Michaelis - Menten equation for degradation of insoluble substrate
DEFF Research Database (Denmark)
Andersen, Morten; Kari, Jeppe; Borch, Kim
2017-01-01
substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations...... are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass...
Chaudhury, Srabanti; Cherayil, Binny J.
2007-09-01
Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder—modeled by the anomalous diffusion of a particle in a harmonic well—are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme β-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.
Goličnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.
Bezerra, Rui M F; Fraga, Irene; Dias, Albino A
2013-01-01
Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Reexamining Michaelis-Menten Enzyme Kinetics for Xanthine Oxidase
Bassingthwaighte, James B.; Chinn, Tamara M.
2013-01-01
Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…
The Michaelis-Menten-Stueckelberg Theorem
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Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Classical Michaelis-Menten and system theory approach to modeling metabolite formation kinetics.
Popović, Jovan
2004-01-01
When single doses of drug are administered and kinetics are linear, techniques, which are based on the compartment approach and the linear system theory approach, in modeling the formation of the metabolite from the parent drug are proposed. Unlike the purpose-specific compartment approach, the methodical, conceptual and computational uniformity in modeling various linear biomedical systems is the dominant characteristic of the linear system approach technology. Saturation of the metabolic reaction results in nonlinear kinetics according to the Michaelis-Menten equation. The two compartment open model with Michaelis-Menten elimination kinetics is theorethicaly basic when single doses of drug are administered. To simulate data or to fit real data using this model, one must resort to numerical integration. A biomathematical model for multiple dosage regimen calculations of nonlinear metabolic systems in steady-state and a working example with phenytoin are presented. High correlation between phenytoin steady-state serum levels calculated from individual Km and Vmax values in the 15 adult epileptic outpatients and the observed levels at the third adjustment of phenytoin daily dose (r=0.961, p<0.01) were found.
Liu, Biao; Wu, Ranchao; Chen, Liping
2018-04-01
Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.
Pereira, Félix Monteiro; Oliveira, Samuel Conceição
2016-11-01
In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.
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Wenzhen Gan
2013-01-01
Full Text Available This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.
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Kevin John Flynn
2016-09-01
Full Text Available Rectangular hyperbolic type 2 (RHt2; Michaelis-Menten or Monod -like functions are commonly used to describe predation kinetics in plankton models, either alone or together with a prey selectivity algorithm deploying the same half-saturation constant for all prey types referenced to external prey biomass abundance. We present an analysis that indicates that such descriptions are liable to give outputs that are not plausible according to encounter theory. This is especially so for multi-prey type applications or where changes are made to the maximum feeding rate during a simulation. The RHt2 approach also gives no or limited potential for descriptions of events such as true de-selection of prey, effects of turbulence on encounters, or changes in grazer motility with satiation. We present an alternative, which carries minimal parameterisation effort and computational cost, linking allometric algorithms relating prey abundance and encounter rates to a prey-selection function controlled by satiation. The resultant Satiation-Controlled-Encounter-Based (SCEB function provides a flexible construct describing numeric predator-prey interactions with biomass-feedback control of grazing. The SCEB function includes an attack component similar to that in the Holling disk equation but SCEB differs in having only a single (satiation-based handling constant and an explicit maximum grazing rate. We argue that there is no justification for continuing to deploy RHt2 functions to describe plankton predator-prey interactions.
Diffusion influence on Michaelis Menten kinetics: II. The low substrate concentration limit
Kim, Hyojoon; Shin, Kook Joe
2007-02-01
The diffusion-influenced Michaelis-Menten kinetics in the low substrate concentration limit is studied in one and three dimensions. For the initial pair distribution of enzyme and substrate, we obtain the exact analytical results. We find that at short times the diffusion effect can make the reaction rate faster. The concentration deviations of the substrate and enzyme show t-1/2 and t-3/2 power-law behaviours in one and three dimensions, respectively, at long times. On the other hand, the average lifetime of the intermediate is independent of the initial state in one dimension, while it depends on the initial state in three dimensions. The ultimate production yield approaches unity in one dimension but it reaches a different value depending on other parameters in three dimensions. We also obtain the analytical results for the initial random distribution.
Diffusion influence on Michaelis-Menten kinetics: II. The low substrate concentration limit
International Nuclear Information System (INIS)
Kim, Hyojoon; Shin, Kook Joe
2007-01-01
The diffusion-influenced Michaelis-Menten kinetics in the low substrate concentration limit is studied in one and three dimensions. For the initial pair distribution of enzyme and substrate, we obtain the exact analytical results. We find that at short times the diffusion effect can make the reaction rate faster. The concentration deviations of the substrate and enzyme show t -1/2 and t -3/2 power-law behaviours in one and three dimensions, respectively, at long times. On the other hand, the average lifetime of the intermediate is independent of the initial state in one dimension, while it depends on the initial state in three dimensions. The ultimate production yield approaches unity in one dimension but it reaches a different value depending on other parameters in three dimensions. We also obtain the analytical results for the initial random distribution
Gejl, Michael; Rungby, Jørgen; Brock, Birgitte; Gjedde, Albert
2014-08-01
Glucagon-like peptide-1 (GLP-1) is a potent insulinotropic incretin hormone with both pancreatic and extrapancreatic effects. Studies of GLP-1 reveal significant effects in regions of brain tissue that regulate appetite and satiety. GLP-1 mimetics are used for the treatment of type 2 diabetes mellitus. GLP-1 interacts with peripheral functions in which the autonomic nervous system plays an important role, and emerging pre-clinical findings indicate a potential neuroprotective role of the peptide, for example in models of stroke and in neurodegenerative disorders. A century ago, Leonor Michaelis and Maud Menten described the steady-state enzyme kinetics that still apply to the multiple receptors, transporters and enzymes that define the biochemical reactions of the brain, including the glucose-dependent impact of GLP-1 on blood-brain glucose transfer and metabolism. This MiniReview examines the potential of GLP-1 as a molecule of interest for the understanding of brain energy metabolism and with reference to the impact on brain metabolism related to appetite and satiety regulation, stroke and neurodegenerative disorders. These effects can be understood only by reference to the original formulation of the Michaelis-Menten equation as applied to a chain of kinetically controlled steps. Indeed, the effects of GLP-1 receptor activation on blood-brain glucose transfer and brain metabolism of glucose depend on the glucose concentration and relative affinities of the steps both in vitro and in vivo, as in the pancreas. © 2014 Nordic Association for the Publication of BCPT (former Nordic Pharmacological Society).
Stability estimation of autoregulated genes under Michaelis-Menten-type kinetics
Arani, Babak M. S.; Mahmoudi, Mahdi; Lahti, Leo; González, Javier; Wit, Ernst C.
2018-06-01
Feedback loops are typical motifs appearing in gene regulatory networks. In some well-studied model organisms, including Escherichia coli, autoregulated genes, i.e., genes that activate or repress themselves through their protein products, are the only feedback interactions. For these types of interactions, the Michaelis-Menten (MM) formulation is a suitable and widely used approach, which always leads to stable steady-state solutions representative of homeostatic regulation. However, in many other biological phenomena, such as cell differentiation, cancer progression, and catastrophes in ecosystems, one might expect to observe bistable switchlike dynamics in the case of strong positive autoregulation. To capture this complex behavior we use the generalized family of MM kinetic models. We give a full analysis regarding the stability of autoregulated genes. We show that the autoregulation mechanism has the capability to exhibit diverse cellular dynamics including hysteresis, a typical characteristic of bistable systems, as well as irreversible transitions between bistable states. We also introduce a statistical framework to estimate the kinetics parameters and probability of different stability regimes given observational data. Empirical data for the autoregulated gene SCO3217 in the SOS system in Streptomyces coelicolor are analyzed. The coupling of a statistical framework and the mathematical model can give further insight into understanding the evolutionary mechanisms toward different cell fates in various systems.
Biphasic character of ribosomal translocation and non-Michaelis-Menten kinetics of translation
Xie, Ping
2014-12-01
We study theoretically the kinetics of mRNA translocation in the wild-type (WT) Escherichia coli ribosome, which is composed of a small 30 S and large 50 S subunit, and the ribosomes with mutations to some intersubunit bridges such as B1a, B4, B7a, and B8. The theoretical results reproduce well the available in vitro experimental data on the biphasic kinetics of the forward mRNA translocation catalyzed by elongation factor G (EF-G) hydrolyzing GTP, which can be best fit by the sum of two exponentials, and the monophasic kinetics of the spontaneous reverse mRNA translocation in the absence of the elongation factor, which can be best fit by a single-exponential function, in both the WT and mutant ribosomes. We show that both the mutation-induced increase in the maximal rate of the slow phase for the forward mRNA translocation and that in the rate of the spontaneous reverse mRNA translocation result from a reduction in the intrinsic energy barrier to resist the rotational movements between the two subunits, giving the same degree of increase in the two rates. The mutation-induced increase in the maximal rate of the fast phase for the forward mRNA translocation results mainly from the increase in the rate of the ribosomal unlocking, a conformational change in the ribosome that widens the mRNA channel for the mRNA translocation to take place, which could be partly due to the effect of the mutation on the intrasubunit 30S head rotation. Moreover, we study the translation rate of the WT and mutant ribosomes. It is shown that the translation rate versus the concentration of EF-G-GTP does not follow the Michaelis-Menten (MM) kinetics, which is in sharp contrast to the general property of other enzymes that the rate of the enzymatic reaction versus the concentration of a substrate follows the MM kinetics. The physical origin of this non-MM kinetics for the ribosome is revealed.
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A. Elhassanein
2014-06-01
Full Text Available This paper introduced a stochastic discretized version of the modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting. The dynamical behavior of the proposed model was investigated. The existence and stability of the equilibria of the skeleton were studied. Numerical simulations were employed to show the model's complex dynamics by means of the largest Lyapunov exponents, bifurcations, time series diagrams and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon were also discussed via simulation.
Yu, Xiao-Zhang; Zhang, Xue-Hong
2016-07-01
Hydroponic experiments were conducted with different species of plants (rice, maize, soybean and willow) exposed to ferri-cyanide to investigate the half-saturation constant (K M ) and the maximal metabolic capacity (v max ) involved in phyto-assimilation. Three varieties for each testing species were collected from different origins. Measured concentrations show that the uptake rates responded biphasically to ferri-cyanide treatments by showing increases linearly at low and almost constant at high concentrations from all treatments, indicating that phyto-assimilation of ferri-cyanide followed the Michaelis-Menten kinetics. Using non-linear regression, the highest v max was by rice, followed by willows. The lowest v max was found for soybean. All plants, except maize (DY26) and rice (XJ12), had a similar K M value, suggesting the same enzyme was active in phyto-assimilation of ferri-cyanide. Transcript level, by real-time quantitative PCR, of enzymes involved in degradation of cyanides showed that the analyzed genes were differently expressed during different cyanides exposure. The expression of CAS and ST genes responded positively to KCN exposure, suggesting that β-CAS and ST pathways were two possible pathways for cyanide detoxification in rice. The transcript level of NIT and ASPNASE genes also showed a remarkable up-regulation to KCN, implying the contribution to the pool of amino acid aspartate, which is an end product of CN metabolism. Up-regulation of GS genes suggests that acquisition of ammonium released from cyanide degradation may be an additional nitrogen source for plant nutrition. Results also revealed that the expressions of these genes, except for GS, were relatively constant during iron cyanide exposure, suggesting that they are likely metabolized by plants through a non-defined pathway rather than the β-CAS pathway.
Gattu, Srikanth; Crihfield, Cassandra L; Holland, Lisa A
2017-01-03
Phospholipid nanogels enhance the stability and performance of the exoglycosidase enzyme neuraminidase and are used to create a fixed zone of enzyme within a capillary. With nanogels, there is no need to covalently immobilize the enzyme, as it is physically constrained. This enables rapid quantification of Michaelis-Menten constants (K M ) for different substrates and ultimately provides a means to quantify the linkage (i.e., 2-3 versus 2-6) of sialic acids. The fixed zone of enzyme is inexpensive and easily positioned in the capillary to support electrophoresis mediated microanalysis using neuraminidase to analyze sialic acid linkages. To circumvent the limitations of diffusion during static incubation, the incubation period is reproducibly achieved by varying the number of forward and reverse passes the substrate makes through the stationary fixed zone using in-capillary electrophoretic mixing. A K M value of 3.3 ± 0.8 mM (V max , 2100 ± 200 μM/min) was obtained for 3'-sialyllactose labeled with 2-aminobenzoic acid using neuraminidase from Clostridium perfringens that cleaves sialic acid monomers with an α2-3,6,8,9 linkage, which is similar to values reported in the literature that required benchtop analyses. The enzyme cleaves the 2-3 linkage faster than the 2-6, and a K M of 2 ± 1 mM (V max , 400 ± 100 μM/min) was obtained for the 6'-sialyllactose substrate. An alternative neuraminidase selective for 2-3 sialic acid linkages generated a K M value of 3 ± 2 mM (V max , 900 ± 300 μM/min) for 3'-sialyllactose. With a knowledge of V max , the method was applied to a mixture of 2-3 and 2-6 sialyllactose as well as 2-3 and 2-6 sialylated triantennary glycan. Nanogel electrophoresis is an inexpensive, rapid, and simple alternative to current technologies used to distinguish the composition of 3' and 6' sialic acid linkages.
More Nuts and Bolts of Michaelis-Menten Enzyme Kinetics
Lechner, Joseph H.
2011-01-01
Several additions to a classroom activity are proposed in which an "enzyme" (the student) converts "substrates" (nut-bolt assemblies) into "products" (separated nuts and bolts) by unscrewing them. (Contains 1 table.)
Use of Mushroom Tyrosinase to Introduce Michaelis-Menten Enzyme Kinetics to Biochemistry Students
Flurkey, William H.; Inlow, Jennifer K.
2017-01-01
An inexpensive enzyme kinetics laboratory exercise for undergraduate biochemistry students is described utilizing tyrosinase from white button mushrooms. The exercise can be completed in one or two three-hour lab sessions. The optimal amounts of enzyme, substrate (catechol), and inhibitor (kojic acid) are first determined, and then kinetic data is…
Stability in a diffusive food chain model with Michaelis-Menten functional response
DEFF Research Database (Denmark)
Lin, Zhigui; Pedersen, Michael
2004-01-01
This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...... for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All...
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B. Godongwana
2010-01-01
Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.
International Nuclear Information System (INIS)
Bardo, R.D.; Wolfsberg, M.
