequently, the model presented here allows for non-zero space charge densities locally at the electrodes, thus extending the frequently used models based on the local electroneutrality condition by including diffuse layer (DL) effects. This extension is necessary since the DLs determine the ion concentration and electrical field at the reaction planes, which uniquely determine the charge transfer at the electrodes. In this work we present numerical results for systems which contain added inert supporting electrolyte using finite element discretization and compare those with semi-analytical results obtained using singular perturbation theory (limit of negligibly thin DLs). In case of negligibly thin DLs the presence of supporting electrolyte will introduce a limiting current below the classical diffusion-limiting current. Just as for systems without supporting electrolyte, the supporting electrolyte induced limiting current formally does not occur for systems having non-negligibly thin double DLs. For thin, however still finite, double layers this limit can still be seen as a steepening of the polarization curve for current vs. voltage.

  5. A DFT Mechanistic Study on Ethylene Tri- and Tetramerization with Cr/PNP Catalysts: Single versus Double Insertion Pathways.

    Science.gov (United States)

    Britovsek, George J P; McGuinness, David S

    2016-11-14

    The mechanism of ethylene trimerization and tetramerization with a chromium-diphosphinoamine (Cr-PNP) catalyst system has been studied by theoretical (DFT) methods. Two representative ligands have been explored, namely Ph 2 PN(Me)PPh 2 and (o-MeC 6 H 4 ) 2 PN(Me)P(o-MeC 6 H 4 ) 2 . Calculations on the former ligand reveal how a combination of single and double ethylene insertion mechanisms may lead to 1-hexene, 1-octene and the major side products (cyclopentanes and n-alkanes). For the latter ligand, introduction of o-alkyl substitution leads to a more sterically congested active species, which suppresses the available pathways for tetramerization and side product formation. Hence, the high selectivity of o-aryl substituted PNP ligands for trimerization can be rationalized. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  6. Impact of Ge profile on the performance of PNP SiGe HBT on thin film SOI

    Science.gov (United States)

    Misra, Prasanna K.; Qureshi, S.

    2012-10-01

    The pnp SiGe HBT on thin film SOI is investigated with different Ge profiles using 2D numerical simulations in MEDICI. The base current, collector current, DC current gain, AC voltage gain, unity current gain frequency and breakdown voltage is obtained for a 0.09 × 1.0 μm2 pnp SiGe HBT with triangular (0%-30%), trapezoidal (10%- 20%) and box (15%) Ge profiles in the base layer. The results obtained with the Ge profiles, has been analyzed and compared. The Ft BVCEO product for triangular, trapezoidal and box Ge profiles has been found as 190.8, 401, and 359.6 GHzV respectively. The tradeoff between voltage gain and unity current gain frequency for the Ge profiles has been analyzed. The simulation result suggests that the pnp SiGe HBT on thin film SOI with trapezoidal Ge profile is a potential candidate for the high speed complementary bipolar circuits that can be used in high performance mixed signal applications.

  7. 4pnp J=0e-2e autoionizing series of calcium: experimental and theoretical analysis

    International Nuclear Information System (INIS)

    Bolovinos, A.; Luc-Koenig, E.; Assimopoulos, S.; Lyras, A.; Karapanagioti, N.E.; Crete Univ., Iraklion; Charalambidis, D.; Crete Univ., Iraklion; Aymar, M.

    1996-01-01

    The even parity 4pnp J=0, 1, 2 doubly excited autoionizing states of neutral calcium in an atomic beam are investigated by a two-step isolated core excitation (ICE) method using two different combinations of polarization of the laser beams. The different excited energy levels are assigned to nine autoionizing Rydberg series 4p 1/2,3/2 np J=0, 1, 2 for 8≤n≤22. The theoretical interpretation is achieved by a combination of the eigenchannel R-matrix theory and the multichannel quantum defect (MQDT) method. Two, five and six closed interacting channels are introduced for the J=0, J=1 and J=2 series respectively. Theoretical energy level positions, autoionization widths and excitation profiles are compared with the experimental data, confirming the identification of the observed structures and providing evidence of extended mixing between the 4p 1/2 np and 4p 3/2 np series. (orig.). With 9 figs., 3 tabs

  8. Carbon dioxide hydrogenation catalysed by well-defined Mn(i) PNP pincer hydride complexes.

    Science.gov (United States)

    Bertini, Federica; Glatz, Mathias; Gorgas, Nikolaus; Stöger, Berthold; Peruzzini, Maurizio; Veiros, Luis F; Kirchner, Karl; Gonsalvi, Luca

    2017-07-01

    The catalytic reduction of carbon dioxide is of great interest for its potential as a hydrogen storage method and to use carbon dioxide as C-1 feedstock. In an effort to replace expensive noble metal-based catalysts with efficient and cheap earth-abundant counterparts, we report the first example of Mn(i)-catalysed hydrogenation of CO 2 to HCOOH. The hydride Mn(i) catalyst [Mn(PNP NH - i Pr)(H)(CO) 2 ] showed higher stability and activity than its Fe(ii) analogue. TONs up to 10 000 and quantitative yields were obtained after 24 h using DBU as the base at 80 °C and 80 bar total pressure. At catalyst loadings as low as 0.002 mol%, TONs greater than 30 000 could be achieved in the presence of LiOTf as the co-catalyst, which are among the highest activities reported for base-metal catalysed CO 2 hydrogenations to date.

  9. Benzylene-linked [PNP] scaffolds and their cyclometalated zirconium and hafnium complexes.

    Science.gov (United States)

    Sietzen, Malte; Batke, Sonja; Antoni, Patrick W; Wadepohl, Hubert; Ballmann, Joachim

    2017-05-09

    The benzylene-linked [PNP] scaffolds HN(CH 2 -o-C 6 H 4 PPh 2 ) 2 ([A]H) and HN(C 6 H 4 -o-CH 2 PPh 2 ) 2 ([B]H) have been used for the synthesis of zirconium and hafnium complexes. For both ligands, the dimethylamides [A]M(NMe 2 ) 3 ([A]1-M) and [B]M(NMe 2 ) 3 ([B]1-M) were prepared and converted to the iodides [A]MI 3 ([A]2-M) and [B]MI 3 ([B]2-M) (M = Zr, Hf). Starting from these iodides, the corresponding benzyl derivatives [A]MBn 3 ([A]3-M) and [B]MBn 3 ([B]3-M) (M = Zr, Hf) were obtained via reaction with Bn 2 Mg(OEt 2 ) 2 . For zirconium, the benzylic ligand positions in [A]3-Zr and [B]3-Zr were found to cyclometalate readily, which led to the corresponding κ 4 -[PCNP]ZrBn 2 complexes [A]4-Zr and [B]4-Zr. As these complexes failed to hydrogenate cleanly, cyclometalated derivatives with only one alkyl substituent were targeted and the mixed benzyl chlorides κ 4 -[PCNP]MBnCl ([B]5-M, M = Zr, Hf) were obtained in the case of ligand [B]. Upon hydrogenation of [B]5-Zr, the η 6 -tolyl complex [B]Zr(η 6 -C 7 H 8 )Cl ([B]6-Zr) was generated cleanly, but the corresponding hafnium complex [B]5-Hf was found to decompose unselectively in the presence of H 2 . Using a closely related carbazole-based [PNP] ligand, Gade and co-workers have shown recently that zirconium η 6 -arene complexes similar to [B]6-Zr may serve as zirconium(ii) synthons, namely when reacted with 2,6-Dipp-NC (L) or pyridine (py). Both these substrates were shown to react cleanly with [B]6-Zr, which led to the formation of the bis-isocyanide complex [B]ZrCl(L) 2 ([B]7-Zr) and the 2,2'-bipyridine derivative [B]ZrCl(bipy) ([B]8-Zr), respectively. Upon reaction of [B]Zr(η 6 -C 7 H 8 )Cl ([B]6-Zr) with NaBEt 3 H, the cyclometalated derivative κ 4 -[PCNP]Zr(η 6 -C 7 H 8 ) ([B]9-Zr) was isolated. In an attempt to synthesise terminal hydrides, complexes [A]MI 3 ([A]2-M) were treated with KBEt 3 H, which led to the isolation of the cyclometalated hydrido complexes κ 4 -[PCNP]M(H)(κ 3 -Et 3 BH) ([A

  10. Experimental Analysis of Proton-Induced Displacement and Ionization Damage Using Gate-Controlled Lateral PNP Bipolar Transistors

    Science.gov (United States)

    Ball, D. R.; Schrimpf, R. D.; Barnaby, H. J.

    2006-01-01

    The electrical characteristics of proton-irradiated bipolar transistors are affected by ionization damage to the insulating oxide and displacement damage to the semiconductor bulk. While both types of damage degrade the transistor, it is important to understand the mechanisms individually and to be able to analyze them separately. In this paper, a method for analyzing the effects of ionization and displacement damage using gate-controlled lateral PNP bipolar junction transistors is described. This technique allows the effects of oxide charge, surface recombination velocity, and bulk traps to be measured independently.

  11. Mechanistic Studies of Ethylene and α-Olefin Co-oligomerization Catalyzed by Chromium-PNP Complexes.

    Science.gov (United States)

    Do, Loi H; Labinger, Jay A; Bercaw, John E

    2012-07-23

    To explore the possibility of producing a narrow distribution of mid- to long-chain hydrocarbons from ethylene as a chemical feedstock, co-oligomerization of ethylene and linear α-olefins (LAOs) was investigated, using a previously reported chromium complex, [CrCl(3)(PNP(OMe))] (1, where PNP(OMe) = N,N-bis(bis(o-methoxyphenyl)phosphino)methylamine). Activation of 1 by treatment with modified methylaluminoxane (MMAO) in the presence of ethylene and 1-hexene afforded mostly C(6) and C(10) alkene products. The identities of the C(10) isomers, assigned by detailed gas chromatographic and mass spectrometric analyses, strongly support a mechanism that involves five- and seven-membered metallacyclic intermediates comprising of ethylene and LAO units. Using 1-heptene as a mechanistic probe, it was established that 1-hexene formation from ethylene is competitive with formation of ethylene/LAO co-trimers, and that co-trimers derived from one ethylene and two LAO molecules are also generated. Complex 1/MMAO is also capable of converting 1-hexene to C(12) dimers and C(18) trimers, albeit with poor efficiency. The mechanistic implications of these studies are discussed and compared to previous reports of olefin co-trimerization.

  12. A Novel Bis(phosphido)pyridine [PNP] 2− Pincer Ligand and Its Potassium and Bis(dimethylamido)zirconium(IV) Complexes

    KAUST Repository

    Winston, Matthew S.

    2010-12-13

    A novel PNP bis(secondary phosphine)pyridine pincer ligand, 2,6-bis(2-(phenylphosphino)phenyl)pyridine, has been prepared in high yield, and the properties of the doubly deprotonated form as a ligand in K 4(PNP)2(THF)6 and (PNP)Zr(NMe2) 2 have been investigated. The neutral PNP ligand has been isolated as a mixture of noninterconverting diastereomers, due to the presence of two chirogenic phosphorus atoms of the secondary phopshines, but coordination of the dianionic form to potassium and zirconium allows for isolation of a single diastereomer in near-quantitative yield. The structure of a bis(dimethylamido) zirconium(IV) derivative of the bis(phosphido)pyridine ligand and DFT calculations suggest that the phosphides do not π-bond to early transition metals, likely due to geometric strain and possibly orbital size mismatch between phosphorus and zirconium. As a result, the soft phosphides are prone to formation of insoluble oligomers with substantial bridging of the phosphido lone pairs to other zirconium centers. © 2010 American Chemical Society.

  13. Lichenoid mucocutaneous syndrome a variant of para neoplastic pemphigus (PNP following the treatment of follicular non-Hodgkin’s lymphoma with fludarabine

    Directory of Open Access Journals (Sweden)

    Katz J

    2013-05-01

    Full Text Available Background: Paraneoplastic pemphigus (PNP is an autoimmune mucocutaneous disease associated with cancer. Since the original description of the condition, various publications have suggested the presence of a heterogeneous spectrum of paraneoplastic mucocutaneous conditions with clinical features of lichenplanus. Several cases of PNP have been reported following treatment with fludarabine. Methods: We present a case of lichenoid syndrome in a follicular B-cell non-Hodgkin lymphoma (NHL patient after treatment with fludarabine and review 8 additional published cases of fludarabine related PNP. Results: Our case is unique due to the fact that the patient presented with lichenoid features both clinically and microscopically and responded well to rituximab therapy. According to literature, both skin and mucosa (eyes and gastrointestinal tract are involved and symptoms start about 1-2 weeks after exposure to fludarabine. Various immunosuppressive treatments have been employed including high dose steroids. Many of these patients developed complications related to the immunosuppressive therapy such as cytomegalovirus, candidiasis and pneumocystis carinii infection and died from respiratory failure. On the other hand, long-term remissions have also been described. Conclusion: Our case represents an unusual case of fludarabine related to mucocutaneous lichenoid syndrome, a variant of PNP, and in view of the outcome in previously described cases, rituximab may be considered a preferred and safe first line therapy for such complication.

  14. The Arabidopsis thaliana natriuretic peptide AtPNP-A is a systemic regulator of leaf dark respiration and signals via the phloem

    KAUST Repository

    Ruzvidzo, Oziniel

    2011-09-01

    Plant natriuretic peptides (PNPs) belong to a novel class of peptidic signaling molecules that share some structural similarity to the N-terminal domain of expansins and affect physiological processes such as water and ion homeostasis at nano-molar concentrations. Here we show that a recombinant Arabidopsis thaliana PNP (AtPNP-A) rapidly increased the rate of dark respiration in treated leaves after 5 min. In addition, we observed increases in lower leaves, and with a lag time of 10 min, the effect spread to the upper leaves and subsequently (after 15 min) to the opposite leaves. This response signature is indicative of phloem mobility of the signal, a hypothesis that was further strengthened by the fact that cold girdling, which affects phloem but not xylem or apoplastic processes, delayed the long distance AtPNP-A effect. We conclude that locally applied AtPNP-A can induce a phloem-mobile signal that rapidly modifies plant homeostasis in distal parts. © 2011 Elsevier GmbH.

  15. Status of the R+D programme in the field of the heat carrying and heat transfer components of the PNP project

    International Nuclear Information System (INIS)

    Mausbeck, H.; Jansing, W.

    1984-01-01

    The PNP Project (Project Nuclear Process Heat) is described. It covers the status of research and development in the field of heat exchange and heat exchanger components; concept of plant for coal gasification; description of large scale test facilities and its components; and the time schedule for the project development

  16. Synthesis and biodistribution of a novel [{sup 99m}TcN(PNP5)(DMCHDTC)]{sup +} complex as a potential myocardial perfusion imaging agent

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Junbo [Key Laboratory of Radiopharmaceuticals (Beijing Normal University), Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875 (China)], E-mail: zhjunbo@bnu.edu.cn; Song Zhixin; Jinfeng Chu; Wang Xuebin [Key Laboratory of Radiopharmaceuticals (Beijing Normal University), Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875 (China)

    2009-09-15

    The [{sup 99m}TcN(PNP5)(DMCHDTC)]{sup +}(DMCHDTC: 2,3-dimethyl cyclohexyl dithiocarbamate, PNP5:bis(dimethoxypropylphosphinoethyl)ethoxyethylamine) complex was synthesized through a ligand-exchange reaction. The two-step procedure involved the initial reaction of {sup 99m}TcO{sub 4}{sup -} with succinic dihydrazide (SDH) as a donor of nitride nitrogen atom (N{sup 3-}) in the presence of stannous chloride dihydrate as reducing agent and propylenediamine tetraacetic acid (PDTA) as complexant, followed by the addition of the PNP5 ligand and the DMCHDTC ligand. The radiochemical purity (RCP) of the product was over 90% as measured by thin layer chromatography (TLC). No decomposition of the complex at room temperature was observed over a period of 6 h. Its partition coefficient indicated that it was a lipophilic complex. The electrophoresis results showed the complex was cationic. The biodistribution results in mice indicated that [{sup 99m}TcN(PNP5)(DMCHDTC)]{sup +} was significantly retained into the heart. The heart uptake (ID%/g) was 14.47, 12.23 and 8.76 at 5, 30 and 60 min post-injection, respectively. The heart/liver, heart/lung and heart/blood ratios of the complex were 1.24, 3.62 and 23.05 at 60 min post-injection, suggesting it will be a potential myocardial imaging agent.

  17. Basic lay-out, arrangement and design criteria of heat components of the ''nuclear coal gasification prototype plant (PNP)''

    International Nuclear Information System (INIS)

    Pruschek, R.