1977-01-01
The wave equation for a nonlinear polyatomic molecule is formulated in molecule-fixed coordinates by a method originally due to Hirschfelder and Wigner. Application is made to a triatomic molecule, and the wave equation is explicitly presented in a useful molecule-fixed coordinate system. The formula for the adiabatic correction to the Born--Oppenheimer approximation for a triatomic molecule is obtained. The extension of the present formulation to larger polyatomic molecules is pointed out. Some terms in the triatomic molecule wave equation are discussed in detail
Interpreting experimental data on egg production--applications of dynamic differential equations.
France, J; Lopez, S; Kebreab, E; Dijkstra, J
2013-09-01
This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.
LeMesurier, Brenton
2012-01-01
A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.
Effective electronic-only Kohn–Sham equations for the muonic molecules
Rayka, Milad; Goli, Mohammad; Shahbazian, Shant
A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the Nuclear-Electronic Orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing muon vibration, which are optimized during the solution of the EKS equations making muon KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a duality between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential maybe derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding muonium atom to ferrocene. In line with previous computational studies, from the six possible species the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.
Effective electronic-only Kohn-Sham equations for the muonic molecules.
Rayka, Milad; Goli, Mohammad; Shahbazian, Shant
2018-03-28
A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.
Single molecule diffusion and the solution of the spherically symmetric residence time equation.
Agmon, Noam
2011-06-16
The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society
Choi, I.-Y.; Lee, S.-P.; Kim, S.-G.; Gruetter, R.
2001-01-01
Glucose is the major substrate that sustains normal brain function. When the brain glucose concentration approaches zero, glucose transport across the blood-brain barrier becomes rate limiting for metabolism during, for example, increased metabolic activity and hypoglycemia. Steady-state brain glucose concentrations in α-chloralose anesthetized rats were measured noninvasively as a function of plasma glucose. The relation between brain and plasma glucose was linear at 4.5 to 30 mmol/L plasma ...
DEFF Research Database (Denmark)
Jensen, Michael Gejl; Rungby, Jørgen; Brock, Birgitte
2014-01-01
Glucagon-like peptide-1 (GLP-1) is a potent insulinotropic incretin hormone with pancreatic and extrapancreatic effects. Studies reveal significant effects in regions of brain tissue that regulate appetite and satiety. The effects cause that mimetics of GLP-1 serves as treatment of type 2 diabete...
Her, Cheenou; Alonzo, Aaron P.; Vang, Justin Y.; Torres, Ernesto; Krishnan, V. V.
2015-01-01
Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the…
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Zhang, Keda; Abraham, Michael H; Liu, Xiangli
2017-04-15
Experimental values of permeability coefficients, as log K p , of chemical compounds across human skin were collected by carefully screening the literature, and adjusted to 37°C for the effect of temperature. The values of log K p for partially ionized acids and bases were separated into those for their neutral and ionic species, forming a total data set of 247 compounds and species (including 35 ionic species). The obtained log K p values have been regressed against Abraham solute descriptors to yield a correlation equation with R 2 =0.866 and SD=0.432 log units. The equation can provide valid predictions for log K p of neutral molecules, ions and ionic species, with predictive R 2 =0.858 and predictive SD=0.445 log units calculated by the leave-one-out statistics. The predicted log K p values for Na + and Et 4 N + are in good agreement with the observed values. We calculated the values of log K p of ketoprofen as a function of the pH of the donor solution, and found that log K p markedly varies only when ketoprofen is largely ionized. This explains why models that neglect ionization of permeants still yield reasonable statistical results. The effect of skin thickness on log K p was investigated by inclusion of two indicator variables, one for intermediate thickness skin and one for full thickness skin, into the above equation. The newly obtained equations were found to be statistically very close to the above equation. Therefore, the thickness of human skin used makes little difference to the experimental values of log K p . Copyright © 2017 Elsevier B.V. All rights reserved.
Boltzmann equation analysis of electron-molecule collision cross sections in water vapor and ammonia
International Nuclear Information System (INIS)
Yousfi, M.; Benabdessadok, M.D.
1996-01-01
Sets of electron-molecule collision cross sections for H 2 O and NH 3 have been determined from a classical technique of electron swarm parameter unfolding. This deconvolution method is based on a simplex algorithm using a powerful multiterm Boltzmann equation analysis established in the framework of the classical hydrodynamic approximation. It is well adapted for the simulation of the different classes of swarm experiments (i.e., time resolved, time of flight, and steady state experiments). The sets of collision cross sections that exist in the literature are reviewed and analyzed. Fitted sets of cross sections are determined for H 2 O and NH 3 which exhibit features characteristic of polar molecules such as high rotational excitation collision cross sections. The hydrodynamic swarm parameters (i.e., drift velocity, longitudinal and transverse diffusion coefficients, ionization and attachment coefficients) calculated from the fitted sets are in excellent agreement with the measured ones. These sets are finally used to calculate the transport and reaction coefficients needed for discharge modeling in two cases of typical gas mixtures for which experimental swarm data are very sparse or nonexistent (i.e., flue gas mixtures and gas mixtures for rf plasma surface treatment). copyright 1996 American Institute of Physics
Coffey, W T; Titov, S V
2003-01-01
A theory of orientational relaxation for the inertial rotational Brownian motion of a symmetric top molecule is developed using the Langevin equation rather than the Fokker-Planck equation. The infinite hierarchy of differential-recurrence relations for the orientational correlation functions for the relaxation behaviour is derived by averaging the corresponding Euler-Langevin equations. The solution of this hierarchy is obtained using matrix continued fractions allowing the calculation of the correlation times and the spectra of the orientational correlation functions for typical values of the model parameters.
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-02-01
The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and HTQ methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke's atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world's most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schrödinger equation of general atoms and molecules.
Rayka, Milad; Goli, Mohammad; Shahbazian, Shant
2018-02-07
An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.
Piephoff, D Evan; Cao, Jianshu
2018-04-23
We recently developed a pathway analysis framework (paper 1) for describing single-molecule kinetics for renewal (i.e., memoryless) processes based on the decomposition of a kinetic scheme into generic structures. In our approach, waiting time distribution functions corresponding to such structures are expressed in terms of self-consistent pathway solutions and concatenated to form measurable probability distribution functions (PDFs), affording a simple way to decompose and recombine a network. Here, we extend this framework to nonrenewal processes, which involve correlations between events, and employ it to formulate waiting time PDFs, including the first-passage time PDF, for a general kinetic network model. Our technique does not require the assumption of Poissonian kinetics, permitting a more general kinetic description than the usual rate approach, with minimal topological restrictiveness. To demonstrate the usefulness of this technique, we provide explicit calculations for our general model, which we adapt to two generic schemes for single-enzyme turnover with conformational interconversion. For each generic scheme, wherein the intermediate state(s) need not undergo Poissonian decay, the functional dependence of the mean first-passage time on the concentration of an external substrate is analyzed. When conformational detailed balance is satisfied, the enzyme turnover rate (related to the mean first-passage time) reduces to the celebrated Michaelis-Menten functional form, consistent with our previous work involving a similar scheme with all rate processes, thereby establishing further generality to this intriguing result. Our framework affords a general and intuitive approach for evaluating measurable waiting time PDFs and their moments, making it a potentially useful kinetic tool for a wide variety of single-molecule processes.
Ikeguchi, Mitsunori; Doi, Junta
1995-09-01
The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.
Hasegawa, Chihiro; Duffull, Stephen B
2018-02-01
Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-05-21
The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.
Integral equations for free-molecule ow in MEMS: recent advancements
Directory of Open Access Journals (Sweden)
Fedeli Patrick
2017-03-01
Full Text Available We address a Boundary Integral Equation (BIE approach for the analysis of gas dissipation in near-vacuum for Micro Electro Mechanical Systems (MEMS. Inspired by an analogy with the radiosity equation in computer graphics, we discuss an efficient way to compute the visible domain of integration. Moreover, we tackle the issue of near singular integrals by developing a set of analytical formulas for planar polyhedral domains. Finally a validation with experimental results taken from the literature is presented.
Energy Technology Data Exchange (ETDEWEB)
Cao, Hui, E-mail: yccaoh@hotmail.com; Zhang, Mingdao; Tao, Tao; Song, Mingxia; Zhang, Chaozhi, E-mail: chzhzhang@sohu.com [Jiangsu Key Laboratory of Atmospheric Environment Monitoring and Pollution Control, School of Environmental Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu (China)
2015-02-28
We have combined the quantum dissipative theory and the time dependent density functional theory to perform the first principle calculation of laser induced quantum dynamical electron transport through a molecule weak bridged to two electrodes. The formalism of hierarchical equations of motion based on non-equilibrium Green’s function theory has been taken in this work. Numerical simulations of optical absorption spectra of benzene, laser induced transient current without and with bias, charge pumping effect, as well as the spectrum analysis from the current in Au-benzene-Au molecular junction are presented and discussed.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
International Nuclear Information System (INIS)
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-01-01
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
Energy Technology Data Exchange (ETDEWEB)
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti, E-mail: arti@iitm.ac.in [Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036 (India)
2016-08-28
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-01
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Palmer, David S; Mišin, Maksim; Fedorov, Maxim V; Llinas, Antonio
2015-09-08
We report a method to predict physicochemical properties of druglike molecules using a classical statistical mechanics based solvent model combined with machine learning. The RISM-MOL-INF method introduced here provides an accurate technique to characterize solvation and desolvation processes based on solute-solvent correlation functions computed by the 1D reference interaction site model of the integral equation theory of molecular liquids. These functions can be obtained in a matter of minutes for most small organic and druglike molecules using existing software (RISM-MOL) (Sergiievskyi, V. P.; Hackbusch, W.; Fedorov, M. V. J. Comput. Chem. 2011, 32, 1982-1992). Predictions of caco-2 cell permeability and hydration free energy obtained using the RISM-MOL-INF method are shown to be more accurate than the state-of-the-art tools for benchmark data sets. Due to the importance of solvation and desolvation effects in biological systems, it is anticipated that the RISM-MOL-INF approach will find many applications in biophysical and biomedical property prediction.
Maggi, Federico; Riley, William J.
2009-12-01
The theoretical formulation of biological kinetic isotope fractionation often assumes first-order or Michaelis-Menten kinetics, the latter solved under the quasi-steady state assumption. Both formulations lead to a constant isotope fractionation factor, therefore they may return incorrect estimations of isotopic effects and misleading interpretations of isotopic signatures when fractionation is not a steady process. We have analyzed the isotopic signature of denitrification in biogeochemical soil systems by Menyailo and Hungate (2006) in which high and variable 15N-N2O enrichment during N2O production and inverse isotope fractionation during N2O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with Michaelis-Menten kinetics. When Michaelis-Menten kinetics were coupled to Monod kinetics to describe biomass and enzyme dynamics, and the quasi-steady state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observed concentrations, and variable and inverse isotope fractionations. These results imply a substantial revision in modeling isotopic effects, suggesting that steady state kinetics such as first-order, Rayleigh, and classic Michaelis-Menten kinetics should be superseded by transient kinetics in conjunction with biomass and enzyme dynamics.
Illien, Bertrand; Ying, Ruifeng
2009-05-11
New static light scattering (SLS) equations for dilute binary solutions are derived. Contrarily to the usual SLS equations [Carr-Zimm (CZ)], the new equations have no need for the experimental absolute Rayleigh ratio of a reference liquid and solely rely on the ratio of scattered intensities of solutions and solvent. The new equations, which are based on polarizability equations, take into account the usual refractive index increment partial differential n/partial differential rho(2) complemented by the solvent specific polarizability and a term proportional to the slope of the solution density rho versus the solute mass concentration rho(2) (density increment). Then all the equations are applied to 21 (macro)molecules with a wide range of molar mass (0.2equations clearly achieve a better agreement with supplier M values. For macromolecules (M>500 kg mol(-1)), for which the scattered intensity is no longer independent of the scattering angle, the new equations give the same value of the radius of gyration as the CZ equation and consistent values of the second virial coefficient.
(CSTR) and 1-plug flow reactor (PFR)
African Journals Online (AJOL)
Administrator
2010-12-27
Dec 27, 2010 ... 2Department of Chemical Engineering, Obafemi Awolowo University, Ile Ife, Osun State, Nigeria. ... modeled as PFR and described by Michaelis. Menten equation. Designed equations derived from the two equations are used for the reactor sizing of ... Herbivores make a living on cellulose by possessing.
Weatherford, C. A.; Onda, K.; Temkin, A.
1985-01-01
The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.
DETERMINATION OF THE SPECIFIC GROWTH RATE ON ...
African Journals Online (AJOL)
Sewage generation is one of the dense problems Nigerians encounter on daily bases, mostly at the urbanized area where factories and industries are located. This paper is aimed at determining the specific growth rate “K” of biological activities on cassava wastewater during degradation using Michaelis-Menten Equation.
Wang and Li Afr J Tradit Complement Altern Med. (2016) 13(1):99 ...
African Journals Online (AJOL)
PROF ADEWUNMI
It possesses antiseptic, anti-inflammatory, analgesic, anti-cancer and antioxidant ... All experiments on animals were conducted in accordance with and after approval by the ... With the content of gallic acid control as horizontal coordinate and the ... The kinetic constants were calculated based on Michaelis-Menten equation ...
Reboucas, G.F.; Moraes Goncalves, de T.; Martines, M.L.; Azevedo Junior, J.; Koops, W.J.
2008-01-01
This study aimed to calculate new accumulated and daily functions based on the Michaelis-Menten equation to estimate the 305-days production of Gir cows using test day milk yields. Data consisted of 7,412 lactation records of 3,416 Gir cows (Bos indicus) collected from 1987 to 2004 in 51 herds
Nonthermal effect of microwave irradiation on nitrite uptake in Chlamydomonas reinhardtii
International Nuclear Information System (INIS)
Pedrajas, C.; Cotrino, J.
1989-01-01
When cells of the unicellular green alga Chlamydomonas reinhardtii were subjected to microwave irradiation at 2.45 GHz, nitrite uptake kinetics still obeyed the Michaelis-Menten equation, the Km of the process remaining constant, whereas V max increased, which indicates an enhanced nonthermal permeability in irradiated cells. (author)
Force-balance and differential equation for the ground-state electron density in atoms and molecules
International Nuclear Information System (INIS)
Amovilli, C.; March, N.H.; Gal, T.; Nagy, A.
2000-01-01
Holas and March (1995) established a force-balance equation from the many-electron Schroedinger equation. Here, the authors propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example they present the simple case of two-electron systems with different external potentials but with weak electron-electron Coulomb repulsion λe 2 /r 12 . In this case first-order Rayleigh-Schroedinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix γ(r,rprime) in terms of its diagonal density ρ(r) and the density corresponding to λ = 0. This result allows the force-balance equation to be written as a third-order linear, differential homogeneous equation for the ground-state electron density ρ(r). The example of the two-electron Hookean atom is treated: For this case one can also transcend the first-order RS perturbation theory and get exact results for discrete choices of force constants (external potential)
Energy Technology Data Exchange (ETDEWEB)
Maggi, F.M.; Riley, W.J.