    1980-01-01

    Since 1975, the companies Bergbau-Forschung GmbH, GHT Gesellschaft fuer Hochtemperaturreaktor-Technik mbH, Hochtemperatur-Reaktorbau GmbH, Kernforschungsanlage Juelich GmbH und Rheinische Braunkohlenwerke AG are working jointly on the Project ''Prototype Plant Nuclear Process Heat (PNP)'', with promotion of the ''Bundesminister fuer Forschung und Technologie'' and of the ''Minister fuer Wirtschaft, Mittelstand und Verkehr des Landes Nordrhein-Westfalen''. The objectives of the project are the development of a high-temperature reactor, with a core outlet temperature of 950 0 C, suitable for various process heat applications, and the development and testing of the appropriate coal gasification technology. The applied gasifications methods comprise endothermal and exothermal reactions. Therefore, various heat transfer components are to be developed. In the context of this Specialists Meeting, only those components will be discussed by which heat is transferred from primary helium to secondary helium or from helium to the working or process fluid

  18. A Logarithmic Response Complementary Metal Oxide Semiconductor Image Sensor with Parasitic P-N-P Bipolar Junction Transistor

    Science.gov (United States)

    Lai, Cheng‑Hsiao; Lai, Liang‑Wei; Chiang, Wen‑Jen; King, Ya‑Chin

    2006-04-01

    Logarithmic-response complementary metal oxide semiconductor (CMOS) active pixel sensors provide a desirable attribute of wide dynamic range even with low supply voltages. In this paper, a log-mode pixel with employing parasitic P-N-P bipolar junction transistor (BJT) to amplify photo-current is investigated and optimized. A new log-mode cell with a calibration transistor is proposed to increase the output voltage swing as well as to reduce the fixed pattern noise. The measurement results demonstrate that, the output voltage swing of this new cell is enhanced by 4× and fixed pattern noise (FPN) of a pixel array can be reduced by 10× comparing to that of a conventional log-mode CMOS active pixel sensor.

  19. Calcium phosphate nanoparticle (CaPNP) for dose-sparing of inactivated whole virus pandemic influenza A (H1N1) 2009 vaccine in mice.

    Science.gov (United States)

    Morçӧl, Tülin; Hurst, Brett L; Tarbet, E Bart

    2017-08-16

    The emergence of pandemic influenza strains, particularly the reemergence of the swine-derived influenza A (H1N1) in 2009, is reaffirmation that influenza viruses are very adaptable and influenza remains as a significant global public health treat. As recommended by the World Health Organization (WHO), the use of adjuvants is an attractive approach to improve vaccine efficacy and allow dose-sparing during an influenza emergency. In this study, we utilized CaPtivate Pharmaceutical's proprietary calcium phosphate nanoparticles (CaPNP) vaccine adjuvant and delivery platform to formulate an inactivated whole virus influenza A/CA/04/2009 (H1N1pdm) vaccine as a potential dose-sparing strategy. We evaluated the relative immunogenicity and the efficacy of the formulation in BALB/c mice following single intramuscularly administration of three different doses (0.3, 1, or 3µg based on HA content) of the vaccine in comparison to non-adjuvanted or alum-adjuvant vaccines. We showed that, addition of CaPNP in vaccine elicited significantly higher hemagglutination inhibition (HAI), virus neutralization (VN), and IgG antibody titers, at all dose levels, relative to the non-adjuvanted vaccine. In addition, the vaccine containing CaPNP provided equal protection with 1/3rd of the antigen dose as compared to the non-adjuvanted or alum-adjuvanted vaccines. Our data provided support to earlier studies indicating that CaPNP is an attractive vaccine adjuvant and delivery system and should play an important role in the development of safe and efficacious dose-sparing vaccines. Our findings also warrant further investigation to validate CaPNP's capacity as an alternative adjuvant to the ones currently licensed for influenza/pandemic influenza vaccination. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. 2D-QSPR/DFT studies of aryl-substituted PNP-Cr-based catalyst systems for highly selective ethylene oligomerization.

    Science.gov (United States)

    Tang, Siyang; Liu, Zhen; Zhan, Xingwen; Cheng, Ruihua; He, Xuelian; Liu, Boping

    2014-03-01

    1-Hexene and 1-octene are important comonomers for the synthesis of high performance polyolefins. Recently, various N-substituted Cr-bis(diphenylphosphino)amine (PNP-Cr) catalysts show the potential as excellent candidates for highly selective ethylene trimerization/tetramerization. In this work, a series of aryl-substituted PNP-Cr catalysts were studied by two-dimensional quantitative structure-property relationship (QSPR) method based on density functional theory (DFT) calculations. The heuristic method (HM) and best multi-linear regression (BMLR) were used to establish the best linear regression models to describe the relationship between selectivities and catalyst structures. Both Cr(I) and Cr(II) active site models for ethylene trimerization/tetramerization were considered. It was found that 1) the relativity and stability of the models were increased by using self-defined descriptors based on DFT calculations; 2) Cr(I)/Cr(III) centers were the most plausible active sites for ethylene trimerization, while Cr(II)/Cr(IV) active sites were most possibly responsible for ethylene tetramerization; and 3) the skeleton structures of the PNP-Cr system with good complanation and symmetry were crucial for achieving excellent catalytic selectivity of 1-octene, while the PNP-Cr backbone with a large steric effect on N atom would benefit ethylene trimerization. Six new PNP ligands with high selectivity toward ethylene trimerization/tetramerization were predicted based on descriptor analysis and the best linear regression models providing a good basis for further development of novel catalyst systems with better performance.

  1. Actinide-pnictide (An-Pn) bonds spanning non-metal, metalloid, and metal combinations (An=U, Th; Pn=P, As, Sb, Bi)

    Energy Technology Data Exchange (ETDEWEB)

    Rookes, Thomas M.; Wildman, Elizabeth P.; Gardner, Benedict M.; Wooles, Ashley J.; Gregson, Matthew; Tuna, Floriana; Liddle, Stephen T. [School of Chemistry, The University of Manchester (United Kingdom); Balazs, Gabor; Scheer, Manfred [Institute of Inorganic Chemistry, University of Regensburg (Germany)

    2018-01-26

    The synthesis and characterisation is presented of the compounds [An(Tren{sup DMBS}){Pn(SiMe_3)_2}] and [An(Tren{sup TIPS}){Pn(SiMe_3)_2}] [Tren{sup DMBS}=N(CH{sub 2}CH{sub 2}NSiMe{sub 2}Bu{sup t}){sub 3}, An=U, Pn=P, As, Sb, Bi; An=Th, Pn=P, As; Tren{sup TIPS}=N(CH{sub 2}CH{sub 2}NSiPr{sup i}{sub 3}){sub 3}, An=U, Pn=P, As, Sb; An=Th, Pn=P, As, Sb]. The U-Sb and Th-Sb moieties are unprecedented examples of any kind of An-Sb molecular bond, and the U-Bi bond is the first two-centre-two-electron (2c-2e) one. The Th-Bi combination was too unstable to isolate, underscoring the fragility of these linkages. However, the U-Bi complex is the heaviest 2c-2e pairing of two elements involving an actinide on a macroscopic scale under ambient conditions, and this is exceeded only by An-An pairings prepared under cryogenic matrix isolation conditions. Thermolysis and photolysis experiments suggest that the U-Pn bonds degrade by homolytic bond cleavage, whereas the more redox-robust thorium compounds engage in an acid-base/dehydrocoupling route. (copyright 2018 The Authors. Published by Wiley-VCH Verlag GmbH and Co. KGaA.)

  2. Unusual non-bifunctional mechanism for Co-PNP complex catalyzed transfer hydrogenation governed by the electronic configuration of metal center.

    Science.gov (United States)

    Hou, Cheng; Jiang, Jingxing; Li, Yinwu; Zhang, Zhihan; Zhao, Cunyuan; Ke, Zhuofeng

    2015-10-07

    The mimic of hydrogenases has unleashed a myriad of bifunctional catalysts, which are widely used in the catalytic hydrogenation of polar multiple bonds. With respect to ancillary ligands, the bifunctional mechanism is generally considered to proceed via the metal-ligand cooperation transition state. Inspired by the interesting study conducted by Hanson et al. (Chem Commun., 2013, 49, 10151), we present a computational study of a distinctive example, where a Co(II)-PNP catalyst with an ancillary ligand exhibits efficient transfer hydrogenation through a non-bifunctional mechanism. Both the bifunctional and non-bifunctional mechanisms are discussed. The calculated results, which are based on a full model of the catalyst, suggest that the inner-sphere non-bifunctional mechanism is more favorable (by ∼11 kcal mol(-1)) than the outer-sphere bifunctional mechanism, which is in agreement with the experimental observations. The origin of this mechanistic preference of the Co(II)-PNP catalyst can be attributed to its preference for the square planar geometry. A traditional bifunctional mechanism is less plausible for Co(II)-PNP due to the high distortion energy caused by the change in electronic configuration with the varied ligand field. Considering previous studies that focus on the development of ligands more often, this computational study indicates that the catalytic hydrogenation mechanism is controlled not only by the structure of the ligand but also by the electronic configuration of the metal center.

  3. Annealing effects and DLTS study on PNP silicon bipolar junction transistors irradiated by 20 MeV Br ions

    Science.gov (United States)

    Liu, Chaoming; Li, Xingji; Yang, Jianqun; Bollmann, Joachim

    2014-01-01

    Isochronal anneal sequences have been carried out on 3CG130 silicon PNP bipolar junction transistors (BJTs) irradiated with 20 MeV bromine (Br) heavy ions. The Gummel curve was utilized to characterize the annealing behavior of defects in both the emitter-base depletion region and the neutral base. The results show that the base current (IB) decreases with the increasing annealing temperature, while the collector current (IC) keeps invariably. The current gain varies slightly, when the annealing temperature (TA) is lower than 500 K, while varies rapidly at TA>550 K, and the current gain of the 3CG130 BJT annealing at 700 K almost restore to that of the pre-radiation transistor. The deep level transient spectroscopy (DLTS) data was used to assign the relative magnitude of each of the important defects. Based on the in situ electrical measurement and DLTS spectra, it is clear that the V2(+/0) trap is the main contribution to the degradation of current gain after the 20 MeV Br ions irradiation. The V2(+/0) peak has many characteristics expected for the current gain degradation.

  4. Annealing effects and DLTS study on PNP silicon bipolar junction transistors irradiated by 20 MeV Br ions

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Chaoming [School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China); Li, Xingji, E-mail: lxj0218@hit.edu.cn [School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China); Yang, Jianqun [School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China); Bollmann, Joachim [Institute of Electronics and Sensor Materials, TU Bergakademie, Freiberg 71691 (Germany)

    2014-01-21

    Isochronal anneal sequences have been carried out on 3CG130 silicon PNP bipolar junction transistors (BJTs) irradiated with 20 MeV bromine (Br) heavy ions. The Gummel curve was utilized to characterize the annealing behavior of defects in both the emitter-base depletion region and the neutral base. The results show that the base current (I{sub B}) decreases with the increasing annealing temperature, while the collector current (I{sub C}) keeps invariably. The current gain varies slightly, when the annealing temperature (T{sub A}) is lower than 500 K, while varies rapidly at T{sub A}>550 K, and the current gain of the 3CG130 BJT annealing at 700 K almost restore to that of the pre-radiation transistor. The deep level transient spectroscopy (DLTS) data was used to assign the relative magnitude of each of the important defects. Based on the in situ electrical measurement and DLTS spectra, it is clear that the V{sub 2}(+/0) trap is the main contribution to the degradation of current gain after the 20 MeV Br ions irradiation. The V{sub 2}(+/0) peak has many characteristics expected for the current gain degradation.

  5. Moderately nonlinear diffuse-charge dynamics under an ac voltage

    Science.gov (United States)

    Stout, Robert F.; Khair, Aditya S.

    2015-09-01

    The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of Vo/(kBT /e ) , where Vo is the amplitude of the driving voltage and kBT /e is the thermal voltage with kB as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D /λDL , where D is the ion diffusivity, λD is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O (Vo3) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in Vo. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing Vo. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

  6. Moderately nonlinear diffuse-charge dynamics under an ac voltage.

    Science.gov (United States)

    Stout, Robert F; Khair, Aditya S

    2015-09-01

    The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

  7. Analyte preconcentration in nanofluidic channels with nonuniform zeta potential

    Science.gov (United States)

    Eden, A.; McCallum, C.; Storey, B. D.; Pennathur, S.; Meinhart, C. D.

    2017-12-01

    It is well known that charged analytes in the presence of nonuniform electric fields concentrate at locations where the relevant driving forces balance, and a wide range of ionic stacking and focusing methods are commonly employed to leverage these physical mechanisms in order to improve signal levels in biosensing applications. In particular, nanofluidic channels with spatially varying conductivity distributions have been shown to provide increased preconcentration of charged analytes due to the existence of a finite electric double layer (EDL), in which electrostatic attraction and repulsion from charged surfaces produce nonuniform transverse ion distributions. In this work, we use numerical simulations to show that one can achieve greater levels of sample accumulation by using field-effect control via wall-embedded electrodes to tailor the surface potential heterogeneity in a nanochannel with overlapped EDLs. In addition to previously demonstrated stacking and focusing mechanisms, we find that the coupling between two-dimensional ion distributions and the axial electric field under overlapped EDL conditions can generate an ion concentration polarization interface in the middle of the channel. Under an applied electric field, this interface can be used to concentrate sample ions between two stationary regions of different surface potential and charge density. Our numerical model uses the Poisson-Nernst-Planck system of equations coupled with the Stokes equation to demonstrate the phenomenon, and we discuss in detail the driving forces behind the predicted sample enhancement. The numerical velocity and salt concentration profiles exhibit good agreement with analytical results from a simplified one-dimensional area-averaged model for several limiting cases, and we show predicted amplification ratios of up to 105.

  8. Spatial profiles of potential, ion concentration and flux in short unipolar and bipolar nanopores.

    Science.gov (United States)

    Tajparast, Mohammad; Virdi, Gautam; Glavinović, Mladen I

    2015-10-01

    During release of vesicular content the resistance of the fusion pore sometimes changes rapidly and repeatedly. However, it is not clear why the pore 'flickers'. Engineered nanopores often rectify, but how different factors influence the rectification requires clarification. To better understand the ionic 'causes' of pore conductivity and its changes we simulated ion transport through a short nanopore using Poisson-Nernst-Planck equations, coupling it to the transport of water using Navier-Stokes equations. We extracted the potential, concentration, and ion flux profiles. In uniformly charged nanopores the voltage bias determines which counter-ion flux dominates, and it is carried by the counter-ions of the highest concentration. In unipolar nanopores this simple rule breaks down. The dominant counter-ion in the charged half is from the adjacent compartment, but the bias determines what counter-ion flux is dominant--the same ion (regular bias), or a different and smaller (reverse bias), and this difference determines the level of rectification. In bipolar nanopores the dominant counter-ions in each half are from the adjacent compartments, and the total ion concentration dips in the middle near the wall. With regular bias the total ion concentration peaks in the pore center; the ions that carry the current through the nanopore start as counter-ions and their fluxes are large. With reverse bias the total concentration dips near the wall and in the center, both dominant ion fluxes through the nanopore start as co-ions and are very small, whereas those starting as counter-ions do not go through. Copyright © 2015 Elsevier B.V. All rights reserved.

  9. Spatial distribution of mechanical forces and ionic flux in electro-kinetic instability near a permselective membrane

    Science.gov (United States)

    Magnico, Pierre

    2018-01-01

    This paper is devoted to the numerical investigation of electro-kinetic instability in a polarization layer next to a cation-exchange membrane. An analysis of some properties of the electro-kinetic instability is followed by a detailed description of the fluid flow structure and of the spatial distribution of the ionic flux. In this aim, the Stokes-Poisson-Nernst-Planck equation set is solved until the Debye length scale. The results show that the potential threshold of the marginal instability and the current density depend on the logarithm of the concentration at the membrane surface. The size of the stable vortices seems to be an increasing function of the potential drop. The fluid motion is induced by the electric force along the maximum concentration in the extended space charge (ESC) region and by the pressure force in the region around the inner edge of the ESC layer. Two spots of kinetic energy are located in the ESC region and between the vortices. The cationic motion, controlled by the electric field and the convection, presents counter-rotating vortices in the stagnation zone located in the fluid ejection region. The anion transport is also characterized by two independent layers which contain counter-rotating vortices. The first one is in contact with the stationary reservoir. In the second layer against the membrane, the convection, and the electric field control, the transversal motion, the Fickian diffusion, and the convection are dominant in the longitudinal direction. Finally, the longitudinal disequilibrium of potential and pressure along the membrane is analyzed.

  10. Numerical modelling of electrochemical polarization around charged metallic particles

    Science.gov (United States)

    Bücker, Matthias; Undorf, Sabine; Flores Orozco, Adrián; Kemna, Andreas

    2017-04-01

    We extend an existing analytical model and carry out numerical simulations to study the polarization process around charged metallic particles immersed in an electrolyte solution. Electro-migration and diffusion processes in the electrolyte are described by the Poisson-Nernst-Planck system of partial differential equations. To model the surface charge density, we consider a time- and frequency-invariant electric potential at the particle surface, which leads to the build-up of a static electrical double layer (EDL). Upon excitation by an external electric field at low frequencies, we observe the superposition of two polarization processes. On the one hand, the induced dipole moment on the metallic particle leads to the accumulation of opposite charges in the electrolyte. This charge polarization corresponds to the long-known response of uncharged metallic particles. On the other hand, the unequal cation and anion concentrations in the EDL give rise to a salinity gradient between the two opposite sides of the metallic particle. The resulting concentration polarization enhances the magnitude of the overall polarization response. Furthermore, we use our numerical model to study the effect of relevant model parameters such as surface charge density and ionic strength of the electrolyte on the resulting spectra of the effective conductivity of the composite model system. Our results do not only give interesting new insight into the time-harmonic variation of electric potential and ion concentrations around charged metallic particle. They are also able to reduce incongruities between earlier model predictions and geophysical field and laboratory measurements. Our model thereby improves the general understanding of IP signatures of metallic particles and represents the next step towards a quantitative interpretation of IP imaging results. Part of this research is funded by the Austrian Federal Ministry of Science, Research and Economy under the Raw Materials Initiative.