2009-06-01
The theoretical formulation of biological kinetic reactions in isotopic applications often assume first-order or Michaelis-Menten-Monod kinetics under the quasi-steady-state assumption to simplify the system kinetics. However, isotopic e ects have the same order of magnitude as the potential error introduced by these simpli cations. Both formulations lead to a constant fractionation factor which may yield incorrect estimations of the isotopic effect and a misleading interpretation of the isotopic signature of a reaction. We have analyzed the isotopic signature of denitri cation in biogeochemical soil systems by Menyailo and Hungate [2006], where high {sup 15}N{sub 2}O enrichment during N{sub 2}O production and inverse isotope fractionation during N{sub 2}O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with the quasi-steady-state Michaelis-Menten-Monod kinetics. When the quasi-steady-state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observations and aided in interpretation of experimental isotopic signatures. These results may imply a substantial revision in using the Rayleigh equation for interpretation of isotopic signatures and in modeling biological kinetic isotope fractionation with first-order kinetics or quasi-steady-state Michaelis-Menten-Monod kinetics.
Weatherford, Charles A.
1993-01-01
One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.
Swartz, Kenneth; Zhang, Yiguan; Valeriote, Frederick; Chen, Ben; Shaw, Jiajiu
2013-12-01
UTL-5g is a novel small-molecule chemoprotector that lowers hepatotoxicity, nephrotoxicity, and myelotoxicity induced by cisplatin through TNF-α inhibition among other factors. As a prelude to investigating the metabolites of UTL-5g, we set out to identify the enzymatic products of UTL-5g under the treatment of both porcine liver esterase (PLE) and rabbit liver esterase (RLE). First, a number of mixtures made by UTL-5g and PLE were incubated at 25°C. At predetermined time points, individual samples were quenched by acetonitrile, vortexed, and centrifuged. The supernatants were then analyzed by reversed-phase HPLC (using a C18 column). The retention times and UV/vis spectra of individual peaks were compared to those of UTL-5g and its two postulated enzymatic products; thus the enzymatic products of UTL-5g were tentatively identified. Secondly, a different HPLC method (providing different retentions times) was used to cross-check and to confirm the identities of the two enzymatic products. Based on the observations, it was concluded that under the treatment of PLE, the major enzymatic products of UTL-5g were 5-methyliosxazole-3-carboxylic acid (ISOX) and 2,4-dichloroaniline (DCA). Treatment of UTL-5g by RLE also provided the same enzymatic products of UTL-5g from esterase. These results indicate that the peptide bond in UTL-5g was cleaved by PLE/RLE. Michaelis-Menten kinetics showed that the Km values of UTL-5g were 2.07mM with PLE and 0.37mM with RLE indicating that UTL-5g had a higher affinity with RLE. In summary, by a simple HPLC approach, we have concluded that the peptide bond in UTL-5g was cleaved by esterase from either porcine liver or rabbit liver in vitro and afforded DCA (at a mole ratio of 1:1) and ISOX. However, further studies are needed in order to determine whether UTL-5g is metabolized by microsomal enzymes to produce ISOX and DCA. Copyright © 2013 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Glushkov, A.V.; Kol'tsova, N.Yu.
1994-01-01
Equations of motion were solved by a modified method in a quasi-particle representation of the density functional taking into account the most important polarization effects, including the so-called 2p-2h two-particle-two-hole interactions. Based on these calculations, spectroscopic data on energies and oscillator strengths of the helium atom (the test computation), carbon monoxide, nitrogen molecule, and ethylene are presented that refine some previously reported experimental and theoretical results. It is shown that in some cases the inclusion of polarization corrections introduced by 2p-2h effects is of basic importance because it provides up to ∼30% contribution to the energies and oscillator strengths. 23 refs., 5 tabs
Ahring, Birgitte K.; Westermann, Peter
1987-01-01
Kinetics of butyrate, acetate, and hydrogen metabolism were determined with butyrate-limited, chemostat-grown tricultures of a thermophilic butyrate-utilizing bacterium together with Methanobacterium thermoautotrophicum and the TAM organism, a thermophilic acetate-utilizing methanogenic rod. Kinetic parameters were determined from progress curves fitted to the integrated form of the Michaelis-Menten equation. The apparent half-saturation constants, Km, for butyrate, acetate, and dissolved hyd...
International Nuclear Information System (INIS)
Choi, B.H.; Poe, R.T.; Tang, K.T.
1978-01-01
The body-fixed (BF) formulation for atom--diatom scatterings is developed to the extent that one can use it to perform accurate close-coupling calculation, without introducing further approximation except truncating a finite basis set of the target molecular wave function, on the same ground as one use the space-fixed (SF) formulation. In this formulation, the coupled differential equations are solved an the boundary conditions matched entirely in the BF coordinate system. A unitary transformation is used to obtain both the coupled differential equation and the boundary condition in BF system system from SF system. All properties of the solution with respect to parity are derived entirely from the transformation, without using the parity eignfunctions of the BF frame. Boundary conditions that yield the scattering (S) matrix and the reactance (R) matrix are presented for each parity in both the far asymptotic region (where the interaction and the centrifugal potentials are both negligible) and the near asymptotic region (where the interaction potential is negligible but the centrifugal potential is not). While our differential equations are the same as those derived by others with different methods, our asymptotic boundary conditions disagree with some existing ones. With a given form of the BF coupled differential equations, the acceptable boundary conditions are discussed
Directory of Open Access Journals (Sweden)
Oldiges Marco
2009-01-01
Full Text Available Abstract Background To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1 experimental measurement of participating molecules, (2 assignment of rate laws to each reaction, and (3 parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem. Results We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1 coarse-grained comparison of the algorithms on all models and (2 fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis. Conclusion A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics
Gerald, II; Rex, E [Brookfield, IL; Klingler, Robert J [Glenview, IL; Rathke, Jerome W [Homer Glen, IL; Diaz, Rocio [Chicago, IL; Vukovic, Lela [Westchester, IL
2009-03-10
A method, apparatus, and system for constructing uniform macroscopic films with tailored geometric assemblies of molecules on the nanometer scale. The method, apparatus, and system include providing starting molecules of selected character, applying one or more force fields to the molecules to cause them to order and condense with NMR spectra and images being used to monitor progress in creating the desired geometrical assembly and functionality of molecules that comprise the films.
Energy Technology Data Exchange (ETDEWEB)
Im, Ji Sun; Yun, Jumi; Kim, Jong Gu [Department of Fine Chemical Engineering and Applied Chemistry, BK21-E2 M, Chungnam National University, Daejeon 305-764 (Korea, Republic of); Bae, Tae-Sung [Department of Fine Chemical Engineering and Applied Chemistry, BK21-E2 M, Chungnam National University, Daejeon 305-764 (Korea, Republic of); Korea Basic Science Institute (KBSI), Jeonju 561-756 (Korea, Republic of); Lee, Young-Seak, E-mail: youngslee@cnu.ac.kr [Department of Fine Chemical Engineering and Applied Chemistry, BK21-E2 M, Chungnam National University, Daejeon 305-764 (Korea, Republic of)
2012-01-15
Glucose-sensing electrodes were constructed from carbon fibers by electrospinning and heat treatment. By controlling the pore size, the specific surface area and pore volume of the electrospun carbon fibers were increased for efficient immobilization of the glucose oxidase. Carbon nanotubes were embedded as an electrically conductive additive to improve the electrical property of the porous carbon fibers. In addition, the surface of the porous carbon fibers was modified with hydrophilic functional groups by direct oxyfluorination to increase the affinity between the hydrophobic carbon surface and the hydrophilic glucose oxidase molecules. The porosity of the carbon fibers was improved significantly with approximately 28- and 35-fold increases in the specific surface area and pore volume, respectively. The number of chemical bonds between carbon and oxygen were increased with higher oxygen content during oxyfluorination based on the X-ray photoelectron spectroscopy results. Glucose sensing was carried out by current voltagram and amperometric methods. A high-performance glucose sensor was obtained with high sensitivity and rapid response time as a result of carbon nanotube addition, physical activation and surface modification. The mechanism of the highly sensitive prepared glucose sensor was modeled by an enzyme kinetics study using the Michaelis-Menten equation.
Thomas, Philipp; Straube, Arthur V.; Grima, Ramon
2011-11-01
It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 14; Issue 4. Molecule Matters – van der Waals Molecules - History and Some Perspectives on Intermolecular Forces. E Arunan. Feature Article Volume 14 Issue 4 April 2009 pp 346-356 ...
International Nuclear Information System (INIS)
Baeck, Kyoung K.; Jeon, Sang Il
2000-01-01
The analytic gradient method for the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) energy has been extended to employ a reduced molecular orbital (MO) space. Not only the innermost core MO s but also some of the outermost virtual MO s can be dropped in the reduced MO space, and a substantial amount of computation time can be reduced without deteriorating the results. In order to study the magnitudes and trends of the effects of the dropped MO s , the geometries and vibrational properties of the ground and excited states of BF, CO, CN, N 2 , AlCl, SiS, P 2 , BCl, AlF, CS, SiO, PN and GeSe are calculated with different sizes of molecular orbital space. The 6-31G and the aug-cc-pVTZ basis sets are employed for all molecules except GeSe for which the 6-311 G and the TZV+f basis sets are used. It is shown that the magnitudes of the drop MO effects are about 0.005 A in bond lengths and about 1% on harmonic frequencies and IR intensities provided that the dropped MO s correspond to (1s), (1s,2s,2p), and (1s,2s,2p,3s,3p) atomic orbitals of the first, the second, and the third row atoms, respectively. The geometries and vibrational properties of the first and the second excited states of HCN and HCN are calculated by using a drastically reduced virtual MO space as well as with the well defined frozen core MO space. The results suggest the possibility of using a very small MO space for qualitative study of valence excited states
Atkins, Peters
2003-01-01
Originally published in 2003, this is the second edition of a title that was called 'the most beautiful chemistry book ever written'. In it, we see the molecules responsible for the experiences of our everyday life - including fabrics, drugs, plastics, explosives, detergents, fragrances, tastes, and sex. With engaging prose Peter Atkins gives a non-technical account of an incredible range of aspects of the world around us, showing unexpected connections, and giving an insight into how this amazing world can be understood in terms of the atoms and molecules from which it is built. The second edition includes dozens of extra molecules, graphical presentation, and an even more accessible and enthralling account of the molecules themselves.
Solomon, Philip M.
1973-01-01
Radioastronomy reveals that clouds between the stars, once believed to consist of simple atoms, contain molecules as complex as seven atoms and may be the most massive objects in our Galaxy. (Author/DF)
Preedy, Victor R
2016-01-01
This book covers the structure and classification of adhesion molecules in relation to signaling pathways and gene expression. It discusses immunohistochemical localization, neutrophil migration, and junctional, functional, and inflammatory adhesion molecules in pathologies such as leukocyte decompression sickness and ischemia reperfusion injury. Highlighting the medical applications of current research, chapters cover diabetes, obesity, and metabolic syndrome; hypoxia; kidney disease; smoking, atrial fibrillation, and heart disease, the brain and dementia; and tumor proliferation. Finally, it looks at molecular imaging and bioinformatics, high-throughput technologies, and chemotherapy.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 12. Molecule Matters - Dinitrogen. A G Samuelson J Jabadurai. Volume 16 Issue 12 ... Author Affiliations. A G Samuelson1 J Jabadurai1. Department of Inroganic and Physical Chemistry, Indian Institute of Science, Bangalore 560 012, India.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 9. Molecule Matters - A Chromium Compound with a Quintuple Bond. K C Kumara Swamy. Feature Article Volume 11 Issue 9 September 2006 pp 72-75. Fulltext. Click here to view fulltext PDF. Permanent link:
Energy Technology Data Exchange (ETDEWEB)
Lee, C G [Michigan Univ., Ann Arbor, MI (United States). Dept. of Chemical Engineering; Kim, C H; Rhee, S K [Korea Inst. of Science and Technology, Taejon (Korea, Republic of). Genetic Engineering Research Inst.
1992-07-01
A mathematical model is described for the simultaneous saccharification and ethanol fermentation (SSF) of sago starch using amyloglycosidase (AMG) and Zymomonas mobilis. By introducing the degree of polymerization (DP) of oligosaccharides produced from sago starch treated with {alpha}-amylase, a series of Michaelis-Menten equations was obtained. After determining kinetic parameters from the results of simple experiments and from the subsite mapping theory, this model was adapted to simulate the SSF process. The results of simulation for SSF are in good agreement with experimental results. (orig.).
Study on kinetics of glucose uptake by some species of plankton
Li, Wenquan; Wang, Xian; Zhang, Yaohua
1993-03-01
The rates of glucose uptake by some species of plankton were determined by3H-glucose tracer method. Experimental results indicated that the observed glucose uptake at natural seawater concentrations by Platymonas subcordiformis and Brachionus plicatilis was principally a metabolic process fitted with the Michaelis-Menten equation in the range of adaptive temperatures. Heterotrophic uptake by Platymonas subcordiformis was mainly dependent on diffusion at high glucose levels. The uptake by Brachionus plicatilis showed active transport even at high glucose levels, indicating its high heterotrophic activity. The uptake rate by Artemia salina was lower, and its V m/K ratio was lower than those of the other two species of plankton.
Solvent 1H/2H isotopic effects in the reaction of the L-Tyrosine oxidation catalyzed by Tyrosinase
International Nuclear Information System (INIS)
Kozlowska, M.; Kanska, M.
2006-01-01
Tyrosinase is well known catalyst in the oxidation of L-Tyrosine to L-DOPA and following oxidation of L-DOPA to dopachinone. The aim of communication is to present the results of studies on the solvent isotopic effects (SIE) in the above reactions for the 1 H/ 2 H in the 3',5' and 2',6' substituted tyrosine. Obtained dependence of the reaction rate on the substrate concentration were applied for optimization of the kinetic parameters, k cat and k cat /K m , in the Michaelis-Menten equation. As a result - better understanding of the L-DOPA creation can be achieved
Phosphotyrosine as a substrate of acid and alkaline phosphatases.
Apostoł, I; Kuciel, R; Wasylewska, E; Ostrowski, W S
1985-01-01
A new spectrophotometric method for following dephosphorylation of phosphotyrosine has been described. The absorption spectra of phosphotyrosine and tyrosine were plotted over the pH range from 3 to 9. The change in absorbance accompanying the conversion of phosphotyrosine to tyrosine was the greatest at 286 nm. The difference absorption coefficients were calculated for several pH values. Dephosphorylation of phosphotyrosine by acid phosphatases from human prostate gland, from wheat germ and potatoes obeys the Michaelis-Menten equation, whereas alkaline phosphatases calf intestine and E. coli are inhibited by excess of substrate.