  11. A model framework for actuation and sensing of ionic polymer-metal composites: prospective on frequency and shear response through simulation tools

    Science.gov (United States)

    Stalbaum, Tyler; Shen, Qi; Kim, Kwang J.

    2017-04-01

    Ionic polymer-metal composite (IPMC) is a promising material for soft-robotic actuator and sensor applications. This material system offers large deformation response for low input voltage and has an aptitude for operation in hydrated environments. Researchers have been developing IPMC actuators and sensors for applications with examples of self-sensing actuators, artificial fish fins and biomimicry of other aquatic lifeforms, and in medical operations such as in guided catheter devices. IPMCs have been developed in a range of geometric configurations, with tube or cylindrical and flat-plate rectangular as the most common shapes. Several mathematical and physics-based models have been developed for describing the transduction effects of IPMCs. In this work, the underlying theories of electromechanical and mechanoelectrical transduction in IPMCs are discussed, and simulated results of frequency response and shear response are presented. A model backbone is utilized which is primarily based on ion-transport and charge dynamics within the polymer membrane. The electromechanical model, that is with an IPMC as an actuator, is caused when an electric field is applied across the membrane causing ionic migration and swelling in the polymer membrane, which is based on the Poisson-Nernst-Planck equations and solid mechanics models. The mechanoelectric model is similar in underlying physics; however, the primary mechanisms of transduction are of different significance, where anion concentrations are as important as cations. COMSOL Multiphysics is utilized for simulations. Example applications of the modeling framework are presented. The simulated results provide additional support for the underlying physics theories discussed.

  12. Estimating vertical and lateral pressures in periodically structured montmorillonite clay particles

    Directory of Open Access Journals (Sweden)

    Guillermo A. Narsilio

    2010-03-01

    Full Text Available Given a montmorillonitic clay soil at high porosity and saturated by monovalent counterions, we investigate the particle level responses of the clay to different external loadings. As analytical solutions are not possible for complex arrangements of particles, we employ computational micromechanical models (based on the solution of the Poisson-Nernst-Planck equations using the finite element method, to estimate counterion and electrical potential distributions for particles at various angles and distances from one another. We then calculate the disjoining pressures using the Van't Hoff relation and Maxwell stress tensor. As the distance between the clay particles decreases and double-layers overlap, the concentration of counterions in the micropores among clay particles increases. This increase lowers the chemical potential of the pore fluid and creates a chemical potential gradient in the solvent that generates the socalled 'disjoining' or 'osmotic' pressure. Because of this disjoining pressure, particles do not need to contact one another in order to carry an 'effective stress'. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micromechanical modelling of particles.Dada uma argila montmorilonítica de alta porosidade e saturada por counteríons monovalentes, investigamos as respostas da argila ao nível de partículas para diferentes cargas externas. Como soluções analíticas não são possíveis para arranjos complexos de partículas, empregamos modelos computacionais micro-mecânicos (baseados na solução das equações de Poisson-Nernst-Planck, utilizando o método de elementos finitos, para estimar counteríons e distribuições de potencial elétrico para partículas em diversos ângulos e distâncias uma da outra. Nós então calculamos as pressões de separação usando a relação de Van't Hoff e a tensão de cisalhamento de Maxwell. À medida que a

  13. Ligand K-edge XAS, DFT, and TDDFT analysis of pincer linker variations in Rh(i) PNP complexes: reactivity insights from electronic structure.

    Science.gov (United States)

    Lee, Kyounghoon; Wei, Haochuan; Blake, Anastasia V; Donahue, Courtney M; Keith, Jason M; Daly, Scott R

    2016-06-14

    Here we report P K-edge, Cl K-edge, and Rh L3-edge X-ray absorption spectroscopy (XAS) data for Rh[C5H3N-2,6-(XP(t)Bu2)2]Cl, where X = O ((tBu)PONOP; ) or CH2 ((tBu)PNP; ). Solid-state XAS data for and were compared to density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations to identify how changing the PNP pincer linker from O to CH2 affected electronic structure and bonding at Rh(i). Pronounced differences in XAS peak intensities and energies were observed. The P K-edge XAS data revealed a large increase in Rh 4dx(2)-y(2) and P 3p orbital-mixing (Rh-P σ*) in compared to , and pronounced transition energy variations reflected marked differences in orbital energies and compositions. By comparison, the Cl K-edge XAS data revealed only subtle differences in Rh-Cl covalency, although larger splitting between the Rh-Cl π* and σ* transitions was observed in . Analysis of the occupied MOs from DFT (HOMO, HOMO-1, HOMO-2, and HOMO-3) and comparison to the unoccupied MOs involved in XAS revealed a relatively uniform energy increase (ca. 0.3-0.5 eV) for all five 4d-derived molecular orbitals in Rh((tBu)PNP)Cl () compared to Rh((tBu)PONOP)Cl (). The energy shift was relatively invariant with respect to differences in orbital symmetry, bonding type (σ or π), and orbital mixing, which suggested that the increase could be attributed to electrostatic effects. The change in d-orbital energies are consistent with known reactivity differences of Rh((tBu)PONOP)(+) and Rh((tBu)PNP)(+) towards CO, H2, and CH2Cl2, and are explained here by considering how d-orbital energies affect covalent L → M σ bonding and M → L π backbonding.

  14. Crystallization and preliminary X-ray diffraction of the DEAD-box protein Mss116p complexed with an RNA oligonucleotide and AMP-PNP

    Energy Technology Data Exchange (ETDEWEB)

    Del Campo, Mark; Lambowitz, Alan M.; (Texas)

    2009-09-02

    The Saccharomyces cerevisiae DEAD-box protein Mss116p is a general RNA chaperone which functions in mitochondrial group I and group II intron splicing, translation and RNA-end processing. For crystallization trials, full-length Mss116p and a C-terminally truncated protein (Mss116p/{Delta}598-664) were overproduced in Escherichia coli and purified to homogeneity. Mss116p exhibited low solubility in standard solutions ({le}1 mg ml{sup -1}), but its solubility could be increased by adding 50 mM L-arginine plus 50 mM L-glutamate and 50% glycerol to achieve concentrations of {approx}10 mg ml{sup -1}. Initial crystals were obtained by the microbatch method in the presence of a U{sub 10} RNA oligonucleotide and the ATP analog AMP-PNP and were then improved by using seeding and sitting-drop vapor diffusion. A cryocooled crystal of Mss116p/{Delta}598-664 in complex with AMP-PNP and U{sub 10} belonged to space group P2{sub 1}2{sub 1}2, with unit-cell parameters a = 88.54, b = 126.52, c = 55.52 {angstrom}, and diffracted X-rays to beyond 1.9 {angstrom} resolution using synchrotron radiation from sector 21 at the Advanced Photon Source.

  15. Penetration equations

    Energy Technology Data Exchange (ETDEWEB)

    Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)

    1997-10-01

    In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.

  16. Mathematical modeling and simulation of nanopore blocking by precipitation

    KAUST Repository

    Wolfram, M-T

    2010-10-29

    High surface charges of polymer pore walls and applied electric fields can lead to the formation and subsequent dissolution of precipitates in nanopores. These precipitates block the pore, leading to current fluctuations. We present an extended Poisson-Nernst-Planck system which includes chemical reactions of precipitation and dissolution. We discuss the mathematical modeling and present 2D numerical simulations. © 2010 IOP Publishing Ltd.

  17. Concentration polarization, surface currents, and bulk advection in a microchannel

    DEFF Research Database (Denmark)

    Nielsen, Christoffer Peder; Bruus, Henrik

    2014-01-01

    We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behavior of the syst...... as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction....

  18. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  19. Nicotinamide riboside promotes Sir2 silencing and extends lifespan via Nrk and Urh1/Pnp1/Meu1 pathways to NAD+.

    Science.gov (United States)

    Belenky, Peter; Racette, Frances G; Bogan, Katrina L; McClure, Julie M; Smith, Jeffrey S; Brenner, Charles

    2007-05-04

    Although NAD(+) biosynthesis is required for Sir2 functions and replicative lifespan in yeast, alterations in NAD(+) precursors have been reported to accelerate aging but not to extend lifespan. In eukaryotes, nicotinamide riboside is a newly discovered NAD(+) precursor that is converted to nicotinamide mononucleotide by specific nicotinamide riboside kinases, Nrk1 and Nrk2. In this study, we discovered that exogenous nicotinamide riboside promotes Sir2-dependent repression of recombination, improves gene silencing, and extends lifespan without calorie restriction. The mechanism of action of nicotinamide riboside is totally dependent on increased net NAD(+) synthesis through two pathways, the Nrk1 pathway and the Urh1/Pnp1/Meu1 pathway, which is Nrk1 independent. Additionally, the two nicotinamide riboside salvage pathways contribute to NAD(+) metabolism in the absence of nicotinamide-riboside supplementation. Thus, like calorie restriction in the mouse, nicotinamide riboside elevates NAD(+) and increases Sir2 function.

  20. Differential geometry based multiscale models.

    Science.gov (United States)

    Wei, Guo-Wei

    2010-08-01

    Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are

  1. Stochastic partial differential equations

    CERN Document Server

    Chow, Pao-Liu

    2014-01-01

    Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad

  2. P=/=NP Category-Semantics(C-S) TRIVIAL Proof: EUCLID!!! [(So Miscalled) ``Computational''-``Complexity''(CC) Jargonial-Obfuscation(J-O); (Which???)MillenniumED-ProblemED(M-P): NO CC, "CS" Feet of Clay!!!

    Science.gov (United States)

    Siegel, Edward; Clay, London

    2010-10-01

    P=/=NP M-P proof is by C-S J-O elimination! C-S P=(?)=NP MEANS (Deterministic).(P-C)=(?)=(NON-D).(P-C)=(NP). C-S P=(?)=NP MEANS (Deterministic). (P-C)=(?)=(Non-D).(P-C) i.e. D.(P)=(?)= N.(P). For inclusion(equality) vs. exclusion(inequality), ir-relevant(P)simply cancels! (Equally any other CC IF both sides identical). Crucial question left(D)=(?)=(N-D), i.e. D =(?)= N. Algorithmics: Deterministic (D) serial vs. Non-deterministic (N) NON-serial, branch fork forms a triangle, its vertices a plane. Menger Dimension-Theory: Dimensionality: D serial is one-dimensional, dim(D) = 1 (definition), versus N non-serial is > one-dimensional, dim(N) = 2(branching; fork; triangle; plane)+ E(probabilistic)> 2 [Sipser [Intro. to Thy. of Comp., PWS Pub. Co.(1997)-p. 49; Fig. 1.15!!!

  3. On-line monitoring of base current and forward emitter current gain of the voltage regulator's serial pnp transistor in a radiation environment

    Directory of Open Access Journals (Sweden)

    Vukić Vladimir Đ.

    2012-01-01

    Full Text Available A method of on-line monitoring of the low-dropout voltage regulator's operation in a radiation environment is developed in this paper. The method had to enable detection of the circuit's degradation during exploitation, without terminating its operation in an ionizing radiation field. Moreover, it had to enable automatic measurement and data collection, as well as the detection of any considerable degradation, well before the monitored voltage regulator's malfunction. The principal parameters of the voltage regulator's operation that were monitored were the serial pnp transistor's base current and the forward emitter current gain. These parameters were procured indirectly, from the data on the voltage regulator's load and quiescent currents. Since the internal consumption current in moderately and heavily loaded devices was used, the quiescent current of a negligibly loaded voltage regulator of the same type served as a reference. Results acquired by on-line monitoring demonstrated marked agreement with the results acquired from examinations of the voltage regulator's maximum output current and minimum dropout voltage in a radiation environment. The results were particularly consistent in tests with heavily loaded devices. Results obtained for moderately loaded voltage regulators and the risks accompanying the application of the presented method, were also analyzed.

  4. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  5. Anomalies in the equilibrium and nonequilibrium properties of correlated ions in complex molecular environments

    Science.gov (United States)

    Mahakrishnan, Sathiya; Chakraborty, Subrata; Vijay, Amrendra

    2017-11-01

    Emergent statistical attributes, and therefore the equations of state, of an assembly of interacting charge carriers embedded within a complex molecular environment frequently exhibit a variety of anomalies, particularly in the high-density (equivalently, the concentration) regime, which are not well understood, because they do not fall under the low-concentration phenomenologies of Debye-Hückel-Onsager and Poisson-Nernst-Planck, including their variants. To go beyond, we here use physical concepts and mathematical tools from quantum scattering theory, transport theory with the Stosszahlansatz of Boltzmann, and classical electrodynamics (Lorentz gauge) and obtain analytical expressions both for the average and the frequency-wave vector-dependent longitudinal and transverse current densities, diffusion coefficient, and the charge density, and therefore the analytical expressions for (a) the chemical potential, activity coefficient, and the equivalent conductivity for strong electrolytes and (b) the current-voltage characteristics for ion-transport processes in complex molecular environments. Using a method analogous to the notion of Debye length and thence the electrical double layer, we here identify a pair of characteristic length scales (longitudinal and the transverse), which, being wave vector and frequency dependent, manifestly exhibit nontrivial fluctuations in space-time. As a unifying theme, we advance a quantity (inverse length dimension), gscat(a ), which embodies all dynamical interactions, through various quantum scattering lengths, relevant to molecular species a, and the analytical behavior which helps us to rationalize the properties of strong electrolytes, including anomalies, in all concentration regimes. As an example, the behavior of gscat(a ) in the high-concentration regime explains the anomalous increase of the Debye length with concentration, as seen in a recent experiment on electrolyte solutions. We also put forth an extension of the

  6. Influence of ion sterics on diffusiophoresis and electrophoresis in concentrated electrolytes

    Science.gov (United States)

    Stout, Robert F.; Khair, Aditya S.

    2017-01-01

    We quantify the diffusiophoresis and electrophoresis of a uniformly charged, spherical colloid in a binary electrolyte using modified Poisson-Nernst-Planck equations that account for steric repulsion between finite sized ions. Specifically, we utilize the Bikerman (Bik) lattice gas model and the Carnahan-Starling (CS) and Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state for monodisperse and polydisperse, respectively, hard spheres. We compute the phoretic mobility for weak applied fields using an asymptotic approach for thin diffuse layers, where ion steric effects are expected to be most prevalent. The thin diffuse layer limit requires λD/R →0 , where λD is the Debye screening length and R is the particle radius; this limit is readily attained for micron-sized colloids in concentrated electrolytic solutions. It is well known that the classic Poisson-Boltzmann (PB) model for pointlike, noninteracting ions leads to a prediction of a maximum in both the diffusiophoretic and electrophoretic mobilities with increasing particle zeta potential (at fixed λD/R ). In contrast, we find that ion sterics essentially eliminate this maximum (for reasonably attainable zeta potentials) and increase the mobility relative to PB. Next, we consider the more experimentally relevant case of a particle with a constant surface charge density and vary the electrolyte concentration, neglecting charge regulation on surface active sites. Rather surprisingly, there is little difference between the predictions of the four models (PB, Bik, CS, and BMCSL) for electrophoretic mobility in concentrated solutions, at reasonable surface charge densities (˜1 -10 μ C /cm2 ). This is because as the concentration increases, the zeta potential is reduced (to below the thermal voltage for concentrations above about 1 M) and therefore the diffuse layer structure is largely unaffected by ion sterics. For gradients of symmetric electrolytes (equal diffusivities, charge, and size

  7. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  8. "In graafika" + PNP = futurism / Siram

    Index Scriptorium Estoniae

    Siram, pseud., 1968-

    2011-01-01

    8. jaan.-l avati Pärnus rahvusvaheline "In graafika" festival ja Pärnu nüüdismuusika päevad "Futurism". Kunstinäitustest, pikemalt Albert Gulgi, Raul Meele ning Marian Kivila, Sandra Vellevoogi ja Ville-Karel Viirelaiu väljapanekutest, Taje Trossi installatsioonist "Eksperimentaalne instrumentaarium"

  9. Difference equations by differential equation methods

    CERN Document Server

    Hydon, Peter E

    2014-01-01

    Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

  10. El empleo del agente encubierto para la lucha contra la criminalidad en el marco de la política de seguridad ciudadana: análisis de los procedimientos de investigación de la división de investigación de robos de la Dirincri PNP año 2015

    OpenAIRE

    Romero Granda, Carlos Javier

    2017-01-01

    El presente estudio analiza los procedimientos de investigación que se utilizan en la División de Investigación de Robos de la DIRICNRI PNP para investigar los delitos de hurto y robo. Como Hipótesis se planteó la interrogante: ¿Fueron adecuados los procedimientos de investigación utilizados por la División de Investigación de Robos de la DIRINCRI PNP en la ciudad de Lima durante el año 2015 para investigar los delitos patrimoniales?. La respuesta a este planteamiento se realizó a tr...