Kinetics of alcoholic fermentation during the culturing of bakers' yeast
Energy Technology Data Exchange (ETDEWEB)
Franz, B
1961-01-01
A synthesis was made of the effects of various factors on the rate of fermentation by Saccharomyces cerevisiae. The rate obeyed the Michaelis-Menten equation, was independent of the concentration of yeast, was maximal at 20/sup 0/ (0.61 ml ethanol/g dry yeast/h), was not significantly affected between pH 6.5 and 3.0 but declined at 3.0, was inhibited by ethanol at a rate proportional to the concentration squared (at ethanol = 12 volume %, the fermentation rate was practically zero), and was enhanced by the addition of phosphorus when a P-poor yeast was employed.
Senthamarai, R.; Jana Ranjani, R.
2018-04-01
In this paper, a mathematical model of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition has been developed. The model is based on time dependent reaction diffusion equation containing a non -linear term related to non -Michaelis - Menten kinetics of the enzymatic reaction. Solution for the concentration of the substrate has been derived for all values of parameters using the homotopy perturbation method. All the approximate analytic expressions of substrate concentration are compared with simulation results using Scilab/Matlab program. Finally, we have given a satisfactory agreement between them.
A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor
Directory of Open Access Journals (Sweden)
B. Godongwana
2015-01-01
Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Molecule Matters van der Waals Molecules
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 14; Issue 12. Molecule Matters van der Waals Molecules - Noble Gas Clusters are London Molecules! E Arunan. Feature Article Volume 14 Issue 12 December 2009 pp 1210-1222 ...
Interstellar molecules and masers
International Nuclear Information System (INIS)
Nguyen-Q-Rieu; Guibert, J.
1978-01-01
The study of dense and dark clouds, in which hydrogen is mostly in molecular form, became possible since the discovery of interstellar molecules, emitting in the centimeter and millimeter wavelengths. The molecular lines are generally not in local thermal equilibrium (LTE). Their intensity can often be explained by invoking a population inversion mechanism. Maser emission lines due to OH, H 2 O and SiO molecules are among the most intense molecular lines. The H 2 CO molecule, detected in absorption in front of the cold cosmic background radiation of 2.7 K, illustrates the inverse phenomenon, the antimaser absorption. For a radio transition of frequency v, the inversion rate Δn (relative population difference between the upper and lower level) as well as the maser gain can be determined from the radio observations. In the case of the OH lines in the 2 PIsub(3/2), J=3/2 state, the inversion rates approximately 1 to 2% derived from the observations, are comparable with those obtained in the laboratory. The determination of the excitation mechanisms of the masers, through the statistical equilibrium and radiative transfer equations, implies the knowledge of collisional and radiative transition probabilities. A pumping model, which can satisfactorily explain the radio observations of some interstellar OH clouds, will be discussed [fr
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
Teaching lasers to control molecules
International Nuclear Information System (INIS)
Judson, R.S.; Rabitz, H.
1992-01-01
We simulate a method to teach a laser pulse sequences to excite specified molecular states. We use a learning procedure to direct the production of pulses based on ''fitness'' information provided by a laboratory measurement device. Over a series of pulses the algorithm learns an optimal sequence. The experimental apparatus, which consists of a laser, a sample of molecules and a measurement device, acts as an analog computer that solves Schroedinger's equation n/Iexactly, in real time. We simulate an apparatus that learns to excite specified rotational states in a diatomic molecule
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Stochastic models for surface diffusion of molecules
Energy Technology Data Exchange (ETDEWEB)
Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2014-07-28
We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Generalizations of the Toda molecule
Van Velthoven, W. P. G.; Bais, F. A.
1986-12-01
Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).
Molecule Matters van der Waals Molecules
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 7. Molecule Matters van der Waals Molecules - Rg•••HF Complexes are Debye Molecules! E Arunan. Feature Article Volume 15 Issue 7 July 2010 pp 667-674. Fulltext. Click here to view fulltext PDF. Permanent link:
The instability of molecules in laser field and isotope separation
International Nuclear Information System (INIS)
Li, K.
1981-01-01
In the present paper the nonlinear differential equation describing the selective decomposition of a molecule as an unimolecular reaction has be deduced from the usual time dependent semi-classical Schroedinger equation. The selective conditions for the instability of a molecule are discussed. The thresholds of the required laser intensities for ICl and HCl diatomic molecules are estimated respectively, where on type of isotope molecules ought to be decomposed for hundred per cent in a laser pulse for different pulse widths. And possibly selective decomposition of the molecule without permanent dipole moment by Raman process is also discussed briefly. (orig.)
Optimization of enzyme parameters for fermentative production of biorenewable fuels and chemicals
Directory of Open Access Journals (Sweden)
Ping Liu
2012-10-01
Full Text Available Microbial biocatalysts such as Escherichia coli and Saccharomyces cerevisiae have been extensively subjected to Metabolic Engineering for the fermentative production of biorenewable fuels and chemicals. This often entails the introduction of new enzymes, deletion of unwanted enzymes and efforts to fine-tune enzyme abundance in order to attain the desired strain performance. Enzyme performance can be quantitatively described in terms of the Michaelis-Menten type parameters Km, turnover number kcat and Ki, which roughly describe the affinity of an enzyme for its substrate, the speed of a reaction and the enzyme sensitivity to inhibition by regulatory molecules. Here we describe examples of where knowledge of these parameters have been used to select, evolve or engineer enzymes for the desired performance and enabled increased production of biorenewable fuels and chemicals. Examples include production of ethanol, isobutanol, 1-butanol and tyrosine and furfural tolerance. The Michaelis-Menten parameters can also be used to judge the cofactor dependence of enzymes and quantify their preference for NADH or NADPH. Similarly, enzymes can be selected, evolved or engineered for the preferred cofactor preference. Examples of exporter engineering and selection are also discussed in the context of production of malate, valine and limonene.
Chen, Xiaojun; Chen, Zixuan; Zhu, Jinwei; Xu, Chenbin; Yan, Wei; Yao, Cheng
2011-10-01
A new kind of gold nanoparticles/self-doped polyaniline nanofibers (Au/SPAN) with grooves has been prepared for the immobilization of horseradish peroxidase (HRP) on the surface of glassy carbon electrode (GCE). The ratio of gold in the composite nanofibers was up to 64%, which could promote the conductivity and biocompatibility of SPAN and increase the immobilized amount of HRP molecules greatly. The electrode exhibits enhanced electrocatalytic activity in the reduction of H(2)O(2) in the presence of the mediator hydroquinone (HQ). The effects of concentration of HQ, solution pH and the working potential on the current response of the modified electrode toward H(2)O(2) were optimized to obtain the maximal sensitivity. The proposed biosensor exhibited a good linear response in the range from 10 to 2000 μM with a detection limit of 1.6 μM (S/N=3) under the optimum conditions. The response showed Michaelis-Menten behavior at larger H(2)O(2) concentrations, and the apparent Michaelis-Menten constant K(m) was estimated to be 2.21 mM. The detection of H(2)O(2) concentration in real sample showed acceptable accuracy with the traditional potassium permanganate titration. Copyright © 2011 Elsevier B.V. All rights reserved.
OPTIMIZATION OF ENZYME PARAMETERS FOR FERMENTATIVE PRODUCTION OF BIORENEWABLE FUELS AND CHEMICALS
Directory of Open Access Journals (Sweden)
Laura R. Jarboe
2012-10-01
Full Text Available Microbial biocatalysts such as Escherichia coli and Saccharomyces cerevisiae have been extensively subjected to Metabolic Engineering for the fermentative production of biorenewable fuels and chemicals. This often entails the introduction of new enzymes, deletion of unwanted enzymes and efforts to fine-tune enzyme abundance in order to attain the desired strain performance. Enzyme performance can be quantitatively described in terms of the Michaelis-Menten type parameters Km, turnover number kcat and Ki, which roughly describe the affinity of an enzyme for its substrate, the speed of a reaction and the enzyme sensitivity to inhibition by regulatory molecules. Here we describe examples of where knowledge of these parameters have been used to select, evolve or engineer enzymes for the desired performance and enabled increased production of biorenewable fuels and chemicals. Examples include production of ethanol, isobutanol, 1-butanol and tyrosine and furfural tolerance. The Michaelis-Menten parameters can also be used to judge the cofactor dependence of enzymes and quantify their preference for NADH or NADPH. Similarly, enzymes can be selected, evolved or engineered for the preferred cofactor preference. Examples of exporter engineering and selection are also discussed in the context of production of malate, valine and limonene.
Energy Technology Data Exchange (ETDEWEB)
Grimes, R.M.
1986-11-01
To further understanding of gas phase collision dynamics involving electronically-excited molecules, a fully quantum mechanical study of He + H/sub 2/(B /sup 1/..sigma../sub u//sup +/) was undertaken. Iterative natural orbital configuration interaction (CI) calculations were performed to obtain the interaction potential between He and H/sub 2/(B /sup 1/..sigma../sub u//sup +/). The potential energy surface (PES) is highly anisotropic and has a van der Waals well of about 0.03 eV for C/sub 2v/ approach. Avoided PES crossings occur with He + H/sub 2/(E,F /sup 1/..sigma../sub g//sup +/) and with He + H/sub 2/(X /sup 1/..sigma../sub g//sup +/) and cause a local maximum and a deep minimum in the He + H/sub 2/(B /sup 1/..sigma../sub u//sup +/) PES, respectively. The crossing with He + H/sub 2/(X /sup 1/..sigma../sub g//sup +/) provides a mechanism for fluorescence quenching. The computed CI energies were combined with previous multi-reference double excitation CI calculations and fit with analytic functions for convenience in scattering calculations. Accurate dipole polarizabilities and quadrupole moment of H/sub 2/(B /sup 1/..sigma../sub u//sup +/) were computed for use in the multipole expansion, which is the analytic form of the long-range PES. 129 refs., 28 figs., 35 tabs.
Taukoorah, Urmeela; Mahomoodally, M. Fawzi
2016-01-01
Aloe vera gel (AVG) is traditionally used in the management of diabetes, obesity, and infectious diseases. The present study aimed to investigate the inhibitory potential of AVG against α-amylase, α-glucosidase, and pancreatic lipase activity in vitro. Enzyme kinetic studies using Michaelis-Menten (K m) and Lineweaver-Burk equations were used to establish the type of inhibition. The antioxidant capacity of AVG was evaluated for its ferric reducing power, 2-diphenyl-2-picrylhydrazyl hydrate scavenging ability, nitric oxide scavenging power, and xanthine oxidase inhibitory activity. The glucose entrapment ability, antimicrobial activity, and total phenolic, flavonoid, tannin, and anthocyanin content were also determined. AVG showed a significantly higher percentage inhibition (85.56 ± 0.91) of pancreatic lipase compared to Orlistat. AVG was found to increase the Michaelis-Menten constant and decreased the maximal velocity (V max) of lipase, indicating mixed inhibition. AVG considerably inhibits glucose movement across dialysis tubes and was comparable to Arabic gum. AVG was ineffective against the tested microorganisms. Total phenolic and flavonoid contents were 66.06 ± 1.14 (GAE)/mg and 60.95 ± 0.97 (RE)/mg, respectively. AVG also showed interesting antioxidant properties. The biological activity observed in this study tends to validate some of the traditional claims of AVG as a functional food. PMID:26880905
Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation.
Directory of Open Access Journals (Sweden)
Andrea Ciliberto
2007-03-01
Full Text Available In metabolic networks, metabolites are usually present in great excess over the enzymes that catalyze their interconversion, and describing the rates of these reactions by using the Michaelis-Menten rate law is perfectly valid. This rate law assumes that the concentration of enzyme-substrate complex (C is much less than the free substrate concentration (S0. However, in protein interaction networks, the enzymes and substrates are all proteins in comparable concentrations, and neglecting C with respect to S0 is not valid. Borghans, DeBoer, and Segel developed an alternative description of enzyme kinetics that is valid when C is comparable to S0. We extend this description, which Borghans et al. call the total quasi-steady state approximation, to networks of coupled enzymatic reactions. First, we analyze an isolated Goldbeter-Koshland switch when enzymes and substrates are present in comparable concentrations. Then, on the basis of a real example of the molecular network governing cell cycle progression, we couple two and three Goldbeter-Koshland switches together to study the effects of feedback in networks of protein kinases and phosphatases. Our analysis shows that the total quasi-steady state approximation provides an excellent kinetic formalism for protein interaction networks, because (1 it unveils the modular structure of the enzymatic reactions, (2 it suggests a simple algorithm to formulate correct kinetic equations, and (3 contrary to classical Michaelis-Menten kinetics, it succeeds in faithfully reproducing the dynamics of the network both qualitatively and quantitatively.
Diatomic Molecules Effective Potential for an Harmonic Oscillator ...
African Journals Online (AJOL)
A model anharmonic potential was considered and was used in the Schrödinger time independent wave equation to describe a carbon monoxide molecule. Central difference scheme was used in approximating the derivative term in the Schrödinger equation leading to a tri-diagonal band system of equation. The method of ...
Kinetic equation of heterogeneous catalytic isotope exchange
Energy Technology Data Exchange (ETDEWEB)
Trokhimets, A I [AN Belorusskoj SSR, Minsk. Inst. Fiziko-Organicheskoj Khimii
1979-12-01
A kinetic equation is derived for the bimolecular isotope exchange reaction between AXsub(n)sup(*) and BXsub(m)sup(o), all atoms of element X in each molecule being equivalent. The equation can be generalized for homogeneous and heterogeneous catalytic isotope exchange.
Some aspects of equations of state
International Nuclear Information System (INIS)
Frisch, H.L.
1979-02-01
Some elementary properties of the equation of state of molecules repulsing each other as point centers of force are developed briefly. An inequality for the Lennard--Jones gas is presented. The scaled particle theory equation of state of hard spheres is also reviewed briefly. Means of possibly applying these concepts to represent thermodynamic data on model detonating gases are suggested
Wave equations for pulse propagation
International Nuclear Information System (INIS)
Shore, B.W.
1987-01-01
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
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
A Biochemist's View of Ecosystem Rates and their Response to Changing Temperature
Arcus, V. L.