  11. Handbook of integral equations

    CERN Document Server

    Polyanin, Andrei D

    2008-01-01

    This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

  12. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  13. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  14. Comparison of immittance spectroscopy analyses of ultra-pure and “pure” water in the lower frequency regime

    International Nuclear Information System (INIS)

    Macdonald, J. Ross

    2014-01-01

    Two different analyses of impedance data obtained from ultra-pure water allowed to equilibrate with the atmosphere have recently appeared. They both thus show much smaller low-frequency resistances than does ultra-pure water. Different fitting models were used in these analyses and led to appreciably different parameter estimates from their data fits. Their two “pure” water experimental data sets are here analyzed with a Poisson-Nernst-Planck model that incorporates the possibility of dissociation of a neutral species to positive and negative charges of arbitrary mobilities, anomalous diffusion in the interface region, and reaction of mobile ions at the electrodes. Complex-nonlinear-least-squares fitting of these data sets with either charges of a single sign mobile or with those of both signs mobile showed that the one-mobile choice was far superior to the two-mobile one. These results were compared both with newly calculated theoretical ultra-pure water immittance ones and with the results obtained in the earlier two papers, where different Poisson-Nernst-Planck-related fitting models were employed. Both involved the restrictive assumptions of full dissociation and two-mobile behavior with equal mobilities of the positive and negative charges. The dominant mobile charge species present in the equilibrated “pure” water data sets (protons for the ultra-pure water), involved mobile impurity ions, possibly oxygen ones. The Poisson-Nernst-Planck model used here is simpler than the other models, and it led to better fits of the data sets and to more physically significant parameter estimates than did the earlier fits

  15. Particle methods for Boltzmann equation

    International Nuclear Information System (INIS)

    Hermeline, F.

    1985-05-01

    This work is aimed at showing how to discretize an equation such as Boltzmann equation in its most general form, by particle methods. Then method is applied to some equations of plasma physics which appear as peculiar cases of Boltzmann equation, such as Vlasov equation, Bhatnager-Gross-Krook equation, Fokker-Planck equation and neutron transport equation [fr

  16. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  17. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  18. The Pendulum Equation

    Science.gov (United States)

    Fay, Temple H.

    2002-01-01

    We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

  19. A Comparison of IRT Equating and Beta 4 Equating

    Science.gov (United States)

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    2005-01-01

    Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equi-percentile equating property. True score…

  20. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  1. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  2. Elliptic partial differential equations

    CERN Document Server

    Volpert, Vitaly

    If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...

  3. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  4. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  5. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  6. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  7. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  8. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  9. The 'golden' algebraic equations

    International Nuclear Information System (INIS)

    Stakhov, A.; Rozin, B.

    2006-01-01

    The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman

  10. Ordinary differential equations

    CERN Document Server

    Pontryagin, Lev Semenovich

    1962-01-01

    Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

  11. fractional differential equations

    Indian Academy of Sciences (India)

    We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced.

  12. Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Hannelore Breckner

    2000-01-01

    Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.

  13. dimensional Fokas equation

    Indian Academy of Sciences (India)

    role in converting the Fokas equation into Hirota's bilinear form. Keywords. Bilinearization; multisoliton solution; Fokas equation; Hirota's bilinear method. PACS Nos 05.45.Yv; 04.20.Jb; 02.30.Jr. 1. Introduction. As pointed out by Drazin and Johnson [1], it is not easy to give a comprehensive and precise definition of a soliton.

  14. The Wouthuysen equation

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1995-01-01

    textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an

  15. Elliptic Quadratic Operator Equations

    OpenAIRE

    Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor

    2017-01-01

    In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.

  16. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...

  17. Partial differential equations

    Indian Academy of Sciences (India)

    been a regular stream of high quality work done in these areas. Talking of elliptic partial differen- tial equations, important contributions have been made in the ...... [6] Evans L C 1992 Periodic homogenisation of certain fully nonlinear partial differential equations; Proc. Roy. Soc. Edinburgh Sect. A 120 No. 3–4, 245–265.

  18. Reduced Braginskii equations

    Energy Technology Data Exchange (ETDEWEB)

    Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.

  19. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

  20. Alternative equations of gravitation

    International Nuclear Information System (INIS)

    Pinto Neto, N.

    1983-01-01

    It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt

  1. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  2. Ordinary differential equations

    CERN Document Server

    Ince, Edward Lindsay

    1956-01-01

    The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a diffe

  3. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  4. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  5. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  6. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  7. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  8. Fully nonlinear elliptic equations

    CERN Document Server

    Caffarelli, Luis A

    1995-01-01

    The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa

  9. Partial differential equations

    CERN Document Server

    Friedman, Avner

    2008-01-01

    This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we

  10. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  11. Modern nonlinear equations

    CERN Document Server

    Saaty, Thomas L

    1981-01-01

    Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.

  12. Equations For Rotary Transformers

    Science.gov (United States)

    Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.

    1988-01-01

    Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.

  13. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  14. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  15. Applied partial differential equations

    CERN Document Server

    DuChateau, Paul

    2012-01-01

    Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

  16. dimensional nonlinear evolution equations

    Indian Academy of Sciences (India)

    –. (4)) by applying the exp-function method. The computer symbolic systems such as. Maple and Mathematica allow us to perform complicated and tedious calculations. 2. Solutions of (N + 1)-dimensional generalized Boussinesq equation.

  17. Problems in differential equations

    CERN Document Server

    Brenner, J L

    2013-01-01

    More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

  18. Regularized Structural Equation Modeling

    Science.gov (United States)

    Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.

    2016-01-01

    A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019

  19. Ordinary differential equations.

    Science.gov (United States)

    Lebl, Jiří

    2013-01-01

    In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.

  20. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    continuous medium is μgrav ≡ μ + 3p/c2. Particular versions of this equation had been obtained earlier, at centers of symmetry by Tolman and Synge (see Raychaud- .... (8) by l ˙l and integrate to find. 3( ˙l)2 − κμl2 − Λl2 = const. (10). This is just the Friedmann equation which governs the time evolution of FLRW universe ...

  1. Equations of radiation hydrodynamics

    International Nuclear Information System (INIS)

    Mihalas, D.

    1982-01-01

    The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

  2. Histocompatible chicken inbred lines: homogeneities in the major histocompatibility complex antigens of the GSP, GSN/1, PNP/DO and BM-C inbred lines assessed by hemagglutination, mixed lymphocyte reaction and skin transplantation.

    Science.gov (United States)

    Valdez, Marcos B; Mizutani, Makoto; Fujiwara, Akira; Yazawa, Hajime; Yamagata, Takahiro; Shimada, Kiyoshi; Namikawa, Takao

    2007-10-01

    Chicken inbred lines of the GSP, GSN/1, PNP/DO and BM-C have been established by selection of a specific allele at the B blood group locus (MHC B-G region) and other polymorphic loci through pedigree mating. To extend the potential of these inbred lines as experimental animals in Aves, we assessed the antigenic homogeneities of the MHC antigens by three immunological methods. Antigenic variations of red blood cells (RBCs) were surveyed in the inbred lines and a random-bred line (NG) derived from the Nagoya breed by using ten kinds of intact antisera produced in the inbred line of chickens against RBCs of a red junglefowl and hybrids. In the hemagglutination test, no individual variations were found within the inbred line at all, while all the ten antisera detected highly heterogeneous reactions in individuals of the NG. The reciprocal one-way mixed lymphocyte reactions gave constantly higher stimulation responses (PGSP and GSN/1 inbred lines both having the B(21) allele. In reciprocal skin transplantation, the transplanted skingrafts within the inbred line and between individuals from the GSP and GSN/1 inbred lines survived more than 100 days, while all the skingrafts showed signs of rejection within 7 days among the inbred lines having different B alleles. The results obtained by the three practical methods coincidentally indicated that the individuals in the respective four inbred lines were histocompatible, and further, that the GSP and GSN/1 individuals were histocompatible.

  3. The Bernoulli-Poiseuille Equation.

    Science.gov (United States)

    Badeer, Henry S.; Synolakis, Costas E.

    1989-01-01

    Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)

  4. Soliton multidimensional equations and integrable evolutions preserving Laplace's equation

    International Nuclear Information System (INIS)

    Fokas, A.S.

    2008-01-01

    The KP equation, which is an integrable nonlinear evolution equation in 2+1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the KP equation, I obtain an integrable nonlinear evolution equation in 4+2. The requirement that real initial conditions remain real under this evolution, implies that the dependent variable satisfies a nonlinear evolution equation in 3+1 coupled with Laplace's equation. A reduction of this system of equations to a single equation in 2+1 contains as particular cases certain singular integro-differential equations which appear in the theory of water waves

  5. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  6. Assessment of the best N3− donors in preparation of [M(N)(PNP)]-based (M = 99mTc-; 188Re) target-specific radiopharmaceuticals: Comparison among succinic dihydrazide (SDH), N-methyl-S-methyl dithiocarbazate (HDTCZ) and PEGylated N-methyl-S-methyl dithiocarbazate (HO2C-PEG600-DTCZ)

    International Nuclear Information System (INIS)

    Carta, Davide; Jentschel, Christian; Thieme, Stefan; Salvarese, Nicola; Morellato, Nicolò; Refosco, Fiorenzo; Ruzza, Paolo; Bergmann, Ralf; Pietzsch, Hans-Jurgen; Bolzati, Cristina

    2014-01-01

    Succinic dihydrazide (SDH), N-methyl-S-methyl dithiocarbazate (HDTCZ) and PEGylated N-methyl-S-methyl dithiocarbazate (HO 2 C-PEG 600 -DTCZ) are nitrido nitrogen atom donors employed for the preparation of nitride [M(N)]‐complexes (M = 99m Tc and 188 Re). This study aims to compare the capability and the efficiency of these three N 3− group donors, in the preparation of [M(N)PNP]-based target-specific compounds (M = 99m Tc, 188 Re; PNP = aminodiphosphine). For this purpose, three different kit formulations (SDH kit; HO 2 C-PEG 600 -DTCZ kit; HDTCZ kit) were assembled and used in the preparation of [M(N)(cys ∼)(PNP3)] 0/+ complexes (cys ∼ = cysteine derivate ligands). For each formulation, the radiochemical yield (RCY) of the [M(N)(∼ cys)(PNP3)] compounds, was determined by HPLC. The deviation of the percentage of RCY, due to changes in concentration of the N 3− donors and of the exchanging ligand, was determined. For 99m Tc, data clearly show that HDTCZ is the most efficient donor of N 3− ; however, SDH is the most suitable nitrido nitrogen atom donor for the preparation of [ 99m Tc(N)(PNP)]-based target-specific agents with high specific activity. When HO 2 C-PEG 600 -DTCZ or HDTCZ are used in N 3− donation, high amounts of the exchanging ligand (10 −4 M) were required for the formation of the final complex in acceptable yield. The possibility to use microgram amounts of HDTCZ also in [ 188 Re(N)] preparation (0.050 mg) reduces its ability to compete in ligand exchange reactions, minimizing the quantity of chelators required to obtain the final complex in high yield. This finding can be exploit for increasing the radiolabeling efficiency in [ 188 Re(N)]-radiopharmaceutical preparations compared to the previously reported HDTCZ-based procedure, notwithstanding a purification process could be necessary to improve the specific activity of the complexes

  7. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  8. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  9. Stochastic porous media equations

    CERN Document Server

    Barbu, Viorel; Röckner, Michael

    2016-01-01

    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  10. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  11. Partial differential equations

    CERN Document Server

    Agranovich, M S

    2002-01-01

    Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener

  12. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2002-01-01

    Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

  13. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  14. Systematic Equation Formulation

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2007-01-01

    A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

  15. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  16. Conservation laws for equations related to soil water equations

    OpenAIRE

    C. M. Khalique; F. M. Mahomed

    2005-01-01

    We obtain all nontrivial conservation laws for a class of ( 2+1 ) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.

  17. Conservation laws for equations related to soil water equations

    Directory of Open Access Journals (Sweden)

    Khalique C. M.

    2005-01-01

    Full Text Available We obtain all nontrivial conservation laws for a class of ( 2+1 nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.

  18. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the ...

  19. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian ...

  20. Model Compaction Equation

    African Journals Online (AJOL)

    Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...

  1. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2013-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

  2. The Freudenstein Equation

    Indian Academy of Sciences (India)

    Design of Four-Link Mechanisms. Ashitava Ghosal. Ashitava Ghosal is a. Professor in the Depart- ment of Mechanical. Engineering and Centre for Product Design, IISc,. Bangalore. His research interests are in the areas of analysis and design of mechanisms and ... Freudenstein's thesis and the equation named af- ter him.

  3. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    Amalkumar Raychaudhuri's remarkable paper [1] for the first time gave a general derivation of the fundamental equation of gravitational attraction for pressure- free matter, showing the repulsive nature of a positive cosmological constant, and underlying the basic singularity theorem (see below). He used special coordinates.

  4. Solving Equations Applet Project

    OpenAIRE

    Thatcher, Kimberly

    2011-01-01

    The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.

  5. Differential Equations as Actions

    DEFF Research Database (Denmark)

    Ronkko, Mauno; Ravn, Anders P.

    1997-01-01

    We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...

  6. Stochastic nonlinear beam equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan

    2005-01-01

    Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005

  7. A Quadratic Spring Equation

    Science.gov (United States)

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  8. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    Department of Civil Engineering. University of Nigeria Nsukka. ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak.

  9. The Freudenstein Equation

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 8. The Freudenstein Equation - Design of Four-Link Mechanisms. Ashitava Ghosal. General Article Volume 15 Issue 8 August 2010 pp 699-710. Fulltext. Click here to view fulltext PDF. Permanent link:

  10. Equational binary decision diagrams

    NARCIS (Netherlands)

    J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)

    2000-01-01

    textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and

  11. An invariance of CDF equation

    International Nuclear Information System (INIS)

    Tian Chou.

    1991-05-01

    It is important but difficult to find the invariant groups for the differential equations. We found a new invariant group for the MKdV equation. In this paper, we present a new invariance for the CDF equation. By using this invariance, we obtain some new solutions of CDF equation. (author). 5 refs

  12. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  13. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  14. Anticipated backward stochastic differential equations

    OpenAIRE

    Peng, Shige; Yang, Zhe

    2007-01-01

    In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.

  15. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  16. Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids.

    Science.gov (United States)

    Eisenberg, Bob; Hyon, Yunkyong; Liu, Chun

    2010-09-14

    component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

  17. Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

    Science.gov (United States)

    Eisenberg, Bob; Hyon, YunKyong; Liu, Chun

    2010-09-01

    component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

  18. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  19. Classical Diophantine equations

    CERN Document Server

    1993-01-01

    The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...

  20. Energy master equation

    DEFF Research Database (Denmark)

    Dyre, Jeppe

    1995-01-01

    energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model—the energy master equation...... (EME)—is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...

  1. Damped nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Nicholson, D.R.; Goldman, M.V.

    1976-01-01

    High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time

  2. Differential equations with Mathematica

    CERN Document Server

    Abell, Martha L

    2004-01-01

    The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica

  3. Fun with Differential Equations

    Indian Academy of Sciences (India)

    IAS Admin

    tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...

  4. Generalized reduced MHD equations

    International Nuclear Information System (INIS)

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

  5. Mathematics and Maxwell's equations

    International Nuclear Information System (INIS)

    Boozer, Allen H

    2010-01-01

    The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.

  6. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  7. Equations of the mixed type

    CERN Document Server

    Bitsadze, A V

    1963-01-01

    Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab

  8. Ordinary differential equations

    CERN Document Server

    Cox, William

    1995-01-01

    Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further

  9. Partial differential equations

    CERN Document Server

    Sloan, D; Süli, E

    2001-01-01

    /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in

  10. Elliptic partial differential equations

    CERN Document Server

    Han, Qing

    2011-01-01

    Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

  11. Hyperbolic partial differential equations

    CERN Document Server

    Lax, Peter D

    2006-01-01

    The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti

  12. Partial differential equations

    CERN Document Server

    Levine, Harold

    1997-01-01

    The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.

  13. Nonelliptic Partial Differential Equations

    CERN Document Server

    Tartakoff, David S

    2011-01-01

    This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this tec

  14. Kuznetsov equation with variable coefficients

    Indian Academy of Sciences (India)

    like solutions of the PDE in (2+1) dimension with variable coefficients. ... Shivamoggi [12] gives only four polynomial conservation laws of the ZK equation ..... [3] P J Olver, Application of Lie group to differential equation (Springer, New York,.

  15. Conservational PDF Equations of Turbulence

    Science.gov (United States)

    Shih, Tsan-Hsing; Liu, Nan-Suey

    2010-01-01

    Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

  16. Functional equations for Feynman integrals

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    2011-01-01

    New types of equations for Feynman integrals are found. It is shown that Feynman integrals satisfy functional equations connecting integrals with different kinematics. A regular method is proposed for obtaining such relations. The derivation of functional equations for one-loop two-, three- and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains

  17. Classical solutions of quasielliptic equations

    International Nuclear Information System (INIS)

    Belonosov, V S

    1999-01-01

    Fundamental solutions of quasielliptic equations are constructed; this allows the author to develop a relevant theory of volume potentials, establish estimates for the Holder norms of solutions of equations with constant coefficients, and extend them after that to equations with variable coefficients. As a result, sharp Schauder-type interior estimates are obtained, of which the well-known classical results for elliptic and parabolic equations are special cases

  18. Solution of Finite Element Equations

    DEFF Research Database (Denmark)

    Krenk, Steen

    An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....

  19. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity; loop quantum cosmology. PACS Nos 04.20.Jb; 04.2 ...

  20. Successfully Transitioning to Linear Equations

    Science.gov (United States)

    Colton, Connie; Smith, Wendy M.

    2014-01-01

    The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

  1. Equation with the many fathers

    DEFF Research Database (Denmark)

    Kragh, Helge

    1984-01-01

    In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...

  2. Completely integrable operator evolutionary equations

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)

  3. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...

  4. Physics Nobel Prize (PNP in 2008

    Directory of Open Access Journals (Sweden)

    José Maria Filardo Bassalo

    2009-08-01

    Full Text Available In this article we will talk about the Nobel Prize in Physics 2008, granted  to  the Japanese  physicists  Yoichiro  Nambu,  Makoto Kobayashi and Toshihide Maskawa,  for  their  discovery  of  the mechanisms involving strong interactions symmetries (quiral, by Nambu, and in weak interactions (charge-parity, by Kobayashi and Maskawa.

  5. Reduction of infinite dimensional equations

    Directory of Open Access Journals (Sweden)

    Zhongding Li

    2006-02-01

    Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

  6. Discovering evolution equations with applications

    CERN Document Server

    McKibben, Mark

    2011-01-01

    Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast

  7. On the helix equation

    Directory of Open Access Journals (Sweden)

    Taouil Hajer

    2012-08-01

    Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ;   H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ;   H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.

  8. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  9. Generalized quantal equation of motion

    International Nuclear Information System (INIS)

    Morsy, M.W.; Embaby, M.

    1986-07-01

    In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)

  10. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2015-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789

  11. Elliptic scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)

    2016-06-16

    Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.

  12. Λ scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)

    2016-06-17

    The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.

  13. Scaling of differential equations

    CERN Document Server

    Langtangen, Hans Petter

    2016-01-01

    The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...

  14. Differential equations with involutions

    CERN Document Server

    Cabada, Alberto

    2015-01-01

    This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

  15. Parabolized stability equations

    Science.gov (United States)

    Herbert, Thorwald

    1994-01-01

    The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.

  16. Mode decomposition evolution equations.

    Science.gov (United States)

    Wang, Yang; Wei, Guo-Wei; Yang, Siyang

    2012-03-01

    Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be

  17. Integral equations and their applications

    CERN Document Server

    Rahman, M

    2007-01-01

    For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...

  18. Differential equations methods and applications

    CERN Document Server

    Said-Houari, Belkacem

    2015-01-01

    This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .

  19. Introduction to partial differential equations

    CERN Document Server

    Borthwick, David

    2016-01-01

    This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

  20. Equations Holding in Hilbert Lattices

    Science.gov (United States)

    Mayet, René

    2006-07-01

    We produce and study several sequences of equations, in the language of orthomodular lattices, which hold in the ortholattice of closed subspaces of any classical Hilbert space, but not in all orthomodular lattices. Most of these equations hold in any orthomodular lattice admitting a strong set of states whose values are in a real Hilbert space. For some of these equations, we give conditions under which they hold in the ortholattice of closed subspaces of a generalised Hilbert space. These conditions are relative to the dimension of the Hilbert space and to the characteristic of its division ring of scalars. In some cases, we show that these equations cannot be deduced from the already known equations, and we study their mutual independence. To conclude, we suggest a new method for obtaining such equations, using the tensorial product.

  1. Stochastic partial differential equations

    CERN Document Server

    Lototsky, Sergey V

    2017-01-01

    Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...

  2. JWL Equation of State

    Energy Technology Data Exchange (ETDEWEB)

    Menikoff, Ralph [Los Alamos National Laboratory

    2015-12-15

    The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.

  3. Hyperbolic Methods for Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Reula Oscar

    1998-01-01

    Full Text Available I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.

  4. The generalized Airy diffusion equation

    Directory of Open Access Journals (Sweden)

    Frank M. Cholewinski

    2003-08-01

    Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

  5. Correct Linearization of Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2006-06-01

    Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

  6. Half-linear differential equations

    CERN Document Server

    Dosly, Ondrej

    2005-01-01

    The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and var

  7. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  8. Equations of motion for cross term modified gravitational field equations

    Energy Technology Data Exchange (ETDEWEB)

    Mueller, V. (Akademie der Wissenschaften der DDR, Potsdam-Babelsberg. Zentralinstitut fuer Astrophysik)

    1982-01-01

    As proposed by Treder, possible consequences of a unitary field theory may be described phenomenologically by additional cross terms in Einstein's equations. The violation of the weak principle of equivalence and potential observable effects are discussed in deriving hydrodynamic EIH equations. Conclusions on gravitational instabilities follow in the quasistatic approximation.

  9. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  10. Solutions to Arithmetic Convolution Equations

    Czech Academy of Sciences Publication Activity Database

    Glöckner, H.; Lucht, L.G.; Porubský, Štefan

    2007-01-01

    Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007

  11. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  12. Averaging of multivalued differential equations

    Directory of Open Access Journals (Sweden)

    G. Grammel

    2003-04-01

    Full Text Available Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of order O(ϵ1/3 as ϵ→0.

  13. Fractals and the Kepler equation

    Science.gov (United States)

    Kasten, Volker

    1992-09-01

    The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.

  14. Enclosing Solutions of Integral Equations

    DEFF Research Database (Denmark)

    Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole

    1996-01-01

    We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...

  15. On asymptotics for difference equations

    NARCIS (Netherlands)

    Rafei, M.

    2012-01-01

    In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the

  16. Students' Understanding of Quadratic Equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  17. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    An example of the soci- etal impact of the famous equation can be discerned in a .... gaseous state and they behaved like a dilute classical gas, as in. Maxwell's kinetic theory. That is to say, the atoms do .... the Sackur–Tetrode equation for the entropy of an ideal gas at high temperatures, that Saha was quite aware of [13].

  18. Higher order equations of motion

    International Nuclear Information System (INIS)

    Bollini, C.G.; Giambiagi, J.J.

    1989-01-01

    The possibility that the motion of elementary particles be described by higher order differential equations induced by supersymmetry in higher dimensional space-time is discussed. The specific example of six dimensions writing the corresponding Lagrangian and equations of motion, is presented. (author) [pt

  19. Solving equations by topological methods

    Directory of Open Access Journals (Sweden)

    Lech Górniewicz

    2005-01-01

    Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

  20. The relativistic electron wave equation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1977-08-01

    The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

  1. Discovering Evolution Equations with Applications, 1 Deterministic Equations

    CERN Document Server

    McKibben, Mark A

    2010-01-01

    Most books written on evolution equations either provide a thorough in-depth treatment of a particular class of equations for beginners or present an assimilation of materials devoted to a very particular timely research direction. This volume offers an engaging, accessible account of a rudimentary core of theoretical results that should be understood by anyone studying evolution equations. The text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. The author's conversational style sets the stage for the next step of theoretical deve

  2. Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

    Science.gov (United States)

    Ozdemir, Burhanettin

    2017-01-01

    The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

  3. Neoclassical MHD equations for tokamaks

    International Nuclear Information System (INIS)

    Callen, J.D.; Shaing, K.C.

    1986-03-01

    The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

  4. Stochastic differential equations, backward SDEs, partial differential equations

    CERN Document Server

    Pardoux, Etienne

    2014-01-01

    This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...

  5. Fractional delayed damped Mathieu equation

    Science.gov (United States)

    Mesbahi, Afshin; Haeri, Mohammad; Nazari, Morad; Butcher, Eric A.

    2015-03-01

    This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system.

  6. Soliton equations and pseudospherical surfaces

    International Nuclear Information System (INIS)

    Sasaki, R.

    1979-03-01

    All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)

  7. Galois theory of difference equations

    CERN Document Server

    Put, Marius

    1997-01-01

    This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

  8. Soliton equations and Hamiltonian systems

    CERN Document Server

    Dickey, L A

    2002-01-01

    The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

  9. Integral equation methods for electromagnetics

    CERN Document Server

    Volakis, John

    2012-01-01

    This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo

  10. Elliptic Yang-Mills equation.

    Science.gov (United States)

    Tian, Gang

    2002-11-26

    We discuss some recent progress on the regularity theory of the elliptic Yang-Mills equation. We start with some basic properties of the elliptic Yang-Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang-Mills connections and compactness theorems on Yang-Mills connections with bounded L(2) norm of curvature. We also discuss in some detail self-dual solutions of the Yang-Mills equation and describe a compactification of their moduli space.

  11. Elliptic Yang–Mills equation

    OpenAIRE

    Tian, Gang

    2002-01-01

    We discuss some recent progress on the regularity theory of the elliptic Yang–Mills equation. We start with some basic properties of the elliptic Yang–Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang–Mills connections and compactness theorems on Yang–Mills connections with bounded L2 norm of curvature. We also discuss in some detail self-dual solutions of the Yang–Mills equation and describe a compactification of the...

  12. Lectures on ordinary differential equations

    CERN Document Server

    Hurewicz, Witold

    1958-01-01

    Hailed by The American Mathematical Monthly as ""a rigorous and lively introduction,"" this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown funct

  13. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  14. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  15. Direct 'delay' reductions of the Toda equation

    International Nuclear Information System (INIS)

    Joshi, Nalini

    2009-01-01

    A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated with this equation is obtained, also by reduction. (fast track communication)

  16. Analytical Solution of Mathieu Equation

    OpenAIRE

    Yerchuck, Dmitri; Dovlatova, Alla; Yerchak, Yauhen; Borovik, Felix

    2014-01-01

    The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.

  17. Kinks and the Dirac equation

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

    In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)

  18. Saha equation in Rindler space

    Indian Academy of Sciences (India)

    The Saha equations for the photoionization process of hydrogen atoms and the creation of electron–positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion. It is known as the Rindler space.

  19. An Investigation on Quadratic Equations.

    Science.gov (United States)

    Hirst, Keith

    1988-01-01

    Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)

  20. Solutions of Nonlocal -Laplacian Equations

    Directory of Open Access Journals (Sweden)

    Mustafa Avci

    2013-01-01

    Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

  1. The quasilinear parabolic kirchhoff equation

    Directory of Open Access Journals (Sweden)

    Dawidowski Łukasz

    2017-04-01

    Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.

  2. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    2015-11-27

    Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quantum gravity; loop quantum cosmology. ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag ...

  3. Geophysical interpretation using integral equations

    CERN Document Server

    Eskola, L

    1992-01-01

    Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu­ med to have a back...

  4. Synthesis and structural characterization of the Zintl phases Na{sub 3}Ca{sub 3}TrPn{sub 4}, Na{sub 3}Sr{sub 3}TrPn{sub 4}, and Na{sub 3}Eu{sub 3}TrPn{sub 4} (Tr=Al, Ga, In; Pn=P, As, Sb)

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yi [Department of Chemistry & Biochemistry, University of Delaware, 304A Drake Hall, Newark, DE 19716 (United States); Suen, Nian-Tzu [Department of Chemistry & Biochemistry, University of Delaware, 304A Drake Hall, Newark, DE 19716 (United States); College of Chemistry and Chemical Engineering, Yangzhou University, Yangzhou 225002 (China); Kunene, Thabiso; Stoyko, Stanislav [Department of Chemistry & Biochemistry, University of Delaware, 304A Drake Hall, Newark, DE 19716 (United States); Bobev, Svilen, E-mail: bobev@udel.edu [Department of Chemistry & Biochemistry, University of Delaware, 304A Drake Hall, Newark, DE 19716 (United States)

    2017-05-15

    15 new quaternary Zintl phases have been synthesized by solid-state reactions from the respective elements, and their structures have been determined by single-crystal X-ray diffraction. Na{sub 3}E{sub 3}TrPn{sub 4} (E=Ca, Sr, Eu; Tr=Al, Ga, In; Pn=P, As, Sb) crystallize in the hexagonal crystal system with the non-centrosymmetric space group P6{sub 3}mc (No. 186). The structure represents a variant of the K{sub 6}HgS{sub 4} structure type (Pearson index hP22) and features [TrPn{sub 4}]{sup 9–} tetrahedral units, surrounded by Na{sup +} and Ca{sup 2+}, Sr{sup 2+}, Eu{sup 2+} cations. The nominal formula rationalization [Na{sup +}]{sub 3}[E{sup 2+}]{sub 3}[TrPn{sub 4}]{sup 9–} follows the octet rule, suggesting closed-shell configurations for all atoms and intrinsic semiconducting behavior. However, structure refinements for several members hint at disorder and mixing of cations that potentially counteract the optimal valence electron count. - Graphical abstract: The hexagonal, non-centrosymmetric structure of Na{sub 3}E{sub 3}TrPn{sub 4} (E=Ca, Sr, Eu; Tr=Al, Ga, In; Pn=P, As, Sb) features [TrPn{sub 4}]{sup 9–} tetrahedral units, surrounded by Na{sup +} and Ca{sup 2+}, Sr{sup 2+}, Eu{sup 2+} cations. - Highlights: • 15 quaternary phosphides, arsenides, and antimonides are synthesized and structurally characterized. • The structure is a variant of the hexagonal K{sub 6}HgS{sub 4}-type, with distinctive pattern for the cations. • Occupational and/or positional disorder of yet unknown origin exists for some members of the series.

  5. Hidden Statistics of Schroedinger Equation

    Science.gov (United States)

    Zak, Michail

    2011-01-01

    Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

  6. Wave equations for pulse propagation

    Energy Technology Data Exchange (ETDEWEB)

    Shore, B.W.

    1987-06-24

    Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.

  7. Geometrical Solutions of Quadratic Equations.

    Science.gov (United States)

    Grewal, A. S.; Godloza, L.

    1999-01-01

    Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

  8. Feynman integrals and difference equations

    International Nuclear Information System (INIS)

    Moch, S.; Schneider, C.

    2007-09-01

    We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

  9. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  10. Equationally Compact Acts : Coproducts / Peeter Normak

    Index Scriptorium Estoniae

    Normak, Peeter

    1998-01-01

    In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact

  11. The soil moisture velocity equation

    Science.gov (United States)

    Ogden, Fred L.; Allen, Myron B.; Lai, Wencong; Zhu, Jianting; Seo, Mookwon; Douglas, Craig C.; Talbot, Cary A.

    2017-06-01

    Numerical solution of the one-dimensional Richards' equation is the recommended method for coupling groundwater to the atmosphere through the vadose zone in hyperresolution Earth system models, but requires fine spatial discretization, is computationally expensive, and may not converge due to mathematical degeneracy or when sharp wetting fronts occur. We transformed the one-dimensional Richards' equation into a new equation that describes the velocity of moisture content values in an unsaturated soil under the actions of capillarity and gravity. We call this new equation the Soil Moisture Velocity Equation (SMVE). The SMVE consists of two terms: an advection-like term that accounts for gravity and the integrated capillary drive of the wetting front, and a diffusion-like term that describes the flux due to the shape of the wetting front capillarity profile divided by the vertical gradient of the capillary pressure head. The SMVE advection-like term can be converted to a relatively easy to solve ordinary differential equation (ODE) using the method of lines and solved using a finite moisture-content discretization. Comparing against analytical solutions of Richards' equation shows that the SMVE advection-like term is >99% accurate for calculating infiltration fluxes neglecting the diffusion-like term. The ODE solution of the SMVE advection-like term is accurate, computationally efficient and reliable for calculating one-dimensional vadose zone fluxes in Earth system and large-scale coupled models of land-atmosphere interaction. It is also well suited for use in inverse problems such as when repeat remote sensing observations are used to infer soil hydraulic properties or soil moisture.type="synopsis">type="main">Plain Language SummarySince its original publication in 1922, the so-called Richards' equation has been the only rigorous way to couple groundwater to the land surface through the unsaturated zone that lies between the water table and land surface. The soil

  12. Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

    International Nuclear Information System (INIS)

    Hendriks, E.M.

    1983-01-01

    Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

  13. Approximations of Stochastic Partial Differential Equations

    OpenAIRE

    Di Nunno, Giulia; Zhang, Tusheng

    2014-01-01

    In this paper we show that solutions of stochastic partial differ- ential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.

  14. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  15. Abstract methods in partial differential equations

    CERN Document Server

    Carroll, Robert W

    2012-01-01

    Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.

  16. How to obtain the covariant form of Maxwell's equations from the continuity equation

    International Nuclear Information System (INIS)

    Heras, Jose A

    2009-01-01

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

  17. Extraction of dynamical equations from chaotic data

    International Nuclear Information System (INIS)

    Rowlands, G.; Sprott, J.C.

    1991-02-01

    A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs

  18. First-order partial differential equations

    CERN Document Server

    Rhee, Hyun-Ku; Amundson, Neal R

    2001-01-01

    This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

  19. Hypergeometric solutions to Schr\\"odinger equations for the quantum Painlev\\'e equations

    OpenAIRE

    Nagoya, Hajime

    2011-01-01

    We consider Schr\\"odinger equations for the quantum Painlev\\'e equations. We present hypergeometric solutions of the Schr\\"odinger equations for the quantum Painlev\\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\\"odinger equations for the quantum Painlev\\'e equations and those of the KZ equation or the confluent KZ equations.

  20. Investigating anomalous transport of electrolytes in charged porous media

    Science.gov (United States)

    Skjøde Bolet, Asger Johannes; Mathiesen, Joachim

    2017-04-01

    Surface charge is know to play an important role in microfluidics devices when dealing with electrolytes and their transport properties. Similarly, surface charge could play a role for transport in porous rock with submicron pore sizes. Estimates of the streaming potentials and electro osmotic are mostly considered in simple geometries both using analytic and numerical tools, however it is unclear at present how realistic complex geometries will modify the dynamics. Our work have focused on doing numerical studies of the full three-dimensional Stokes-Poisson-Nernst-Planck problem for electrolyte transport in porous rock. As the numerical implementation, we have used a finite element solver made using the FEniCS project code base, which can both solve for a steady state configuration and the full transient. In the presentation, we will show our results on anomalous transport due to electro kinetic effects such as the streaming potential or the electro osmotic effect.