2017-12-01
Enzyme kinetics lie at the heart of biochemistry and the Michaelis-Menten equation that defines the relationship between substrate and rate is over 100 years old. About 80 years ago Eyring and Polyani formulated Transistion State Theory (TST) which describes the temperature-dependence of chemical reaction rates and the precise relationship between activation energy and the rate. TST provided a robust theoretical foundation for the Arrhenius equation and together, these equations are the foundation equations for the biochemist. Can these equations provide any insights into rates at larger scales, such as organism growth rates and those rates that interest ecosystem scientists (e.g. heterotrophic respiration, gross primary production)? Let us begin by considering a microbial cell. Microbial growth (i.e. cell division) requires the coordinated kinetics of thousands of enzymes including DNA/RNA polymerases, ribosomes, biosynthetic enzymes - all under a regime of highly complex regulatory effects. There is no a priori reason to expect that Michaelis-Menten kinetics and TST will adequately describe this vastly complex process. Indeed, Lloyd and Taylor showed 23 years ago that soil respiration is not well described by the Arrhenius function. More recently, Heskel and colleagues showed that leaf respiration is also not well described by the Arrhenius function. It is the same case for rates of photosynthesis. Despite this failure of the basic equations of biochemistry to map to biological rates at greater scales, what insights can biochemistry provide to ecosystem science? As nearly all of biological metabolism is mediated through enzyme kinetics, I will begin with the Michaelis-Menten equation under regimes of low and high substrate concentrations. This simplified view can provide surprising insights into processes at larger scales. I will also consider the relationship between the activation energy and the reaction rate. Many, many ecosystem-rate papers focus on the
Multiphoton dissociation of polyatomic molecules
International Nuclear Information System (INIS)
Schulz, P.A.
1979-10-01
The dynamics of infrared multiphoton excitation and dissociation of SF 6 was investigated under collision free conditions by a crossed laser-molecular beam method. In order to understand the excitation mechanism and to elucidate the requirements of laser intensity and energy fluence, a series of experiments were carried out to measure the dissociation yield dependences on energy fluence, vibrational temperature of SF 6 , the pulse duration of the CO 2 laser and the frequency in both one and two laser experiments. Translational energy distributions of the SF 5 dissociation product measured by time of flight and angular distributions and the dissociation lifetime of excited SF 6 as inferred from the observation of secondary dissociation of SF 5 into SF 4 and F during the laser pulse suggest that the dynamics of dissociation of excited molecules is dominated by complete energy randomization and rapid intramolecular energy transfer on a nanosecond timescale, and can be adequately described by RRKM theory. An improved phenomenological model including the initial intensity dependent excitation, a rate equation describing the absorption and stimulated emission of single photons, and the unimolecular dissociation of excited molecules is constructed based on available experimental results. The model shows that the energy fluence of the laser determines the excitation of molecules in the quasi-continuum and the excess energy with which molecules dissociate after the laser pulse. The role played by the laser intensity in multiphoton dissociation is more significant than just that of overcoming the intensity dependent absorption in the lowest levels. 63 references
Ordinary differential equation for local accumulation time.
Berezhkovskii, Alexander M
2011-08-21
Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics
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
Formation of Ultracold Molecules
Energy Technology Data Exchange (ETDEWEB)
Cote, Robin [Univ. of Connecticut, Storrs, CT (United States)
2016-01-28
Advances in our ability to slow down and cool atoms and molecules to ultracold temperatures have paved the way to a revolution in basic research on molecules. Ultracold molecules are sensitive of very weak interactions, even when separated by large distances, which allow studies of the effect of those interactions on the behavior of molecules. In this program, we have explored ways to form ultracold molecules starting from pairs of atoms that have already reached the ultracold regime. We devised methods that enhance the efficiency of ultracold molecule production, for example by tuning external magnetic fields and using appropriate laser excitations. We also investigates the properties of those ultracold molecules, especially their de-excitation into stable molecules. We studied the possibility of creating new classes of ultra-long range molecules, named macrodimers, thousand times more extended than regular molecules. Again, such objects are possible because ultra low temperatures prevent their breakup by collision. Finally, we carried out calculations on how chemical reactions are affected and modified at ultracold temperatures. Normally, reactions become less effective as the temperature decreases, but at ultracold temperatures, they can become very effective. We studied this counter-intuitive behavior for benchmark chemical reactions involving molecular hydrogen.
Determining "small parameters" for quasi-steady state
Goeke, Alexandra; Walcher, Sebastian; Zerz, Eva
2015-08-01
For a parameter-dependent system of ordinary differential equations we present a systematic approach to the determination of parameter values near which singular perturbation scenarios (in the sense of Tikhonov and Fenichel) arise. We call these special values Tikhonov-Fenichel parameter values. The principal application we intend is to equations that describe chemical reactions, in the context of quasi-steady state (or partial equilibrium) settings. Such equations have rational (or even polynomial) right-hand side. We determine the structure of the set of Tikhonov-Fenichel parameter values as a semi-algebraic set, and present an algorithmic approach to their explicit determination, using Groebner bases. Examples and applications (which include the irreversible and reversible Michaelis-Menten systems) illustrate that the approach is rather easy to implement.
A linear algebraic approach to electron-molecule collisions
International Nuclear Information System (INIS)
Collins, L.A.; Schnieder, B.I.
1982-01-01
The linear algebraic approach to electron-molecule collisions is examined by firstly deriving the general set of coupled integrodifferential equations that describe electron collisional processes and then describing the linear algebraic approach for obtaining a solution to the coupled equations. Application of the linear algebraic method to static-exchange, separable exchange and effective optical potential, is examined. (U.K.)
International Nuclear Information System (INIS)
Barnes, T.; Oak Ridge National Lab., TN; Tennessee Univ., Knoxville, TN
1994-06-01
This report summarizes the experimental and theoretical status of hadronic molecules, which are weakly-bound states of two or more hadrons. We begin with a brief history of the subject and discuss a few good candidates, and then abstract some signatures for molecules which may be of interest in the classification of possible molecule states. Next we argue that a more general understanding of 2 → 2 hadron-hadron scattering amplitudes will be crucial for molecule searches, and discuss some of our recent work in this area. We conclude with a discussion of a few more recent molecule candidates (notably the f o (1710)) which are not well established as molecules but satisfy some of the expected signatures. (Author)
Raithel, Georg; Zhao, Jianming
2017-04-01
Cold atomic systems have opened new frontiers at the interface of atomic and molecular physics. These include research on novel types of Rydberg molecules. Three types of molecules will be reviewed. Long-range, homonuclear Rydberg molecules, first predicted in [1] and observed in [2], are formed via low-energy electron scattering of the Rydberg electron from a ground-state atom within the Rydberg atom's volume. The binding mostly arises from S- and P-wave triplet scattering. We use a Fermi model that includes S-wave and P-wave singlet and triplet scattering, the fine structure coupling of the Rydberg atom and the hyperfine structure coupling of the 5S1/2 atom (in rubidium [3]). The hyperfine structure gives rise to mixed singlet-triplet potentials for both low-L and high-L Rydberg molecules [3]. A classification into Hund's cases [3, 4, 5] will be discussed. The talk further includes results on adiabatic potentials and adiabatic states of Rydberg-Rydberg molecules in Rb and Cs. These molecules, which have even larger bonding length than Rydberg-ground molecules, are formed via electrostatic multipole interactions. The leading interaction term of neutral Rydberg-Rydberg molecules is between two dipoles, while for ionic Rydberg molecules it is between a dipole and a monopole. NSF (PHY-1506093), NNSF of China (61475123).
Partial Differential Equations
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.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Synthetic, structural mimetics of the β-hairpin flap of HIV-1 protease inhibit enzyme function.
Chauhan, Jay; Chen, Shen-En; Fenstermacher, Katherine J; Naser-Tavakolian, Aurash; Reingewertz, Tali; Salmo, Rosene; Lee, Christian; Williams, Emori; Raje, Mithun; Sundberg, Eric; DeStefano, Jeffrey J; Freire, Ernesto; Fletcher, Steven
2015-11-01
Small-molecule mimetics of the β-hairpin flap of HIV-1 protease (HIV-1 PR) were designed based on a 1,4-benzodiazepine scaffold as a strategy to interfere with the flap-flap protein-protein interaction, which functions as a gated mechanism to control access to the active site. Michaelis-Menten kinetics suggested our small-molecules are competitive inhibitors, which indicates the mode of inhibition is through binding the active site or sterically blocking access to the active site and preventing flap closure, as designed. More generally, a new bioactive scaffold for HIV-1PR inhibition has been discovered, with the most potent compound inhibiting the protease with a modest K(i) of 11 μM. Copyright © 2015 Elsevier Ltd. All rights reserved.
Indian Academy of Sciences (India)
Atoms in a molecule generally prefer, particularly among the neighbouring ones, certain optimmn geometrical relationships. These are manifested in specific ranges of bond lengths, bond angles, torsion angles etc. As it always happens, chemists are interested in making molecules where these 'standard relationships' are ...
Indian Academy of Sciences (India)
Cyclo bu tadiene (1) has been one of the most popular molecules for experimentalists and theoreticians. This molecule is unstable as . it is antiaromatic ( 4,n electrons in a cyclic array). Even though some highly substituted cyclobutadienes, for example, compound 2 and the Fe(CO)3 complex of cyclobutadiene (3) are ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 2. Single-Molecule Spectroscopy: Every Molecule is Different! Kankan Bhattacharyya. General Article Volume 20 Issue 2 February 2015 pp 151-164. Fulltext. Click here to view fulltext PDF. Permanent link:
Willems, R.
2008-01-01
This thesis represents an excursion into the world of molecular electronics, i.e. the field of research trying to use individual (organic) molecules as electronic components; in this work various experimental methods have been explored to connect individual molecules to metallic contacts and
Self-dual monopoles and toda molecules
Ganoulis, N.; Goddard, P.; Olive, D.
1982-07-01
Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.
International Nuclear Information System (INIS)
Tsuji, T.
1986-01-01
Recently, research related to molecules in stars has rapidly expanded because of progress in related fields. For this reason, it is almost impossible to cover all the topics related to molecules in stars. Thus, here the authors focus their attention on molecules in the atmospheres of cool stars and do not cover in any detail topics related to circumstellar molecules originating from expanding envelopes located far from the stellar surface. However, the authors do discuss molecules in quasi-static circumstellar envelopes (a recently discovered new component of circumstellar envelopes) located near the stellar surface, since molecular lines originating from such envelopes show little velocity shift relative to photospheric lines, and hence they directly affect the interpretation and analysis of stellar spectra
International Nuclear Information System (INIS)
Sheehan, Daniel M.
2006-01-01
We tested the hypothesis that no threshold exists when estradiol acts through the same mechanism as an active endogenous estrogen. A Michaelis-Menten (MM) equation accounting for response saturation, background effects, and endogenous estrogen level fit a turtle sex-reversal data set with no threshold and estimated the endogenous dose. Additionally, 31 diverse literature dose-response data sets were analyzed by adding a term for nonhormonal background; good fits were obtained but endogenous dose estimations were not significant due to low resolving power. No thresholds were observed. Data sets were plotted using a normalized MM equation; all 178 data points were accommodated on a single graph. Response rates from ∼1% to >95% were well fit. The findings contradict the threshold assumption and low-dose safety. Calculating risk and assuming additivity of effects from multiple chemicals acting through the same mechanism rather than assuming a safe dose for nonthresholded curves is appropriate
Dynamics of Activated Molecules
Energy Technology Data Exchange (ETDEWEB)
Mullin, Amy S. [Univ. of Maryland, College Park, MD (United States)
2016-11-16
Experimental studies have been performed to investigate the collisional energy transfer processes of gas-phase molecules that contain large amounts of internal energy. Such molecules are prototypes for molecules under high temperature conditions relevant in combustion and information about their energy transfer mechanisms is needed for a detailed understanding and modeling of the chemistry. We use high resolution transient IR absorption spectroscopy to measure the full, nascent product distributions for collisions of small bath molecules that relax highly vibrationally excited pyrazine molecules with E=38000 cm-1 of vibrational energy. To perform these studies, we developed new instrumentation based on modern IR light sources to expand our experimental capabilities to investigate new molecules as collision partners. This final report describes our research in four areas: the characterization of a new transient absorption spectrometer and the results of state-resolved collision studies of pyrazine(E) with HCl, methane and ammonia. Through this research we have gained fundamental new insights into the microscopic details of relatively large complex molecules at high energy as they undergo quenching collisions and redistribute their energy.
Dissociation in small molecules
International Nuclear Information System (INIS)
Dehmer, P.M.
1982-01-01
The study of molecular dissociation processes is one of the most interesting areas of modern spectroscopy owing to the challenges presented bt even the simplest of diatomic molecules. This paper reviews the commonly used descriptions of molecular dissociation processes for diatomic molecules, the selection rules for predissociation, and a few of the principles to be remembered when one is forced to speculate about dissociation mechanisms in a new molecule. Some of these points will be illustrated by the example of dissociative ionization in O 2
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
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.
Single molecules and nanotechnology
Vogel, Horst
2007-01-01
This book focuses on recent advances in the rapidly evolving field of single molecule research. These advances are of importance for the investigation of biopolymers and cellular biochemical reactions, and are essential to the development of quantitative biology. Written by leading experts in the field, the articles cover a broad range of topics, including: quantum photonics of organic dyes and inorganic nanoparticles their use in detecting properties of single molecules the monitoring of single molecule (enzymatic) reactions single protein (un)folding in nanometer-sized confined volumes the dynamics of molecular interactions in biological cells The book is written for advanced students and scientists who wish to survey the concepts, techniques and results of single molecule research and assess them for their own scientific activities.
Takayanagi, Kazuo
1984-01-01
Scattering phenomena play an important role in modern physics. Many significant discoveries have been made through collision experiments. Amongst diverse kinds of collision systems, this book sheds light on the collision of an electron with a molecule. The electron-molecule collision provides a basic scattering problem. It is scattering by a nonspherical, multicentered composite particle with its centers having degrees of freedom of motion. The molecule can even disintegrate, Le., dissociate or ionize into fragments, some or all of which may also be molecules. Although it is a difficult problem, the recent theoretical, experimental, and computational progress has been so significant as to warrant publication of a book that specializes in this field. The progress owes partly to technical develop ments in measurements and computations. No less important has been the great and continuing stimulus from such fields of application as astrophysics, the physics of the earth's upper atmosphere, laser physics, radiat...
Indian Academy of Sciences (India)
evolved as a new line of thinking wherein a single molecule or perhaps a collection .... In photonic communication processes, laser light has to be modulated and .... The author wishes to thank G Rajaram for a critical reading of the manuscript.
Indian Academy of Sciences (India)
IAS Admin
overall absorption spectrum of a molecule is a superposition of many such sharp lines .... dilute solution of the enzyme and the substrate over few drops of silicone oil placed ..... Near-field Scanning Optical Microscopy (NSOM): Development.
Wu, Jiang
2014-01-01
This book reviews recent advances in the exciting and rapidly growing field of quantum dot molecules (QDMs). It offers state-of-the-art coverage of novel techniques and connects fundamental physical properties with device design.
Indian Academy of Sciences (India)
Molecule of the Month - Adamantane - A Plastic Piece of Diamond. J Chandrasekhar. Volume 16 Issue 12 ... Keywords. Adamantane; diamondoid systems; plastic crystals. ... Resonance – Journal of Science Education | News. © 2017 Indian ...
International Nuclear Information System (INIS)
Kaushik, R.; Rosenfeld, Clint A.; Sultatos, L.G.
2007-01-01
For many decades it has been thought that oxygen analogs (oxons) of organophosphorus insecticides phosphorylate the catalytic site of acetylcholinesterase by a mechanism that follows simple Michaelis-Menten kinetics. More recently, the interactions of at least some oxons have been shown to be far more complex and likely involve binding of oxons to a second site on acetylcholinesterase that modulates the inhibitory capacity of other oxon molecules at the catalytic site. The current study has investigated the interactions of chlorpyrifos oxon and methyl paraoxon with human recombinant acetylcholinesterase. Both chlorpyrifos oxon and methyl paraoxon were found to have k i 's that change as a function of oxon concentration. Furthermore, 10 nM chlorpyrifos oxon resulted in a transient increase in acetylthiocholine hydrolysis, followed by inhibition. Moreover, in the presence of 100 nM chlorpyrifos oxon, acetylthiocholine was found to influence both the K d (binding affinity) and k 2 (phosphorylation constant) of this oxon. Collectively, these results demonstrate that the interactions of chlorpyrifos oxon and methyl paraoxon with acetylcholinesterase cannot be described by simple Michaelis-Menten kinetics but instead support the hypothesis that these oxons bind to a secondary site on acetylcholinesterase, leading to activation/inhibition of the catalytic site, depending on the nature of the substrate and inhibitor. Additionally, these data raise questions regarding the adequacy of estimating risk of low levels of insecticide exposure from direct extrapolation of insecticide dose-response curves since the capacity of individual oxon molecules at low oxon levels could be greater than individual oxon molecules in vivo associated with the dose-response curve
The Approach to Equilibrium: Detailed Balance and the Master Equation
Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.
2011-01-01
The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…
Kinetic characterisation of primer mismatches in allele-specific PCR: a quantitative assessment.
Waterfall, Christy M; Eisenthal, Robert; Cobb, Benjamin D
2002-12-20
A novel method of estimating the kinetic parameters of Taq DNA polymerase during rapid cycle PCR is presented. A model was constructed using a simplified sigmoid function to represent substrate accumulation during PCR in combination with the general equation describing high substrate inhibition for Michaelis-Menten enzymes. The PCR progress curve was viewed as a series of independent reactions where initial rates were accurately measured for each cycle. Kinetic parameters were obtained for allele-specific PCR (AS-PCR) amplification to examine the effect of mismatches on amplification. A high degree of correlation was obtained providing evidence of substrate inhibition as a major cause of the plateau phase that occurs in the later cycles of PCR.
Energy Technology Data Exchange (ETDEWEB)
Oddone, S.; Grasselli, M.; Cuellas, A.
2010-07-01
Advances in the design of a bioreactor in the fats and oils industry have permitted the hydrolysis of triglycerides in mild conditions and improved productivity while avoiding the formation of unwanted byproducts. The present work develops a mathematical model that describes the hydrolytic activity of a tubular reactor with immobilized lipases for the production of glycerol and fatty acids from the oil trade. Runge Kuttas numerical method of high order has been applied, considering that there is no accumulation of the substratum in the surface of the membrane, where the enzyme is. At the same time, different equations based on the kinetic model of Michaelis Mentens and the Ping-Pong bi-bi mechanism were examined. Experimental data in discontinuous systems are the basis for the development of the quantitative mathematical model that was used to simulate the process computationally. The obtained results allow for optimizing both the operative variables and the economic aspects of industrial processes. (Author)
DEFF Research Database (Denmark)
Rasmussen, Peter Have; Knudsen, I.; Elmholt, S.
2002-01-01
the Hanes-Wolf transformation of the Michaelis-Menten equation. Soil samples from 6 to 13 cm depth were collected in the early spring as undisturbed blocks from 10 arable soils with different physico-chemical properties and cultivation history. Significant correlations were found between soil suppresiveness......The objective was to investigate the relationship between soil suppression of seedling blight of barley caused by Fusarium culmorum (W.G. Smith) Sacc. and the soil cellulolytic activity of beta-glucosidase, cellobiohydrolase and endocellulase. Disease suppression was investigated in bioassays...... with test soils mixed with sand, and barley seeds inoculated with F. culmorum. After 19 days, disease severity was evaluated on the barley seedlings. Soil cellulolytic activities were measured using 4-methylumbelliferyl-labelled fluorogenic substrates, and were expressed as V-max values obtained by using...
Enzyme activity and kinetics in substrate-amended river sediments
Energy Technology Data Exchange (ETDEWEB)
Duddridge, J E; Wainwright, M
1982-01-01
In determining the effects of heavy metals in microbial activity and litter degradation in river sediments, one approach is to determine the effects of these pollutants on sediment enzyme activity and synthesis. Methods to assay amylase, cellulase and urease activity in diverse river sediments are reported. Enzyme activity was low in non-amended sediments, but increased markedly when the appropriate substrate was added, paralleling both athropogenic and natural amendment. Linear relationships between enzyme activity, length of incubation, sample size and substrate concentration were established. Sediment enzyme activity generally obeyed Michaelis-Menton kinetics, but of the three enzymes, urease gave least significant correlation coefficients when the data for substrate concentration versus activity was applied to the Eadie-Hofstee transformation of the Michaelis-Menten equation. K/sub m/ and V/sub max/ for amylase, cellulase and urease in sediments are reported. (JMT)
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Tyurin, D. V.; Zaitseva, S. V.; Kudrik, E. V.
2018-05-01
It is found for the first time that μ-carbido-dimeric iron(IV) octapropylporphyrazinate displays catalytic activity in the oxidation reaction of natural flavonol morin with tert-butyl hydroperoxide, with the catalyst being stable under conditions of the reaction. The kinetics of this reaction are studied. It is shown the reaction proceeds via tentative formation of a complex between the catalyst and the oxidant, followed by O‒O bond homolytic cleavage. The kinetics of the reaction is described in the coordinates of the Michaelis-Menten equation. A linear dependence of the apparent reaction rate constant on the concentration of the catalyst is observed, testifying to its participation in the limiting reaction step. The equilibrium constants and rates of interaction are found. A mechanism is proposed for the reaction on the basis of the experimental data.
Characterization of lipase in reversed micelles formulated by Cibacron Blue F-3GA modified Span 85
DEFF Research Database (Denmark)
Zhang, Dong Hao; Guo, Zheng; Sun, Yan
2007-01-01
Sorbitan trioleate (Span 85) modified by Cibacron Blue F-3GA (CB) was prepared and used as an affinity surfactant to formulate a reversed micellar system for Candida rugosa lipase (CRL) solubilization. The system was characterized and evaluated by employing CRL-catalyzed hydrolysis of olive oil...... of the encapsulated lipase remained unchanged, but the apparent activity was significantly higher than that of the native enzyme in bulk solution. Kinetic studies indicated that the encapsulated lipase in the reversed micelles of CB-formulated Span 85 followed the Michaelis-Menten equation. The Michaelis constant...... was found to decrease with increasing surfactant concentration, suggesting an increase of the enzyme affinity for the substrate. Stability of the lipase in the reversed micelles was negatively correlated to W0. Introduction Reversed micelles are nanometer-scale transparent aggregates of water and surfactant...
A century of enzyme kinetic analysis, 1913 to 2013.
Johnson, Kenneth A
2013-09-02
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Kim, Seongho; Li, Lang
2014-02-01
The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiability of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Maciej Leszczyński
2017-01-01
Full Text Available We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics is modelled by a Hill function (i.e., Michaelis-Menten type kinetics. The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
Practical steady-state enzyme kinetics.
Lorsch, Jon R
2014-01-01
Enzymes are key components of most biological processes. Characterization of enzymes is therefore frequently required during the study of biological systems. Steady-state kinetics provides a simple and rapid means of assessing the substrate specificity of an enzyme. When combined with site-directed mutagenesis (see Site-Directed Mutagenesis), it can be used to probe the roles of particular amino acids in the enzyme in substrate recognition and catalysis. Effects of interaction partners and posttranslational modifications can also be assessed using steady-state kinetics. This overview explains the general principles of steady-state enzyme kinetics experiments in a practical, rather than theoretical, way. Any biochemistry textbook will have a section on the theory of Michaelis-Menten kinetics, including derivations of the relevant equations. No specific enzymatic assay is described here, although a method for monitoring product formation or substrate consumption over time (an assay) is required to perform the experiments described. © 2014 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Shimamura, I.; Takayanagi, K.
1984-01-01
The study of collision processes plays an important research role in modern physics. Many significant discoveries have been made by means of collision experiments. Based on theoretical, experimental, and computational studies, this volume presents an overview detailing the basic processes of electron-molecule collisions. The editors have collected papers-written by a group of international experts-that consider a diverse range of phenomena occurring in electronmolecule collisions. The volume discusses first the basic formulation for scattering problems and then gives an outline of the physics of electron-molecule collisions. The main topics covered are rotational transitions, vibrational transitions, dissociation of molecules in slow collisions, the electron-molecule collision as a spectroscopic tool for studying molecular electronic structures, and experimental and computational techniques for determining the cross sections. These well-referenced chapters are self-contained and can be read independently or consecutively. Authoritative and up-to-date, Electron-Molecule Collisions is a useful addition to the libraries of students and researchers in the fields of atomic, molecular, and chemical physics, and physical chemistry
Introduction to differential equations
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
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
International Nuclear Information System (INIS)
Loinard, Laurent; Menten, Karl M.; Güsten, Rolf; Zapata, Luis A.; Rodríguez, Luis F.
2012-01-01
We report the detection toward η Carinae of six new molecules, CO, CN, HCO + , HCN, HNC, and N 2 H + , and of two of their less abundant isotopic counterparts, 13 CO and H 13 CN. The line profiles are moderately broad (∼100 km s –1 ), indicating that the emission originates in the dense, possibly clumpy, central arcsecond of the Homunculus Nebula. Contrary to previous claims, CO and HCO + do not appear to be underabundant in η Carinae. On the other hand, molecules containing nitrogen or the 13 C isotope of carbon are overabundant by about one order of magnitude. This demonstrates that, together with the dust responsible for the dimming of η Carinae following the Great Eruption, the molecules detected here must have formed in situ out of CNO-processed stellar material.
Electron Accumulative Molecules.
Buades, Ana B; Sanchez Arderiu, Víctor; Olid-Britos, David; Viñas, Clara; Sillanpää, Reijo; Haukka, Matti; Fontrodona, Xavier; Paradinas, Markos; Ocal, Carmen; Teixidor, Francesc
2018-02-28
With the goal to produce molecules with high electron accepting capacity and low reorganization energy upon gaining one or more electrons, a synthesis procedure leading to the formation of a B-N(aromatic) bond in a cluster has been developed. The research was focused on the development of a molecular structure able to accept and release a specific number of electrons without decomposing or change in its structural arrangement. The synthetic procedure consists of a parallel decomposition reaction to generate a reactive electrophile and a synthesis reaction to generate the B-N(aromatic) bond. This procedure has paved the way to produce the metallacarboranylviologen [M(C 2 B 9 H 11 )(C 2 B 9 H 10 )-NC 5 H 4 -C 5 H 4 N-M'(C 2 B 9 H 11 )(C 2 B 9 H 10 )] (M = M' = Co, Fe and M = Co and M' = Fe) and semi(metallacarboranyl)viologen [3,3'-M(8-(NC 5 H 4 -C 5 H 4 N-1,2-C 2 B 9 H 10 )(1',2'-C 2 B 9 H 11 )] (M = Co, Fe) electron cumulative molecules. These molecules are able to accept up to five electrons and to donate one in single electron steps at accessible potentials and in a reversible way. By targeted synthesis and corresponding electrochemical tests each electron transfer (ET) step has been assigned to specific fragments of the molecules. The molecules have been carefully characterized, and the electronic communication between both metal centers (when this situation applies) has been definitely observed through the coplanarity of both pyridine fragments. The structural characteristics of these molecules imply a low reorganization energy that is a necessary requirement for low energy ET processes. This makes them electronically comparable to fullerenes, but on their side, they have a wide range of possible solvents. The ET from one molecule to another has been clearly demonstrated as well as their self-organizing capacity. We consider that these molecules, thanks to their easy synthesis, ET, self-organizing capacity, wide range of solubility, and easy processability, can
Liang, Xin-Li; Zhang, Jing; Liao, Zheng-Gen; Zhao, Guo-Wei; Luo, Yun; Li, Zhe; Satterlee, Andrew
2015-06-15
The objective of this study was to establish a quantitative method to evaluate the biotransportation of a drug across the cell membrane. Through the application of the law of mass conservation, the drug transportation rate was calculated based on Fick's law of passive diffusion and the Michaelis-Menten equation. The overall membrane-transportation rate was the sum of the passive diffusion rate and the carrier-mediated diffusion rate, which were calculated as the transportation mass divided by the respective rate. The active ingredients of Puerariae lobatae Radix and Chuanxiong rhizoma, namely, puerarin and ferulic acid, respectively, were used as two model drugs. The transportation rates of puerarin and ferulic acid were obtained by fitting a model that includes both Fick's law of diffusion and the Michaelis-Menten equation. Compared with the overall transportation, the carrier-mediated transport and passive diffusion of 1.59 mmol/L puerarin were -35.07% and 64.93%, respectively, whereas the respective transportation modes of 0.1 mmol/L ferulic acid were -35.40% and 64.60%, respectively. Verapamil and MK-571 increased the overall transport rate and ratio, and MK-571 treatment changed the carrier-mediated transport from negative to positive. However, the transport rate and ratio of ferulic acid did not change significantly. The cell transportation mechanisms of puerarin and ferulic acid primarily involve simple passive diffusion and carrier-mediated transportation. Moreover, P-glycoprotein and multidrug resistance-associated protein efflux proteins, and other transportation proteins were found to be involved in the transportation of puerarin. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Grima, Ramon
2011-11-01
The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
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
Beginning partial differential equations
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
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 2. Molecule of the Month Isomers of Benzene - Still Pursuing Dreams. J Chandrasekhar. Feature Article Volume 1 Issue 2 February 1996 pp 80-83. Fulltext. Click here to view fulltext PDF. Permanent link:
Atoms, Molecules, and Compounds
Manning, Phillip
2007-01-01
Explores the atoms that govern chemical processes. This book shows how the interactions between simple substances such as salt and water are crucial to life on Earth and how those interactions are predestined by the atoms that make up the molecules.