  1. Students' understanding of quadratic equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  2. Integration of quantum hydrodynamical equation

    Science.gov (United States)

    Ulyanova, Vera G.; Sanin, Andrey L.

    2007-04-01

    Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.

  3. Dynamics of partial differential equations

    CERN Document Server

    Wayne, C Eugene

    2015-01-01

    This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation.   The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...

  4. Introductory course on differential equations

    CERN Document Server

    Gorain, Ganesh C

    2014-01-01

    Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.

  5. Integration rules for scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center,Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)

    2015-09-21

    As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.

  6. Numerical integration of variational equations.

    Science.gov (United States)

    Skokos, Ch; Gerlach, E

    2010-09-01

    We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing well-known properties of chaos indicators such as the Lyapunov characteristic exponents and the generalized alignment indices. We find that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton equations of motion by the repeated action of a symplectic map S , while the corresponding tangent map TS is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.

  7. Integration rules for scattering equations

    International Nuclear Information System (INIS)

    Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.

    2015-01-01

    As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.

  8. The respiratory system in equations

    CERN Document Server

    Maury, Bertrand

    2013-01-01

    The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

  9. Quantum Gross-Pitaevskii Equation

    Directory of Open Access Journals (Sweden)

    Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

    2017-07-01

    Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

  10. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    (G /G)-expansion method for finding exact travelling wave solutions of Higgs field equa- tion. Section 3.2 is devoted to find travelling wave solutions of Hamiltonian amplitude equation. In §4, some conclusions are given. 2. Lie symmetry analysis. Lie's method [8–10] is an effective method and is the simplest among group ...

  11. FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

    African Journals Online (AJOL)

    eobe

    rived equation based on the concept of specific resistance, was used to i was used to i drying bed as a slud ... the sludge, it was observed that the specific resistance decreases with incr ng results: D ng results: Dosage increase of 10g, ..... Assessment of the Suitability of Anaerobic Digestion. Effluent for Direct Application as ...

  12. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs field equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...

  13. Stability theory of differential equations

    CERN Document Server

    Bellman, Richard Ernest

    1953-01-01

    Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from

  14. Fundamentals of equations of state

    CERN Document Server

    Eliezer, Shalom; Hora, Heinrich

    2002-01-01

    The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg

  15. Nielsen number and differential equations

    Directory of Open Access Journals (Sweden)

    Andres Jan

    2005-01-01

    Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.

  16. The nuclear equation of state

    International Nuclear Information System (INIS)

    Kahana, S.

    1986-01-01

    The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab

  17. The nuclear equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Kahana, S.

    1986-01-01

    The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.

  18. Applied analysis and differential equations

    CERN Document Server

    Cârj, Ovidiu

    2007-01-01

    This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.

  19. Group analysis of differential equations

    CERN Document Server

    Ovsiannikov, L V

    1982-01-01

    Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g

  20. Partial differential equations an introduction

    CERN Document Server

    Colton, David

    2004-01-01

    Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of

  1. Basic linear partial differential equations

    CERN Document Server

    Treves, Francois

    1975-01-01

    Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their

  2. Einstein Equations from Varying Complexity

    Science.gov (United States)

    Czech, Bartłomiej

    2018-01-01

    A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of tensor network renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.

  3. Sequent Calculus and Equational Programming

    Directory of Open Access Journals (Sweden)

    Nicolas Guenot

    2015-07-01

    Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.

  4. Radar equations for modern radar

    CERN Document Server

    Barton, David K

    2012-01-01

    Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo

  5. dimensional KdV equation

    Indian Academy of Sciences (India)

    is to study the interaction properties between the periodic waves. Here, we take the (2+1)-dimensional KdV equation .... In fact, such limit for the present family of doubly periodic waves is especially rich, since one can proceed with the long .... ematical Society, Providence, 1997). [11] K Chandrasekharan, Elliptic functions ...

  6. Stability of Functional Differential Equations

    CERN Document Server

    Lemm, Jeffrey M

    1986-01-01

    This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.

  7. Sonar equations for planetary exploration.

    Science.gov (United States)

    Ainslie, Michael A; Leighton, Timothy G

    2016-08-01

    The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.

  8. Sonar equations for planetary exploration

    NARCIS (Netherlands)

    Ainslie, M.A.; Leighton, T.G.

    2016-01-01

    The set of formulations commonly known as “the sonar equations” have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and ocalize objects submerged in seawater. The efficacy of the sonar equations, with individualterms evaluated in decibels,

  9. Saha equation in Rindler space

    Indian Academy of Sciences (India)

    Sanchari De

    MS received 21 October 2016; revised 3 January 2017; accepted 25 January 2017; published online 31 May 2017. Abstract. The Saha equations for the photoionization process of hydrogen atoms .... [3] C W Misner, Kip S Thorne and J A Wheeler, Gravitation (W.H.. Freeman and Company, New York, 1972). [4] W Rindler ...

  10. Equations for formally real meadows

    NARCIS (Netherlands)

    Bergstra, J.A.; Bethke, I.; Ponse, A.

    2015-01-01

    We consider the signatures Σm = (0,1,−,+,⋅,−1)  of meadows and (Σm,s)  of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom

  11. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    On the Saha Ionization Equation. Sushanta Dattagupta. General Article Volume 23 Issue 1 January 2018 pp 41-55. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/023/01/0041-0055. Keywords. Ionization, astrophysics, spectroscopy, chemical reaction, transition state. Abstract.

  12. Pendulum Motion and Differential Equations

    Science.gov (United States)

    Reid, Thomas F.; King, Stephen C.

    2009-01-01

    A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…

  13. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  14. Transport equation and shock waves

    International Nuclear Information System (INIS)

    Besnard, D.

    1981-04-01

    A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma

  15. Benjamin–Bona–Mahony equation

    Indian Academy of Sciences (India)

    Abstract. By applying the bifurcation theory of dynamical system to the generalized. KP–BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves.

  16. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...

  17. Renaissance Learning Equating Study. Report

    Science.gov (United States)

    Sewell, Julie; Sainsbury, Marian; Pyle, Katie; Keogh, Nikki; Styles, Ben

    2007-01-01

    An equating study was carried out in autumn 2006 by the National Foundation for Educational Research (NFER) on behalf of Renaissance Learning, to provide validation evidence for the use of the Renaissance Star Reading and Star Mathematics tests in English schools. The study investigated the correlation between the Star tests and established tests.…

  18. A generalized advection dispersion equation

    Indian Academy of Sciences (India)

    This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.

  19. Quasi-gas dynamic equations

    CERN Document Server

    Elizarova, Tatiana G

    2009-01-01

    This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.

  20. Slave equations for spin models

    International Nuclear Information System (INIS)

    Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

    1992-01-01

    We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

  1. Solutions of equations in languages

    NARCIS (Netherlands)

    Hesselink, Wim H.

    A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar

  2. A Versatile Technique for Solving Quintic Equations

    Science.gov (United States)

    Kulkarni, Raghavendra G.

    2006-01-01

    In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

  3. Functional equations in matrix normed spaces

    Indian Academy of Sciences (India)

    Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces. Keywords. Operator space; fixed point; Hyers–Ulam stability; Cauchy additive functional equation; quadratic functional equation. 2000 Mathematics Subject Classification. 47L25, 47H10, 39B82, 46L07, 39B52. 1.

  4. Analytical solution of population balance equation involving ...

    Indian Academy of Sciences (India)

    This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation ...

  5. An analytical solution of fractional burgers equation

    Directory of Open Access Journals (Sweden)

    Pang Jing

    2017-01-01

    Full Text Available Using the fractional complex transform, the fractional partial differential equations can be reduced to ordinary differential equations which can be solved by the auxiliary equation method. Non-linear superposition formulation of Riccati equation is applied, and a complex infinite sequence solution is obtained.

  6. The Complexity of One-Step Equations

    Science.gov (United States)

    Ngu, Bing

    2014-01-01

    An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

  7. Algebraic entropy for differential-delay equations

    OpenAIRE

    Viallet, Claude M.

    2014-01-01

    We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

  8. Interplays between Harper and Mathieu equations.

    Science.gov (United States)

    Papp, E; Micu, C

    2001-11-01

    This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Mathieu equation. This leads to the derivation of two kinds of energy formulas working in terms of cubic and quadratic algebraic equations, respectively. Combining such results yields quadratic equations to the energy description of the Harper equation, incorporating all parameters needed.

  9. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  10. Maxwell's equations of electrodynamics an explanation

    CERN Document Server

    Ball, David W

    2012-01-01

    Maxwell's Equations of Electrodynamics: An Explanation is a concise discussion of Maxwell's four equations of electrodynamics - the fundamental theory of electricity, magnetism, and light. It guides readers step-by-step through the vector calculus and development of each equation. Pictures and diagrams illustrate what the equations mean in basic terms. The book not only provides a fundamental description of our universe but also explains how these equations predict the fact that light is better described as "electromagnetic radiation."

  11. The equations icons of knowledge

    CERN Document Server

    Bais, Sander

    2005-01-01

    For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.

  12. Nonlocal higher order evolution equations

    KAUST Repository

    Rossi, Julio D.

    2010-06-01

    In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.

  13. MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE

    Directory of Open Access Journals (Sweden)

    Francisco Frutos Alfaro

    2017-04-01

    Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.

  14. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  15. Equation of State Project Overview

    Energy Technology Data Exchange (ETDEWEB)

    Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-09-11

    A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.

  16. A generalized advection dispersion equation

    Indian Academy of Sciences (India)

    Multiplication. If ux, f (x) and g(x) are differentiable in the opened interval D, then: D ux [f(x) · g(x)]=g(x)f (x) + f(x)g (x). + (gf + fg )(x)ux + u x. (f(x)g(x)). (2.5) ..... for solution of various nonlinear problems without usual restrictive assumptions. To solve equation. (4.2) by means of variational iteration method, we put (4.2) as ...

  17. BERNULLI DIFFERENTIAL EQUATION AND CHAOS

    Directory of Open Access Journals (Sweden)

    V. Ye. Belozerov

    2013-03-01

    Full Text Available Existence conditions of homoclinic orbits for some systems of ordinary quadratic dif­ferential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic systems. In addition, a chaotic behavior of the solutions of these systems is determined by one-dimensional discrete map at some values of parameters. Examples are given.

  18. Handbook of structural equation modeling

    CERN Document Server

    Hoyle, Rick H

    2012-01-01

    The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu

  19. Integration of Chandrasekhar's integral equation

    International Nuclear Information System (INIS)

    Tanaka, Tasuku

    2003-01-01

    We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness

  20. Deriving the bond pricing equation

    Directory of Open Access Journals (Sweden)

    Kožul Nataša

    2014-01-01

    Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.

  1. Wave equations in higher dimensions

    CERN Document Server

    Dong, Shi-Hai

    2011-01-01

    Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

  2. Effective Schroedinger equations on submanifolds

    Energy Technology Data Exchange (ETDEWEB)

    Wachsmuth, Jakob

    2010-02-11

    In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.

  3. Handbook of differential equations stationary partial differential equations

    CERN Document Server

    Chipot, Michel

    2006-01-01

    This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke

  4. Partial differential equations of mathematical physics and integral equations

    CERN Document Server

    Guenther, Ronald B

    1996-01-01

    This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t

  5. Partial differential equations for scientists and engineers

    CERN Document Server

    Farlow, Stanley J

    1993-01-01

    Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

  6. Semilinear Schrödinger equations

    CERN Document Server

    Cazenave, Thierry

    2003-01-01

    The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique

  7. General and exact pressure evolution equation

    Science.gov (United States)

    Toutant, Adrien

    2017-11-01

    A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. This new pressure equation is valid for all real dense fluids for which the pressure tensor is isotropic. It is argued that this new pressure equation allows unifying compressible, low-Mach and incompressible approaches. Moreover, this equation should be able to replace the Poisson equation in isothermal incompressible fluids. For computational fluid dynamics, it can be seen as an alternative to Lattice Boltzmann methods and as the physical justification of artificial compressibility.

  8. Using fundamental equations to describe basic phenomena

    DEFF Research Database (Denmark)

    Jakobsen, Arne; Rasmussen, Bjarne D.

    1999-01-01

    When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equation...... and subcooling are introduced. Since the degree of freedom was equal to one, using both the superheat and subcooling require that one of the fundamental equations must be omitted from the equation system.The main purpose of the paper is to clarify the relation between the fundamental balance equations...

  9. International Workshop on Elliptic and Parabolic Equations

    CERN Document Server

    Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

    2015-01-01

    This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

  10. A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

    International Nuclear Information System (INIS)

    Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

    2014-01-01

    In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

  11. Algorithm for research of mathematical physics equations symmetries. Symmetries of the free Schroedinger equation

    International Nuclear Information System (INIS)

    Kotel'nikov, G.A.

    1994-01-01

    An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry

  12. Stochastic Differential Equations in Banach Spaces : Decoupling, Delay Equations, and Approximations in Space and Time

    NARCIS (Netherlands)

    Cox, S.G.

    2012-01-01

    The thesis deals with various aspects of the study of stochastic partial differential equations driven by Gaussian noise. The approach taken is functional analytic rather than probabilistic: the stochastic partial differential equation is interpreted as an ordinary stochastic differential equation

  13. On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

    Science.gov (United States)

    Savoye, Philippe

    2009-01-01

    In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

  14. Reduction of lattice equations to the Painlevé equations: PIV and PV

    Science.gov (United States)

    Nakazono, Nobutaka

    2018-02-01

    In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

  15. Techniques for estimating allometric equations.

    Science.gov (United States)

    Manaster, B J; Manaster, S

    1975-11-01

    Morphologists have long been aware that differential size relationships of variables can be fo great value when studying shape. Allometric patterns have been the basis of many interpretations of adaptations, biomechanisms, and taxonomies. It is of importance that the parameters of the allometric equation be as accurate estimates as possible since they are so commonly used in such interpretations. Since the error term may come into the allometric relation either exponentially or additively, there are at least two methods of estimating the parameters of the allometric equation. That most commonly used assumes exponentiality of the error term, and operates by forming a linear function by a logarithmic transformation and then solving by the method of ordinary least squares. On the other hand, if the rrror term comes into the equation in an additive way, a nonlinear method may be used, searching the parameter space for those parameters which minimize the sum of squared residuals. Study of data on body weight and metabolism in birds explores the issues involved in discriminating between the two models by working through a specific example and shows that these two methods of estimation can yield highly different results. Not only minimizing the sum of squared residuals, but also the distribution and randomness of the residuals must be considered in determing which model more precisely estimates the parameters. In general there is no a priori way to tell which model will be best. Given the importance often attached to the parameter estimates, it may be well worth considerable effort to find which method of solution is appropriate for a given set of data.

  16. Differential Equations and Computational Simulations

    Science.gov (United States)

    1999-06-18

    given in (6),(7) in Taylor series of e. Equating coefficients of same power of e in both side of equity , we obtain a sequence of linear boundary value...fields, 3). structural instability and block stability of divergence-free vector fields on 2D compact manifolds with nonzero genus , and 4). structural...circle bands. Definition 3.1 Let N be a compact manifold without boundary and with genus k > 0. A closed domain fi C N is called a pseudo-manifold

  17. Ising models and soliton equations

    International Nuclear Information System (INIS)

    Perk, J.H.H.; Au-Yang, H.

    1985-01-01

    Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained

  18. BMN correlators by loop equations

    International Nuclear Information System (INIS)

    Eynard, Bertrand; Kristjansen, Charlotte

    2002-01-01

    In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction. (author)

  19. Numerical Solution of Parabolic Equations

    DEFF Research Database (Denmark)

    Østerby, Ole

    approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...... ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal...

  20. Introduction to partial differential equations with applications

    CERN Document Server

    Zachmanoglou, E C

    1988-01-01

    This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

  1. Feedback stabilization of semilinear heat equations

    Directory of Open Access Journals (Sweden)

    V. Barbu

    2003-01-01

    Full Text Available This paper is concerned with the internal and boundary stabilization of the steady-state solutions to quasilinear heat equations via internal linear feedback controllers provided by an LQ control problem associated with the linearized equation.

  2. Regional Screening Levels (RSLs) - Equations (November 2017 )

    Science.gov (United States)

    Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

  3. On oscillatory solutions of certain difference equations

    Directory of Open Access Journals (Sweden)

    Grzegorz Grzegorczyk

    2006-01-01

    Full Text Available Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.

  4. Linear superposition solutions to nonlinear wave equations

    International Nuclear Information System (INIS)

    Liu Yu

    2012-01-01

    The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

  5. The stochastic Swift-Hohenberg equation

    Science.gov (United States)

    Gao, Peng

    2017-09-01

    In this paper, we will study the stochastic Swift-Hohenberg equation. The weak martingale solution, stationary martingale solution, invariant measures, mild solution, large deviation principle and random attractors for the stochastic Swift-Hohenberg equation will be considered.

  6. On linear equations with general polynomial solutions

    Science.gov (United States)

    Laradji, A.

    2018-04-01

    We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation.

  7. PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS

    Directory of Open Access Journals (Sweden)

    Korhan KARABULUT

    1998-03-01

    Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.

  8. Partial differential equations of mathematical physics

    CERN Document Server

    Sobolev, S L

    1964-01-01

    Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math

  9. About the solvability of matrix polynomial equations

    OpenAIRE

    Netzer, Tim; Thom, Andreas

    2016-01-01

    We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

  10. Hybrid quantum-classical master equations

    International Nuclear Information System (INIS)

    Diósi, Lajos

    2014-01-01

    We discuss hybrid master equations of composite systems, which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested. Its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurement (monitoring). (paper)

  11. Solutions manual to accompany Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  12. Numerical methods for stochastic differential equations.

    Science.gov (United States)

    Wilkie, Joshua

    2004-01-01

    Stochastic differential equations (SDE's) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here. High-order numerical methods are developed for the integration of stochastic differential equations with strong solutions. We demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for SDE's which have known exact solutions.

  13. Notes on the infinity Laplace equation

    CERN Document Server

    Lindqvist, Peter

    2016-01-01

    This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

  14. Ramanujan's modular equations of degree 5

    Indian Academy of Sciences (India)

    Abstract. We provide alternative derivations of theta function identities associ- ated with modular equations of degree 5. We then use the identities to derive the corresponding modular equations. Keywords. Theta-function; elliptic integral; modular equation; multiplier. 1. Introduction. Ramanujan's general theta-function f (a, ...

  15. Explicit solutions of the Rand Equation

    African Journals Online (AJOL)

    user

    We perform a classical Lie Group analysis to analyze the point symmetries. By using a similarity ... Keywords: Nonlinear partial differential equations, evolution equations, symmetries, similarity solutions, Rand Equation. PACS-Code: .... The table is skew-symmetric and the diagonal elements vanish. The coefficient kji.

  16. Fuzzy Stability of Quadratic Functional Equations

    Directory of Open Access Journals (Sweden)

    Jang Sun-Young

    2010-01-01

    Full Text Available The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and    in fuzzy Banach spaces.

  17. Fuzzy Stability of Quadratic Functional Equations

    OpenAIRE

    Dong Yun Shin; Choonkil Park; Sun-Young Jang; Jung Rye Lee

    2010-01-01

    The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and    in fuzzy Banach spaces.

  18. Some Functional Equations Originating from Number Theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  19. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations. Keywords. Functional equation; stability; multiplicative function. 1. Introduction. In 1940, Ulam gave a wide ranging talk before the Mathematics ...

  20. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  1. Managing Element Interactivity in Equation Solving

    Science.gov (United States)

    Ngu, Bing Hiong; Phan, Huy P.; Yeung, Alexander Seeshing; Chung, Siu Fung

    2018-01-01

    Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

  2. A reliable treatment for nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.

    2007-01-01

    Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation

  3. On the (colored Yang-Baxter Equation

    Directory of Open Access Journals (Sweden)

    Florin Felix Nichita

    2010-06-01

    Full Text Available The quantum Yang-Baxter equation ¯rst appeared in theoretical physics and statistical mechanics. Afterwards, it has proved to be
    important also in knot theory, quantum groups, etc. This paper deals with the (colored Yang-Baxter equation and computational methods. A new result about the set-theoretical Yang-Baxter equation is presented.

  4. Elliptic Hypergeometric Solutions to Elliptic Difference Equations

    Directory of Open Access Journals (Sweden)

    Alphonse P. Magnus

    2009-03-01

    Full Text Available It is shown how to define difference equations on particular lattices {x_n}, n in Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice. Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.

  5. Elliptic Hypergeometric Solutions to Elliptic Difference Equations

    Science.gov (United States)

    Magnus, Alphonse P.

    2009-03-01

    It is shown how to define difference equations on particular lattices {xn}, n Î Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.

  6. New solitons connected to the Dirac equation

    International Nuclear Information System (INIS)

    Grosse, H.

    1984-01-01

    Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)

  7. Comparison of the Schrodinger and Salpeter equations

    International Nuclear Information System (INIS)

    Jacobs, S.; Olsson, M.G.

    1985-01-01

    A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation

  8. Numerical Solutions to Fractional Perturbed Volterra Equations

    Directory of Open Access Journals (Sweden)

    B. Bandrowski

    2012-01-01

    Full Text Available In the paper, a class of perturbed Volterra equations of convolution type with three kernel functions is considered. The kernel functions , , , correspond to the class of equations interpolating heat and wave equations. The results obtained generalize our previous results from 2010.

  9. Equations of state for light water

    International Nuclear Information System (INIS)

    Rubin, G.A.; Granziera, M.R.

    1983-01-01

    The equations of state for light water were developed, based on the tables of Keenan and Keyes. Equations are presented, describing the specific volume, internal energy, enthalpy and entropy of saturated steam, superheated vapor and subcooled liquid as a function of pressure and temperature. For each property, several equations are shown, with different precisions and different degress of complexity. (Author) [pt

  10. Derivation of the neutron diffusion equation

    International Nuclear Information System (INIS)

    Mika, J.R.; Banasiak, J.

    1994-01-01

    We discuss the diffusion equation as an asymptotic limit of the neutron transport equation for large scattering cross sections. We show that the classical asymptotic expansion procedure does not lead to the diffusion equation and present two modified approaches to overcome this difficulty. The effect of the initial layer is also discussed. (authors). 9 refs

  11. The Modified Enskog Equation for Mixtures

    NARCIS (Netherlands)

    Beijeren, H. van; Ernst, M.H.

    1973-01-01

    In a previous paper it was shown that a modified form of the Enskog equation, applied to mixtures of hard spheres, should be considered as the correct extension of the usual Enskog equation to the case of mixtures. The main argument was that the modified Enskog equation leads to linear transport

  12. Completely integrable operator evolution equations. II

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)

  13. Symmetries of nonlinear ordinary differential equations: The ...

    Indian Academy of Sciences (India)

    2015-10-21

    Oct 21, 2015 ... equation and showed that it admits sl(3, R) algebra and constructed a linearizing trans- formation from ... ers of ˙x to zero, one obtains a set of linear partial differential equations for the unknown functions ξ and η. ...... [11] N H Ibragimov, Elementary Lie group analysis and ordinary differential equations (John.

  14. Positive Integer Solutions of Certain Diophantine Equations

    Indian Academy of Sciences (India)

    29

    An important area of number theory is devoted to finding solutions of equations where the solutions are restricted to the set of integers. Diophantine equations get their name from Diophantus of. Alexandria and they are algebraic equations for which rational or integer solutions are sought. Many researchers considered the ...

  15. Entropy Bounds and Field Equations

    Directory of Open Access Journals (Sweden)

    Alessandro Pesci

    2015-08-01

    Full Text Available For general metric theories of gravity, we compare the approach that describes/derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of the matter entropy flux across (Rindler horizons, studied by making use of the notion of a limiting thermodynamic scale l* of matter, previously introduced in the context of entropy bounds. In doing this: (i a bound for the entropy of any lump of matter with a given energy-momentum tensor Tab is considered, in terms of a quantity, which is independent of the theory of gravity that we use; this quantity is the variation of the Clausius entropy of a suitable horizon when the element of matter crosses it; (ii by making use of the equations of motion of the theory, the same quantity is then expressed as the variation of Wald’s entropy of that horizon (and this leads to a generalized form of the generalized covariant entropy bound, applicable to general diffeomorphism-invariant theories of gravity; and (iii a notion of l* for horizons, as well as an expression for it, is given.

  16. Equations of state for hydrocodes

    Science.gov (United States)

    Lomonosov, I.

    2013-06-01

    The equation of state (EOS) governing the system of gas dynamic equations defines significantly accuracy and reliability of results of numerical modeling. In our report, we will formulate main mathematical and physical demands to wide-range EOS for hydrocodes. Our semi-empirical EOS model fully assigns the free energy thermodynamic potential for metals over entire phase diagram region of practical interest. It accounts for solid, liquid, plasma states as well as two-phase regions of melting and evaporation. Available now are wide-range multi-phase EOS for 30 simple and transition metals of the most practical interest. Their direct usage in computer codes leads to complicated and not economy calculations, so they are usually involved in numerical modeling in tabular form. The EOS code for calculation of tables can produce the complete set of thermodynamic derivatives (such as pressure, sound velocity, heat capacity) using any one of input pairs: volume-temperature, volume-internal energy or volume-pressure. The input grid can be linear, logarithmic or arbitrary; each point in 2D output tables is marked by symbol which indicates the physical state, such as solid, liquid, gas, plasma or mesh. We also present in our talk estimations of shock melting and evaporating and importance of these effects for results of numerical modeling.

  17. Sobolev gradients and differential equations

    CERN Document Server

    Neuberger, J W

    2010-01-01

    A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...

  18. Wave-equation Q tomography

    KAUST Repository

    Dutta, Gaurav

    2016-10-12

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

  19. Jacobi equations as Lagrange equations of the deformed Lagrangian

    International Nuclear Information System (INIS)

    Casciaro, B.

    1995-03-01

    We study higher-order variational derivatives of a generic Lagrangian L 0 = L 0 (t,q,q). We introduce two new Lagrangians, L 1 and L 2 , associated to the first and second-order deformations of the original Lagrangian L 0 . In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L 1 . We can furthermore introduce an associated Hamiltonian H 1 = H 1 (t,q,q radical,η,η radical) with η equivalent to δq. If L 0 is independent of time then H 1 is a conserved quantity. (author). 15 refs

  20. Numerical solutions of diffusive logistic equation

    International Nuclear Information System (INIS)

    Afrouzi, G.A.; Khademloo, S.

    2007-01-01

    In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

  1. Monge-Ampere equations and tensorial functors

    International Nuclear Information System (INIS)

    Tunitsky, Dmitry V

    2009-01-01

    We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

  2. Developments in functional equations and related topics

    CERN Document Server

    Ciepliński, Krzysztof; Rassias, Themistocles

    2017-01-01

    This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

  3. Generalization of Einstein's gravitational field equations

    Science.gov (United States)

    Moulin, Frédéric

    2017-12-01

    The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

  4. From ordinary to partial differential equations

    CERN Document Server

    Esposito, Giampiero

    2017-01-01

    This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

  5. The Acoustic Limit for the Boltzmann Equation

    Science.gov (United States)

    Bardos, Claude; Golse, François; Levermore, C. David

    The acoustic equations are the linearization of the compressible Euler equations about a spatially homogeneous fluid state. We first derive them directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. We then establish this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L1) to a unique limit governed by a solution of the acoustic equations for all time, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L2 initial data of the acoustic equations. The associated local conservation laws are recovered in the limit.

  6. equate: An R Package for Observed-Score Linking and Equating

    Directory of Open Access Journals (Sweden)

    Anthony D. Albano

    2016-10-01

    Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

  7. Computing singularly perturbed differential equations

    Science.gov (United States)

    Chatterjee, Sabyasachi; Acharya, Amit; Artstein, Zvi

    2018-02-01

    A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the averaging of Hamiltonian as well as dissipative microscopic dynamics whose 'slow' variables, defined in a precise sense, can often display mixed slow-fast response as in relaxation oscillations, and dependence on initial conditions of the fast variables. Also covered is the case where the quasi-static assumption in solid mechanics is violated. The computational tool is demonstrated to capture all of these behaviors in an accurate and robust manner, with significant savings in time. A practically useful strategy for accurately initializing short bursts of microscopic runs for the evolution of slow variables is integral to our scheme, without the requirement that the slow variables determine a unique invariant measure of the microscopic dynamics.

  8. Teaching materials of algebraic equation

    Science.gov (United States)

    Widodo, S. A.; Prahmana, R. C. I.; Purnami, A. S.; Turmudi

    2017-12-01

    The purpose of this paper is to know the effectiveness of teaching materials algebraic equation. This type of research used experimental method. The population in this study is all students of mathematics education who take numerical method in sarjanawiyata tamansiswa of university; the sample is taken using cluster random sampling. Instrument used in this research is test and questionnaire. The test is used to know the problem solving ability and achievement, while the questionnaire is used to know the student's response on the teaching materials. Data Analysis technique of quantitative used Wilcoxon test, while the qualitative data used grounded theory. Based on the results of the test can be concluded that the development of teaching materials can improve the ability to solve problems and achievement.

  9. An introduction to differential equations

    CERN Document Server

    Ladde, Anil G

    2012-01-01

    This is a twenty-first century book designed to meet the challenges of understanding and solving interdisciplinary problems. The book creatively incorporates "cutting-edge" research ideas and techniques at the undergraduate level. The book also is a unique research resource for undergraduate/graduate students and interdisciplinary researchers. It emphasizes and exhibits the importance of conceptual understandings and its symbiotic relationship in the problem solving process. The book is proactive in preparing for the modeling of dynamic processes in various disciplines. It introduces a "break-down-the problem" type of approach in a way that creates "fun" and "excitement". The book presents many learning tools like "step-by-step procedures (critical thinking)", the concept of "math" being a language, applied examples from diverse fields, frequent recaps, flowcharts and exercises. Uniquely, this book introduces an innovative and unified method of solving nonlinear scalar differential equations. This is called ...

  10. The Seiberg-Witten equations

    OpenAIRE

    Alcides de Carvalho Junior

    2016-01-01

    Resumo: Nesta dissertação faremos uma apresentação das equações de Seiberg-Witten. Mostraremos a não existência de soluções não triviais em variedades com curvatura escalar não negativa. Este último resultado será apresentado como uma consequência da fórmula de Weizenböck para o operador de Dirac. ;;Abstract:In this work we do an presentation of the equation of Seiberg-Witten. We show the non-existence of non-trivial solutions in manifolds with scalar curvature non-negative. This latter resu...

  11. Stochastic integration and differential equations

    CERN Document Server

    Protter, Philip E

    2003-01-01

    It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...

  12. Inferring Mathematical Equations Using Crowdsourcing.

    Directory of Open Access Journals (Sweden)

    Szymon Wasik

    Full Text Available Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.

  13. Inferring Mathematical Equations Using Crowdsourcing.

    Science.gov (United States)

    Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw

    2015-01-01

    Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.

  14. A new auxiliary equation and exact travelling wave solutions of nonlinear equations

    International Nuclear Information System (INIS)

    Sirendaoreji

    2006-01-01

    A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

  15. Equating Subscores under the Nonequivalent Anchor Test (NEAT) Design

    Science.gov (United States)

    Puhan, Gautam; Liang, Longjuan

    2011-01-01

    The study examined two approaches for equating subscores. They are (1) equating subscores using internal common items as the anchor to conduct the equating, and (2) equating subscores using equated and scaled total scores as the anchor to conduct the equating. Since equated total scores are comparable across the new and old forms, they can be used…

  16. Some New Integrable Equations from the Self-Dual Yang-Mills Equations

    International Nuclear Information System (INIS)

    Ivanova, T.A.; Popov, A.D.

    1994-01-01

    Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

  17. Exact and explicit solitary wave solutions to some nonlinear equations

    International Nuclear Information System (INIS)

    Jiefang Zhang

    1996-01-01

    Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ 4 -model equation, the generalized Fisher equation, and the elastic-medium wave equation

  18. Stochastic differential equation model to Prendiville processes

    International Nuclear Information System (INIS)

    Granita; Bahar, Arifah

    2015-01-01

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

  19. Stochastic differential equation model to Prendiville processes

    Energy Technology Data Exchange (ETDEWEB)

    Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

    2015-10-22

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

  20. On stochastic differential equations with random delay

    International Nuclear Information System (INIS)

    Krapivsky, P L; Luck, J M; Mallick, K

    2011-01-01

    We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an nth-order equation with random delay, the corresponding deterministic equation has order n + 1. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as exp((3/2) t 2/3 ) in reduced units. We then investigate the effect of introducing a discrete time step ε. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as ε goes to zero is studied in detail on the example of a first-order linear differential equation

  1. Pseudodifferential equations over non-Archimedean spaces

    CERN Document Server

    Zúñiga-Galindo, W A

    2016-01-01

    Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...

  2. Diffusion phenomenon for linear dissipative wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

  3. Introduction to complex theory of differential equations

    CERN Document Server

    Savin, Anton

    2017-01-01

    This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.

  4. Equations of macrotransport in reactor fuel assemblies

    International Nuclear Information System (INIS)

    Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.

    1986-01-01

    The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given

  5. Weak self-adjoint differential equations

    International Nuclear Information System (INIS)

    Gandarias, M L

    2011-01-01

    The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57; 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)

  6. Interactive differential equations modeling program

    International Nuclear Information System (INIS)

    Rust, B.W.; Mankin, J.B.

    1976-01-01

    Due to the recent emphasis on mathematical modeling, many ecologists are using mathematics and computers more than ever, and engineers, mathematicians and physical scientists are now included in ecological projects. However, the individual ecologist, with intuitive knowledge of the system, still requires the means to critically examine and adjust system models. An interactive program was developed with the primary goal of allowing an ecologist with minimal experience in either mathematics or computers to develop a system model. It has also been used successfully by systems ecologists, engineers, and mathematicians. This program was written in FORTRAN for the DEC PDP-10, a remote terminal system at Oak Ridge National Laboratory. However, with relatively minor modifications, it can be implemented on any remote terminal system with a FORTRAN IV compiler, or equivalent. This program may be used to simulate any phenomenon which can be described as a system of ordinary differential equations. The program allows the user to interactively change system parameters and/or initial conditions, to interactively select a set of variables to be plotted, and to model discontinuities in the state variables and/or their derivatives. One of the most useful features to the non-computer specialist is the ability to interactively address the system parameters by name and to interactively adjust their values between simulations. These and other features are described in greater detail

  7. Quantum - statistical equation of state

    International Nuclear Information System (INIS)

    Kalitkin, N.N.; Kuz'mina, L.V.