Indian Academy of Sciences (India)
structure and properties (includingreactivt'ty) - both static (independent of time) and ... Furthermore, since the energy of H2 + in the ground state must be lower than that of .... (Figure 2b); note also that dp is positive in parts of the antibinding regions behind the two ... But, now both the sizes and shapes of molecules enter into.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 12. Molecule of the Month - A Stable Dibismuthene - A Compound with a Bi-Bi Double Bond. V Chandrasekhar. Volume 16 ... Author Affiliations. V Chandrasekhar1. Department of Chemistry, Indian Institute of Technology, Kanpur 208 016, India.
Peironcely, J.E.; Rojas-Chertó, M.; Fichera, D.; Reijmers, T.; Coulier, L.; Faulon, J.-L.; Hankemeier, T.
2012-01-01
Computer Assisted Structure Elucidation has been used for decades to discover the chemical structure of unknown compounds. In this work we introduce the first open source structure generator, Open Molecule Generator (OMG), which for a given elemental composition produces all non-isomorphic chemical
Indian Academy of Sciences (India)
Administrator
Employing self-assembly methods, it is possible to engineer a bulk molecular material ... synthesis of molecular magnets in 1986, a large variety of them have been synthesized, which can be catego- ... maintained stably per organic molecule, stabilization of a ..... rotating freely under an applied field because it is a magne-.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 5. Molecule of the Month Molecular–Chameleon: Solvatochromism at its Iridescent Best! Photon Rao. Feature Article Volume 2 Issue 5 May 1997 pp 69-72. Fulltext. Click here to view fulltext PDF. Permanent link:
International Nuclear Information System (INIS)
Portier, M.
2007-12-01
We study the photo-association of an ultracold cloud of magnetically trapped helium atoms: pairs of colliding atoms interact with one or two laser fields to produce a purely long range 4 He 2 (2 3 S 1 -2 3 P 0 ) molecule, or a 4 He 2 (2 3 S 1 -2 3 S 1 ) long range molecule. Light shifts in one photon photo-association spectra are measured and studied as a function of the laser polarization and intensity, and the vibrational state of the excited molecule. They result from the light-induced coupling between the excited molecule, and bound and scattering states of the interaction between two metastable atoms. Their analysis leads to the determination of the scattering length a = (7.2 ± 0.6) ruling collisions between spin polarized atoms. The two photon photo-association spectra show evidence of the production of polarized, long-range 4 He 2 (2 3 S 1 -2 3 S 1 ) molecules. They are said to be exotic as they are made of two metastable atoms, each one carrying a enough energy to ionize the other. The corresponding lineshapes are calculated and decomposed in sums and products of Breit-Wigner and Fano profiles associated to one and two photon processes. The experimental spectra are fit, and an intrinsic lifetime τ = (1.4 ± 0.3) μs is deduced. It is checked whether this lifetime could be limited by spin-dipole induced Penning autoionization. This interpretation requires that there is a quasi-bound state close to the dissociation threshold in the singlet interaction potential between metastable helium atoms for the theory to match the experiment. (author)
Peironcely, Julio E; Rojas-Chertó, Miguel; Fichera, Davide; Reijmers, Theo; Coulier, Leon; Faulon, Jean-Loup; Hankemeier, Thomas
2012-09-17
Computer Assisted Structure Elucidation has been used for decades to discover the chemical structure of unknown compounds. In this work we introduce the first open source structure generator, Open Molecule Generator (OMG), which for a given elemental composition produces all non-isomorphic chemical structures that match that elemental composition. Furthermore, this structure generator can accept as additional input one or multiple non-overlapping prescribed substructures to drastically reduce the number of possible chemical structures. Being open source allows for customization and future extension of its functionality. OMG relies on a modified version of the Canonical Augmentation Path, which grows intermediate chemical structures by adding bonds and checks that at each step only unique molecules are produced. In order to benchmark the tool, we generated chemical structures for the elemental formulas and substructures of different metabolites and compared the results with a commercially available structure generator. The results obtained, i.e. the number of molecules generated, were identical for elemental compositions having only C, O and H. For elemental compositions containing C, O, H, N, P and S, OMG produces all the chemically valid molecules while the other generator produces more, yet chemically impossible, molecules. The chemical completeness of the OMG results comes at the expense of being slower than the commercial generator. In addition to being open source, OMG clearly showed the added value of constraining the solution space by using multiple prescribed substructures as input. We expect this structure generator to be useful in many fields, but to be especially of great importance for metabolomics, where identifying unknown metabolites is still a major bottleneck.
Directory of Open Access Journals (Sweden)
Peironcely Julio E
2012-09-01
Full Text Available Abstract Computer Assisted Structure Elucidation has been used for decades to discover the chemical structure of unknown compounds. In this work we introduce the first open source structure generator, Open Molecule Generator (OMG, which for a given elemental composition produces all non-isomorphic chemical structures that match that elemental composition. Furthermore, this structure generator can accept as additional input one or multiple non-overlapping prescribed substructures to drastically reduce the number of possible chemical structures. Being open source allows for customization and future extension of its functionality. OMG relies on a modified version of the Canonical Augmentation Path, which grows intermediate chemical structures by adding bonds and checks that at each step only unique molecules are produced. In order to benchmark the tool, we generated chemical structures for the elemental formulas and substructures of different metabolites and compared the results with a commercially available structure generator. The results obtained, i.e. the number of molecules generated, were identical for elemental compositions having only C, O and H. For elemental compositions containing C, O, H, N, P and S, OMG produces all the chemically valid molecules while the other generator produces more, yet chemically impossible, molecules. The chemical completeness of the OMG results comes at the expense of being slower than the commercial generator. In addition to being open source, OMG clearly showed the added value of constraining the solution space by using multiple prescribed substructures as input. We expect this structure generator to be useful in many fields, but to be especially of great importance for metabolomics, where identifying unknown metabolites is still a major bottleneck.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Dual Schroedinger Equation as Global Optimization Algorithm
International Nuclear Information System (INIS)
Huang Xiaofei; eGain Communications, Mountain View, CA 94043
2011-01-01
The dual Schroedinger equation is defined as replacing the imaginary number i by -1 in the original one. This paper shows that the dual equation shares the same stationary states as the original one. Different from the original one, it explicitly defines a dynamic process for a system to evolve from any state to lower energy states and eventually to the lowest one. Its power as a global optimization algorithm might be used by nature for constructing atoms and molecules. It shall be interesting to verify its existence in nature.
Differential Equations Models to Study Quorum Sensing.
Pérez-Velázquez, Judith; Hense, Burkhard A
2018-01-01
Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.
Friedman, Jonathan R.; Sarachik, Myriam P.
2010-04-01
Single-molecule magnets straddle the classical and quantum mechanical worlds, displaying many fascinating phenomena. They may have important technological applications in information storage and quantum computation. We review the physical properties of two prototypical molecular nanomagnets, Mn12-acetate and Fe8: Each behaves as a rigid, spin-10 object and exhibits tunneling between up and down directions. As temperature is lowered, the spin-reversal process evolves from thermal activation to pure quantum tunneling. At low temperatures, magnetic avalanches occur in which the magnetization of an entire sample rapidly reverses. We discuss the important role that symmetry-breaking fields play in driving tunneling and in producing Berry-phase interference. Recent experimental advances indicate that quantum coherence can be maintained on timescales sufficient to allow a meaningful number of quantum computing operations to be performed. Efforts are under way to create monolayers and to address and manipulate individual molecules.
Superexcited states of molecules
International Nuclear Information System (INIS)
Nakamura, Hiroki; Takagi, Hidekazu.
1990-01-01
The report addresses the nature and major features of molecule's superexcited states, focusing on their involvement in dynamic processes. It also outlines the quantum defect theory which allows various processes involving these states to be treated in a unified way. The Rydberg state has close relation with an ionized state with a positive energy. The quantum defect theory interprets such relation. Specifically, the report first describes the quantum defect theory focusing on its basic principle. The multi-channel quantum defect theory is then outlined centering on how to describe a Rydberg-type superexcited state. Description of a dissociative double-electron excited state is also discussed. The quantum defect theory is based on the fact that the physics of the motion of a Rydberg electron vary with the region in the electron's coordinate space. Finally, various molecular processes that involve a superexcited state are addressed focusing on autoionization, photoionization, dissociative recombination and bonding ionization of diatomic molecules. (N.K.)
Directory of Open Access Journals (Sweden)
A. Agah
2012-12-01
Full Text Available Risk-based assessment methods are commonly used at the contaminated sites by hydrocarbon pollutants. This paper presents the results of a two-dimensional finite volume model of reactive transport of biodegradable BTEX which have been developed for the saturated zone of an unconfined aquifer in the Pump station area of Tehran oil refinery, Iran. The model governing equations were numerically solved by modification of a general commercial software called PHOENICS. To reduce costs in general, many input parameters of a model are often approximated based on the used values in the contaminated sites with same conditions. It was not fully recognised the effect of errors in these inputs on modelling outputs. Thus, a sensitivity analysis was carried out to determine the influence of parameters variability on the results of model. For this analysis, the sensitivity of the model to changes in the dispersivity, distribution coefficient, parameters of Monod, Michaelis-Menten, first- and zero- order kinetics modes on the BTEX contaminant plume were examined by performing several simulations. It was found that the model is sensitive to changes in dispersivity and parameters of Michaelis-Menten, first- and zero- order kinetics model. On the other hand, the predictions for plumes assuming Monod kinetics are similar, even if different values for parameterization are chosen. The reason for this insensibility is that degradation is not limited by microbial kinetics in the simulation, but by dispersive mixing. Quantifying the effect of changes in model input parameters on the modelling results is essential when it is desired to recognise which model parameters are more vital on the fate and transport of reactive pollutants. Furthermore, this process can provide an insight into understanding pollutant transportation mechanisms.
Graybill, George
2007-01-01
Young scientists will be thrilled to explore the invisible world of atoms, molecules and elements. Our resource provides ready-to-use information and activities for remedial students using simplified language and vocabulary. Students will label each part of the atom, learn what compounds are, and explore the patterns in the periodic table of elements to find calcium (Ca), chlorine (Cl), and helium (He) through hands-on activities.
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
Photonic Molecule Lasers Revisited
Gagnon, Denis; Dumont, Joey; Déziel, Jean-Luc; Dubé, Louis J.
2014-05-01
Photonic molecules (PMs) formed by coupling two or more optical resonators are ideal candidates for the fabrication of integrated microlasers, photonic molecule lasers. Whereas most calculations on PM lasers have been based on cold-cavity (passive) modes, i.e. quasi-bound states, a recently formulated steady-state ab initio laser theory (SALT) offers the possibility to take into account the spectral properties of the underlying gain transition, its position and linewidth, as well as incorporating an arbitrary pump profile. We will combine two theoretical approaches to characterize the lasing properties of PM lasers: for two-dimensional systems, the generalized Lorenz-Mie theory will obtain the resonant modes of the coupled molecules in an active medium described by SALT. Not only is then the theoretical description more complete, the use of an active medium provides additional parameters to control, engineer and harness the lasing properties of PM lasers for ultra-low threshold and directional single-mode emission. We will extend our recent study and present new results for a number of promising geometries. The authors acknowledge financial support from NSERC (Canada) and the CERC in Photonic Innovations of Y. Messaddeq.
Environmental effects on molecules immersed in liquids
International Nuclear Information System (INIS)
Sese, L.M.
1990-01-01
A methodology to study environmental effects is thoroughly discussed. It combines molecular quantum mechanics and classical statistical mechanics of molecular fluids. Pair distribution functions collecting statistical information appear quite naturally in the quantum equations describing a single molecule. As well as allowing the computation of any individual molecular property in a liquid phase, this approach satisfies a number of theoretical requirements (dependence on density and temperature, validity in the thermodynamic limit). In a sense, it can be regarded as a useful alternative to the well-known Monte Carlo averaging processes for calculating molecular properties. Numerical applications studying liquid carbon disulphide and liquid carbon tetrachloride at several state points are given. Results cover typical RHF information (CNDO/2) on molecules, and show the sensitivity of the presented methodology to structural changes in liquids. (orig.)
Functional equations with causal operators
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.
The damped wave equation with unbounded damping
Czech Academy of Sciences Publication Activity Database
Freitas, P.; Siegl, Petr; Tretter, C.
2018-01-01
Roč. 264, č. 12 (2018), s. 7023-7054 ISSN 0022-0396 Institutional support: RVO:61389005 Keywords : damped wave equation * unbounded damping * essential spectrum * quadratic operator funciton with unbounded coefficients * Schrodinger operators with complex potentials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016
Memory effects in single-molecule spectroscopy
International Nuclear Information System (INIS)
Schmitt, Daniel T.; Schulz, Michael; Reineker, Peter
2007-01-01
From the time series of LH2 optical single-molecule fluorescence excitation spectra of Rhodospirillum molischianum the memory function of the Mori-Zwanzig equation for the optical intensity is derived numerically. We show that the time dependence of the excited states is determined by at least three different non-Markovian stochastic processes with decay constants for the Mori-Zwanzig kernel on the order of 1-5min -1 . We suggest that this decay stems from the conformational motion of the protein scaffold of LH2
Partial differential equations
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...
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.
Differential equations for dummies
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.
Degenerate nonlinear diffusion equations
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...
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Reactimeter dispersion equation
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...
Differential equations I essentials
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.
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
Nonlinear Poisson equation for heterogeneous media.
Hu, Langhua; Wei, Guo-Wei
2012-08-22
The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.
The symbolic language of substances and molecules: noise or ...
African Journals Online (AJOL)
Most substances are given names and formulae based upon knowledge of their molecules. However for substances most commonly met in elementary chemistry courses, especially inorganic substances, this is often not the case. The potential noise is amplified further when dealing with chemical reaction equations.
Quark chemistry: charmonium molecules
International Nuclear Information System (INIS)
De Rujula, A.; Jaffe, R.L.
1977-01-01
The theoretical and experimental evidence for two quark-two antiquark hadrons is reviewed. Concentration is placed on predictions for S-wave ''charmonium molecules,'' built of a c anti c charmonium pair and a light quark-antiquark pair. Their spectrum and quantum numbers are predicted and an estimate of their decay couplings and their prediction in monochromatic pion decays from charmonium resonances produced in e + e - -annihilation is given. Some S-wave charmonium resonances should be detectable in these decays, but typical branching ratios are only at the 1% level. 19 references
Ultra-cold molecule production
International Nuclear Information System (INIS)
Ramirez-Serrano, Jamie; Chandler, David W.; Strecker, Kevin; Rahn, Larry A.