    1976-01-01

    An atom model is considered which allows uniform description of the equation of an equilibrium plasma state in the range of densities from gas to superhigh ones and in the temperature range from 1-5 eV to a ten of keV. Quantum and exchange corrections to the Thomas-Fermi thermodynamic functions at non zero temperatures have been calculated. The calculated values have been compared with experimental data and with calculations performed by more accurate models. The differences result from the fact that a quantum approach does not allow for shell effects. The evaluation of these differences makes it possible to indicate the limits of applicability of the Thomas-Fermi model with quantum and exchange corrections. It turns out that if at zero temperature the model may be applied only for high compressions, at the temperature more than 1 eV it well describes the behaviour of plasma in a very wide range of densities and agrees satisfactorily with experiment even for non-ideal plasma

  8. Integral equations with contrasting kernels

    Directory of Open Access Journals (Sweden)

    Theodore Burton

    2008-01-01

    Full Text Available In this paper we study integral equations of the form $x(t=a(t-\\int^t_0 C(t,sx(sds$ with sharply contrasting kernels typified by $C^*(t,s=\\ln (e+(t-s$ and $D^*(t,s=[1+(t-s]^{-1}$. The kernel assigns a weight to $x(s$ and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for $a\\in L^2[0,\\infty$, then solutions are largely indistinguishable regardless of which kernel is used. This is a surprise and it leads us to study the essential differences. In fact, those differences become large as the magnitude of $a(t$ increases. The form of the kernel alone projects necessary conditions concerning the magnitude of $a(t$ which could result in bounded solutions. Thus, the next project is to determine how close we can come to proving that the necessary conditions are also sufficient. The third project is to show that solutions will be bounded for given conditions on $C$ regardless of whether $a$ is chosen large or small; this is important in real-world problems since we would like to have $a(t$ as the sum of a bounded, but badly behaved function, and a large well behaved function.

  9. The transport equation for cosmic rays

    International Nuclear Information System (INIS)

    Henning, J.J.

    1980-03-01

    The transport equation for charged particles in a moving irregular magnetic field is derived in the dipole approximation. The contribution of Parker's spiral field for the transport equation is shown to be more than just a drift velocity or a divergence of an antisymmetric diffusion tensor. Without solving the transport equations these results are shown to give better agreement with experimental densities of cosmic rays in the interplanetary space [af

  10. The Boltzmann equation in the difference formulation

    Energy Technology Data Exchange (ETDEWEB)

    Szoke, Abraham [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks III, Eugene D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-05-06

    First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

  11. Field equation for baryons with arbitrary spin

    International Nuclear Information System (INIS)

    Vaklev, J.S.; Ivanov, M.I.; Nikolov, A.V.

    1979-01-01

    Field equation for byryons with arbitrary spin, which is a generalization of the Dirac equation, is suggested on the basis of the group scheme. This group scheme provides good possibilities for investigation of the solutions of the equation suggested. Such an investigation is performed in detail in the spirit of the Dirac theory. The operation of the charge conjugation is generalized too. Here the free fields are considered only; a corresponding theory of the interacting fields will be a subject of forthcoming research

  12. Survey Propagation as local equilibrium equations

    OpenAIRE

    Braunstein, A.; Zecchina, R.

    2003-01-01

    It has been shown experimentally that a decimation algorithm based on Survey Propagation (SP) equations allows to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum-product equations for the computation of marginals in an extended space where the variables are allowed to take an additional value -- $*$ -- when they are not forced by the combinatorial constraints. An appropriate ``local equilibrium condition'' cost/energy functi...

  13. Spirometric reference equations for Swedish adults.

    Science.gov (United States)

    Brisman, Jonas; Kim, Jeong-Lim; Olin, Anna-Carin; Torén, Kjell; Bake, Björn

    2017-11-01

    New spirometric reference equations for Swedish adults are required. Three different older sets of reference equations clinically used in Sweden have various drawbacks and the recently published 'The Global Lung Function 2012 (GLI) equations' have been shown not to be adequate for Swedish normal, healthy non-smokers. We have recently concluded that a piecewise linear model presented by Lubinski and Gólczewski accurately describes the distribution of spirometric variables in a large Swedish random population sample. This piecewise linear model also offers the important advantage of implementing easily physiologically interpretable coefficients. The present study aimed at presenting piecewise linear reference equations for Swedish adults based on a random population sample of 6685 individuals aged 25-75 years. Predicted normal values by the piecewise linear reference equations and lower limit normal (LLN) were compared with the three reference equations frequently used clinically in Sweden and the GLI equations. We found predicted normal values according to the present piecewise linear reference equations close to 100% predicted normal as expected, whereas the other equations either overestimated or underestimated normal subjects. Concerning LLN, the present equations, i.e. 1·645 × RSD, showed the least deviation from the expected 5% and, e.g., the GLI equations systematically identified too few subjects below LLN. We conclude that the present piecewise linear reference equations, based on a relatively large general population sample, ought to be considered for clinical use in Sweden. Application of 1·645 × RSD below predicted value gave an acceptably accurate LLN. © 2016 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.

  14. Generalized Harnack Inequality for Nonhomogeneous Elliptic Equations

    Science.gov (United States)

    Julin, Vesa

    2015-05-01

    This paper is concerned with nonlinear elliptic equations in nondivergence form where F has a drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative solutions do not satisfy the classical Harnack inequality. This paper presents a new generalization of the Harnack inequality for such equations. As a corollary we obtain the optimal Harnack type of inequality for p( x)-harmonic functions which quantifies the strong minimum principle.

  15. Reaction diffusion equations with boundary degeneracy

    Directory of Open Access Journals (Sweden)

    Huashui Zhan

    2016-03-01

    Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.

  16. On Some Functional-Differential Equation

    Directory of Open Access Journals (Sweden)

    N.P. Evlampiev

    2016-06-01

    Full Text Available The necessary and sufficient conditions for the existence and uniqueness of a solution of the problem for the functional-differential equation are established. The special case of this equation is the functional-differential equation deduced previously by us for the distribution density of light brightness in the interstellar space when there are some absorbing clouds distributed uniformly in the equatorial plane of the Galaxy and having different optical transparency.

  17. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

  18. On deformations of the dispersionless Hirota equation

    Science.gov (United States)

    Kryński, Wojciech

    2018-04-01

    The class of hyper-CR Einstein-Weyl structures on R3 can be described in terms of the solutions to the dispersionless Hirota equation. In the present paper we show that simple geometric constructions on the associated twistor space lead to deformations of the Hirota equation that have been introduced recently by B. Kruglikov and A. Panasyuk. Our method produces also the hyper-CR equation and can be applied to other geometric structures related to different twistor constructions.

  19. Statistical Methods for Stochastic Differential Equations

    CERN Document Server

    Kessler, Mathieu; Sorensen, Michael

    2012-01-01

    The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp

  20. Resonance regions of extended Mathieu equation

    Science.gov (United States)

    Semyonov, V. P.; Timofeev, A. V.

    2016-02-01

    One of the mechanisms of energy transfer between degrees of freedom of dusty plasma system is based on parametric resonance. Initial stage of this process can de described by equation similar to Mathieu equation. Such equation is studied by analytical and numerical approach. The numerical solution of the extended Mathieu equation is obtained for a wide range of parameter values. Boundaries of resonance regions, growth rates of amplitudes and times of onset are obtained. The energy transfer between the degrees of freedom of dusty plasma system can occur over a wide range of frequencies.

  1. Symmetric solutions of evolutionary partial differential equations

    Science.gov (United States)

    Bruell, Gabriele; Ehrnström, Mats; Geyer, Anna; Pei, Long

    2017-10-01

    We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms of three principles, based on the structure of the equations. The first principle covers equations that allow for steady solutions and shows that any spatially symmetric solution is in fact steady with a speed determined by the motion of the axis of symmetry at the initial time. The second principle includes equations that admit breathers and steady waves, and therefore is less strong: it holds that the axes of symmetry are constant in time. The last principle is a mixed case, when the equation contains terms of the kind from both earlier principles, and there may be different outcomes; for a class of such equations one obtains that a spatially symmetric solution must be constant in both time and space. We list and give examples of more than 30 well-known equations and systems in one and several dimensions satisfying these principles; corresponding results for weak formulations of these equations may be attained using the same techniques. Our investigation is a generalisation of a local and one-dimensional version of the first principle from Ehrnström et al (2009 Int. Math. Res. Not. 2009 4578-96) to nonlocal equations, systems and higher dimensions, as well as a study of the standing and mixed cases.

  2. General particle transport equation. Final report

    International Nuclear Information System (INIS)

    Lafi, A.Y.; Reyes, J.N. Jr.

    1994-12-01

    The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

  3. Kinetic equations for longitudinal stochastic cooling

    International Nuclear Information System (INIS)

    Bisognano, J.J.

    1980-07-01

    A kinetic equation approach to stochastic cooling is presented. Equations for one and two particle distribution functions are derived from the principle of conservation of the number of ensemble systems. The violation of Liouville's theorem is expressed by certain self-interaction terms. The two-particle distribution describes Schottky noise and feedback effects and is analyzed by techniques of the Lenard-Balescu equation for plasmas. The resulting expression for the one particle distribution is of the form of a Fokker-Planck equation. The suppression of Schottky signals for arbitrary machine impedance is discussed in terms of particle correlations

  4. Trajectory attractors of equations of mathematical physics

    International Nuclear Information System (INIS)

    Vishik, Marko I; Chepyzhov, Vladimir V

    2011-01-01

    In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.

  5. Kinetic Boltzmann, Vlasov and Related Equations

    CERN Document Server

    Sinitsyn, Alexander; Vedenyapin, Victor

    2011-01-01

    Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

  6. Hartree--Fock density matrix equation

    International Nuclear Information System (INIS)

    Cohen, L.; Frishberg, C.

    1976-01-01

    An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does

  7. Modelling conjugation with stochastic differential equations

    DEFF Research Database (Denmark)

    Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

    2010-01-01

    using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...

  8. Geometrical and Graphical Solutions of Quadratic Equations.

    Science.gov (United States)

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  9. Random operator equations in mathematical physics. I

    Science.gov (United States)

    Adomian, G.

    1970-01-01

    Stochastic differential equations objectives, limitations and restrictive assumptions in physical problems, discussing electromagnetic wave propagation in random continuum or random dAlembertian operator

  10. FDTD for Hydrodynamic Electron Fluid Maxwell Equations

    Directory of Open Access Journals (Sweden)

    Yingxue Zhao

    2015-05-01

    Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.

  11. On implicit abstract neutral nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br [Universidade de São Paulo, Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto (Brazil); O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie [National University of Ireland, School of Mathematics, Statistics and Applied Mathematics (Ireland)

    2016-04-15

    In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

  12. Numerical Methods for Partial Differential Equations

    CERN Document Server

    Guo, Ben-yu

    1987-01-01

    These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

  13. On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

    KAUST Repository

    Zygalakis, K. C.

    2011-01-01

    In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.

  14. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  15. Smoothing and Decay Estimates for Nonlinear Diffusion Equations Equations of Porous Medium Type

    CERN Document Server

    Vázquez, Juan Luis

    2006-01-01

    This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porou

  16. High-order finite element approximations of the Maxwell equations

    NARCIS (Netherlands)

    Sarmany, D.

    2010-01-01

    This thesis discusses numerical approximations of electromagnetic wave propagation, which is mathematically described by the Maxwell equations. These equations are typically either formulated as integral equations or as (partial) differential equations. Throughout this thesis, the numerical

  17. Minimal solution for inconsistent singular fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    M. Nikuie

    2013-10-01

    Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

  18. Applications of the g-Drazin Inverse to the Heat Equation and a Delay Differential Equation

    Directory of Open Access Journals (Sweden)

    Alrazi Abdeljabbar

    2017-01-01

    Full Text Available We consider applications of the g-Drazin inverse to some classes of abstract Cauchy problems, namely, the heat equation with operator coefficient and delay differential equations in Banach space.

  19. On Fractional Order Hybrid Differential Equations

    Directory of Open Access Journals (Sweden)

    Mohamed A. E. Herzallah

    2014-01-01

    Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

  20. Singular multiparameter dynamic equations with distributional ...

    African Journals Online (AJOL)

    In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at ...

  1. Entropy viscosity method applied to Euler equations

    International Nuclear Information System (INIS)

    Delchini, M. O.; Ragusa, J. C.; Berry, R. A.

    2013-01-01

    The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

  2. A mixed system of equations of elasticity

    Science.gov (United States)

    Shul'ga, M. O.

    2010-09-01

    A mixed system of six equations of elasticity is represented as a Hamiltonian (canonical) operator system in one of the spatial coordinates. It is shown that this system is the Euler equations for the Hellinger-Reissner principle with an appropriately modified integrand. One more functional with an operator integrand from which the canonical operator system can be derived is set up

  3. Oscillation theory of linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Došlý, Ondřej

    2000-01-01

    Roč. 36, č. 5 (2000), s. 329-343 ISSN 0044-8753 R&D Projects: GA ČR GA201/98/0677 Keywords : discrete oscillation theory %Sturm-Liouville equation%Riccati equation Subject RIV: BA - General Mathematics

  4. An analysis of the nonlinear equation

    Indian Academy of Sciences (India)

    optimal ... Equation (2) will admit a one-dimensional Lie algebra with the basis ...... u)ux + p(x, u) conditional equivalence groups. They also looked at the determination of conservation laws. All their results will apply to our equation when eq.

  5. On exact solutions of the Bogoyavlenskii equation

    Indian Academy of Sciences (India)

    Abstract. Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a ...

  6. Solving Cubic Equations by Polynomial Decomposition

    Science.gov (United States)

    Kulkarni, Raghavendra G.

    2011-01-01

    Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

  7. Constitutive equations for two-phase flows

    International Nuclear Information System (INIS)

    Boure, J.A.

    1974-12-01

    The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

  8. Recent Methodological Advances in Economic Equation Systems.

    Science.gov (United States)

    Theil, Henri; Clements, Kenneth W.

    1980-01-01

    Examines economic equation systems by describing the simultaneous equation model, its application to the economy as a whole, and a systemwide approach to microeconomics. The systems approach focuses on particular segments of the economy such as consumer spending. (Author/KC)

  9. Regression Equations for Birth Weight Estimation using ...

    African Journals Online (AJOL)

    In this study, Birth Weight has been estimated from anthropometric measurements of hand and foot. Linear regression equations were formed from each of the measured variables. These simple equations can be used to estimate Birth Weight of new born babies, in order to identify those with low birth weight and referred to ...

  10. Singularities in the nonisotropic Boltzmann equation

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

    1987-09-01

    We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

  11. Semigroup methods for evolution equations on networks

    CERN Document Server

    Mugnolo, Delio

    2014-01-01

    This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations.  Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations.      This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...

  12. A Practical Approach to Quadratic Equations.

    Science.gov (United States)

    Light, Peter

    1983-01-01

    The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)

  13. Fourth Power Diophantine Equations in Gaussian Integers

    Indian Academy of Sciences (India)

    25

    Fourth Power Diophantine Equations in Gaussian Integers. 7. 7. U. Schneiders and H.G. Zimmer, The rank of elliptic curves upon quadratic extensions,. Computational Number Theory (A. Petho, H.C. Williams,H.G. Zimmer, eds.), de Gruyter,. 239-260, Berlin, (1991). 8. Y. Suzuki, On the Diophantine Equation 2aX4 + 2bY 4 ...

  14. Compatible taper equation for loblolly pine

    Science.gov (United States)

    J. P. McClure; R. L. Czaplewski

    1986-01-01

    Cao's compatible, segmented polynomial taper equation (Q. V. Cao, H. E. Burkhart, and T. A. Max. For. Sci. 26: 71-80. 1980) is fitted to a large loblolly pine data set from the southeastern United States. Equations are presented that predict diameter at a given height, height to a given top diameter, and volume below a given position on the main stem. All...

  15. Operational equations for data in common arrays

    Energy Technology Data Exchange (ETDEWEB)

    Silver, G.L.

    2000-10-01

    A new method for interpolating experimental data by means of the shifting operator was introduced in 1985. This report illustrates new interpolating equations for data in the five-point rectangle and diamond configurations, new measures of central tendency, and new equations for data at the vertices of a cube.

  16. Lie algebras and linear differential equations.

    Science.gov (United States)

    Brockett, R. W.; Rahimi, A.

    1972-01-01

    Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

  17. Backward stochastic differential equations with Young drift

    OpenAIRE

    Diehl, Joscha; Zhang, Jianfeng

    2016-01-01

    We prove via a direct fixpoint argument the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite $p$-variation with $p \\in [1,2)$. An application to the Feynman-Kac representation of semilinear rough partial differential equations is given.

  18. Equipercentile Equating via Data-Imputation Techniques.

    Science.gov (United States)

    Liou, Michelle; Cheng, Philip E.

    1995-01-01

    Different data imputation techniques that are useful for equipercentile equating are discussed, and empirical data are used to evaluate the accuracy of these techniques as compared with chained equipercentile equating. The kernel estimator, the EM algorithm, the EB model, and the iterative moment estimator are considered. (SLD)

  19. Sonar Equations for Planets and Moons

    NARCIS (Netherlands)

    Ainslie, M.A.; Leighton, T.G.

    2015-01-01

    A set of equations to describe the performance of sonar systems, collectively known as the “sonar equations”, was developed during and after the Second World War. These equations assumed that both the sonar equipment and the object to be detected (usually a submarine) would be submerged in one of

  20. Soliton equations solved by the boundary CFT

    OpenAIRE

    Saito, Satoru; Sato, Ryuichi

    2003-01-01

    Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under the influence of the boundary is calculated explicitly and is shown that it is frozen at the Dirichlet limit.