2005-01-01
The production of Ultra-cold molecules is a goal of many laboratories through out the world. Here we are pursuing a unique technique that utilizes the kinematics of atomic and molecular collisions to achieve the goal of producing substantial numbers of sub Kelvin molecules confined in a trap. Here a trap is defined as an apparatus that spatially localizes, in a known location in the laboratory, a sample of molecules whose temperature is below one degree absolute Kelvin. Further, the storage time for the molecules must be sufficient to measure and possibly further cool the molecules. We utilize a technique unique to Sandia to form cold molecules from near mass degenerate collisions between atoms and molecules. This report describes the progress we have made using this novel technique and the further progress towards trapping molecules we have cooled
Manca, V.; Salibra, A.; Scollo, Giuseppe
1990-01-01
Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either
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
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.
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
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1994-01-01
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 the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation
African Journals Online (AJOL)
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
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
The generalized Fermat equation
Beukers, F.
2006-01-01
This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would
Applied partial differential equations
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...
Passing Current through Touching Molecules
DEFF Research Database (Denmark)
Schull, G.; Frederiksen, Thomas; Brandbyge, Mads
2009-01-01
The charge flow from a single C-60 molecule to another one has been probed. The conformation and electronic states of both molecules on the contacting electrodes have been characterized using a cryogenic scanning tunneling microscope. While the contact conductance of a single molecule between two...
A general mixture theory. I. Mixtures of spherical molecules
Hamad, Esam Z.
1996-08-01
We present a new general theory for obtaining mixture properties from the pure species equations of state. The theory addresses the composition and the unlike interactions dependence of mixture equation of state. The density expansion of the mixture equation gives the exact composition dependence of all virial coefficients. The theory introduces multiple-index parameters that can be calculated from binary unlike interaction parameters. In this first part of the work, details are presented for the first and second levels of approximations for spherical molecules. The second order model is simple and very accurate. It predicts the compressibility factor of additive hard spheres within simulation uncertainty (equimolar with size ratio of three). For nonadditive hard spheres, comparison with compressibility factor simulation data over a wide range of density, composition, and nonadditivity parameter, gave an average error of 2%. For mixtures of Lennard-Jones molecules, the model predictions are better than the Weeks-Chandler-Anderson perturbation theory.
LOW-TEMPERATURE EQUATION OF STATE OF SOLID METHANE
Directory of Open Access Journals (Sweden)
L. N. Yakub
2016-02-01
Full Text Available The theoretical equation of state for solid methane, developed within the framework of perturbation theory, with the crystal consisting of spherical molecules as zero-order approximation, and octupole – octupole interaction of methane molecules as a perturbation, is proposed. Thermodynamic functions are computed on the sublimation line up to the triple point. The contribution of the octupole – octupole interaction to the thermodynamic properties of solid methane is estimated.
Lanthanide single molecule magnets
Energy Technology Data Exchange (ETDEWEB)
Tang, Jinkui; Zhang, Peng [Chinese Academy of Sciences, Changchun (China). Changchun Inst. of Applied Chemistry
2015-10-01
This book begins by providing basic information on single-molecule magnets (SMMs), covering the magnetism of lanthanide, the characterization and relaxation dynamics of SMMs and advanced means of studying lanthanide SMMs. It then systematically introduces lanthanide SMMs ranging from mononuclear and dinuclear to polynuclear complexes, classifying them and highlighting those SMMs with high barrier and blocking temperatures - an approach that provides some very valuable indicators for the structural features needed to optimize the contribution of an Ising type spin to a molecular magnet. The final chapter presents some of the newest developments in the lanthanide SMM field, such as the design of multifunctional and stimuli-responsive magnetic materials as well as the anchoring and organization of the SMMs on surfaces. In addition, the crystal structure and magnetic data are clearly presented with a wealth of illustrations in each chapter, helping newcomers and experts alike to better grasp ongoing trends and explore new directions.
Lanthanide single molecule magnets
Tang, Jinkui
2015-01-01
This book begins by providing basic information on single-molecule magnets (SMMs), covering the magnetism of lanthanide, the characterization and relaxation dynamics of SMMs, and advanced means of studying lanthanide SMMs. It then systematically introduces lanthanide SMMs ranging from mononuclear and dinuclear to polynuclear complexes, classifying them and highlighting those SMMs with high barrier and blocking temperatures – an approach that provides some very valuable indicators for the structural features needed to optimize the contribution of an Ising type spin to a molecular magnet. The final chapter presents some of the newest developments in the lanthanide SMM field, such as the design of multifunctional and stimuli-responsive magnetic materials as well as the anchoring and organization of the SMMs on surfaces. In addition, the crystal structure and magnetic data are clearly presented with a wealth of illustrations in each chapter, helping newcomers and experts alike to better grasp ongoing trends and...
Energy Technology Data Exchange (ETDEWEB)
Cryan, James
2010-01-26
SLAC has just unveiled the world's first X-ray laser, the LCLS. This machine produces pulses of X-rays that are ten billion times brighter than those from conventional sources. One of the goals of this machine is to make movies of chemical reactions, including reactions necessary for life and reactions that might power new energy technologies. This public lecture will show the first results from the LCLS. As a first target, we have chosen nitrogen gas, the main component of the air we breathe. Using the unprecedented power of the LCLS X-rays as a blasting torch, we have created new forms of this molecule and with unique electronic arrangements. Please share with us the first insights from this new technology.
Magnetic field modification of ultracold molecule-molecule collisions
International Nuclear Information System (INIS)
Tscherbul, T V; Suleimanov, Yu V; Aquilanti, V; Krems, R V
2009-01-01
We present an accurate quantum mechanical study of molecule-molecule collisions in the presence of a magnetic field. The work focuses on the analysis of elastic scattering and spin relaxation in collisions of O 2 ( 3 Σ g - ) molecules at cold (∼0.1 K) and ultracold (∼10 -6 K) temperatures. Our calculations show that magnetic spin relaxation in molecule-molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T=0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1x10 -11 cm -3 s -1 . The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ∼100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule-molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.
Ordinary differential equations with applications in molecular biology.
Ilea, M; Turnea, M; Rotariu, M
2012-01-01
Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances
Hyperbolic partial differential equations
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
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
Differential equations problem solver
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
Supersymmetric quasipotential equations
International Nuclear Information System (INIS)
Zaikov, R.P.
1981-01-01
A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru
Local instant conservation equations
International Nuclear Information System (INIS)
Delaje, Dzh.
1984-01-01
Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface
Beginning partial differential equations
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
Ordinary differential equations
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,
Uncertain differential equations
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.
Phase space structure of triatomic molecules
International Nuclear Information System (INIS)
Lu, Z.; Kellman, M.E.
1997-01-01
The bifurcation structure is investigated for a Hamiltonian for the three coupled nonlinear vibrations of a highly excited triatomic molecule. The starting point is a quantum Hamiltonian used to fit experimental spectra. This Hamiltonian includes 1:1 Darling endash Dennison resonance coupling between the stretches, and 2:1 Fermi resonance coupling between the stretches and bend. A classical Hamiltonian is obtained using the Heisenberg correspondence principle. Surfaces of section show a pronounced degree of chaos at high energies, with a mixture of chaotic and regular dynamics. The large-scale bifurcation structure is found semianalytically, without recourse to numerical solution of Hamilton close-quote s equations, by taking advantage of the fact that the spectroscopic Hamiltonian has a conserved polyad quantum number, corresponding to an approximate constant of the motion of the molecule. Bifurcation diagrams are analyzed for a number of molecules including H 2 O, D 2 O, NO 2 , ClO 2 , O 3 , and H 2 S. copyright 1997 American Institute of Physics
Applied partial differential equations
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...
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.
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Equations For Rotary Transformers
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.
Problems in differential equations
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.
Applied partial differential equations
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.
Nonlinear differential equations
International Nuclear Information System (INIS)
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
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.
Orientation of KRb molecules in a switched electrostatic field
International Nuclear Information System (INIS)
Huang Yun-Xia; Xu Shu-Wu; Yang Xiao-Hua
2013-01-01
We theoretically investigate the orientation of the cold KRb molecules induced in a switched electrostatic field by numerically solving the full time-dependent Schrödinger equation. The results show that the periodic field-free molecular orientation can be realized for the KRb molecules by rapidly switching off the electrostatic field. Meanwhile, by varying the switching times of the electrostatic field, the adiabatic and nonadiabatic interactions of the molecules with the applied field can be realized. Moreover, the influences of the electrostatic field strength and the rotational temperature to the degree of the molecular orientation are studied. The investigations show that increasing the electrostatic field will increase the degree of the molecular orientation, both in the constant-field regime and in the field-free regime, while the increasing of the rotational temperature of the cold molecules will greatly decrease the degree of the molecular orientation. (atomic and molecular physics)
application of ascorbic acid 2-phosphate as a new voltammetric
African Journals Online (AJOL)
a
acid 2-phosphate (AAP) as a new voltammetric substrate has been described in this paper. In the alkaline buffer .... ALP labeled goat anti-rabbit ..... Classical Michaelis-Menten kinetic experiments were carried out to measure the maximum.
Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp
DEFF Research Database (Denmark)
Williams, J. E.; Nygaard, Nicolai; Clark, C. W.
2006-01-01
Starting with coupled atom-molecule Boltzmann equations, we develop a simplified model to understand molecule formation observed in recent experiments. Our theory predicts several key features: (1) the effective adiabatic rate constant is proportional to density; (2) in an adiabatic ramp...... show qualitative agreement with the data from [Hodby et al, Phys. Rev. Lett. 94, 120402 (2005)] without the use of adjustable parameters....
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
Electron-excited molecule interactions
International Nuclear Information System (INIS)
Christophorou, L.G.; Tennessee Univ., Knoxville, TN
1991-01-01
In this paper the limited but significant knowledge to date on electron scattering from vibrationally/rotationally excited molecules and electron scattering from and electron impact ionization of electronically excited molecules is briefly summarized and discussed. The profound effects of the internal energy content of a molecule on its electron attachment properties are highlighted focusing in particular on electron attachment to vibrationally/rotationally and to electronically excited molecules. The limited knowledge to date on electron-excited molecule interactions clearly shows that the cross sections for certain electron-molecule collision processes can be very different from those involving ground state molecules. For example, optically enhanced electron attachment studies have shown that electron attachment to electronically excited molecules can occur with cross sections 10 6 to 10 7 times larger compared to ground state molecules. The study of electron-excited molecule interactions offers many experimental and theoretical challenges and opportunities and is both of fundamental and technological significance. 54 refs., 15 figs
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
Quantum linear Boltzmann equation
International Nuclear Information System (INIS)
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Covariant field equations in supergravity
Energy Technology Data Exchange (ETDEWEB)
Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2017-12-15
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Covariant field equations in supergravity
International Nuclear Information System (INIS)
Vanhecke, Bram; Proeyen, Antoine van
2017-01-01
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc
2012-12-11
The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.
Organic Molecules in Meteorites
Martins, Zita
2015-08-01
Carbonaceous meteorites are primitive samples from the asteroid belt, containing 3-5wt% organic carbon. The exogenous delivery of organic matter by carbonaceous meteorites may have contributed to the organic inventory of the early Earth. The majority (>70%) of the meteoritic organic material consist of insoluble organic matter (IOM) [1]. The remaining meteoritic organic material (meteorites contain soluble organic molecules with different abundances and distributions, which may reflect the extension of aqueous alteration or thermal metamorphism on the meteorite parent bodies. Extensive aqueous alteration on the meteorite parent body may result on 1) the decomposition of α-amino acids [5, 6]; 2) synthesis of β- and γ-amino acids [2, 6-9]; 3) higher relative abundances of alkylated polycyclic aromatic hydrocarbons (PAHs) [6, 10]; and 4) higher L-enantiomer excess (Lee) value of isovaline [6, 11, 12].The soluble organic content of carbonaceous meteorites may also have a contribution from Fischer-Tropsch/Haber-Bosch type gas-grain reactions after the meteorite parent body cooled to lower temperatures [13, 14].The analysis of the abundances and distribution of the organic molecules present in meteorites helps to determine the physical and chemical conditions of the early solar system, and the prebiotic organic compounds available on the early Earth.[1] Cody and Alexander (2005) GCA 69, 1085. [2] Cronin and Chang (1993) in: The Chemistry of Life’s Origin. pp. 209-258. [3] Martins and Sephton (2009) in: Amino acids, peptides and proteins in organic chemistry. pp. 1-42. [4] Martins (2011) Elements 7, 35. [5] Botta et al. (2007) MAPS 42, 81. [6] Martins et al. (2015) MAPS, in press. [7] Cooper and Cronin (1995) GCA 59, 1003. [8] Glavin et al. (2006) MAPS. 41, 889. [9] Glavin et al. (2011) MAPS 45, 1948. [10] Elsila et al. (2005) GCA 5, 1349. [11] Glavin and Dworkin (2009) PNAS 106, 5487. [12] Pizzarello et al. (2003) GCA 67, 1589. [13] Chan et al. (2012) MAPS. 47, 1502
Differential Equation over Banach Algebra
Kleyn, Aleks
2018-01-01
In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.
International Nuclear Information System (INIS)
Jarvis, P.D.; Bulte, D.P.
1998-01-01
A quantum-mechanical description of tunnelling is presented for a one-dimensional system with internal oscillator degrees of freedom. The 'charged diatomic molecule' is frustrated on encountering a barrier potential by its centre of charge not being coincident with its centre of mass, resulting in transitions amongst internal states. In an adiabatic limit, the tunnelling of semiclassical coherent-like oscillator states is shown to exhibit the Hartman and Bueuttiker-Landauer times t H and t BL , with the time dependence of the coherent state parameter for the tunnelled state given by α(t) = α e -iω(t+Δt) , Δt = t H - it BL . A perturbation formalism is developed, whereby the exact transfer matrix can be expanded to any desired accuracy in a suitable limit. An 'intrinsic' time, based on the oscillator transition rate during tunnelling, transmission or reflection, is introduced. In simple situations the resulting intrinsic tunnelling time is shown to vanish to lowest order. In the general case a particular (nonzero) parametrisation is inferred, and its properties discussed in comparison with the literature on tunnelling times for both wavepackets and internal clocks. Copyright (1998) CSIRO Australia
Shera, E. Brooks
1988-01-01
A detection system is provided for identifying individual particles or molecules having characteristic emission in a flow train of the particles in a flow cell. A position sensitive sensor is located adjacent the flow cell in a position effective to detect the emissions from the particles within the flow cell and to assign spatial and temporal coordinates for the detected emissions. A computer is then enabled to predict spatial and temporal coordinates for the particle in the flow train as a function of a first detected emission. Comparison hardware or software then compares subsequent detected spatial and temporal coordinates with the predicted spatial and temporal coordinates to determine whether subsequently detected emissions originate from a particle in the train of particles. In one embodiment, the particles include fluorescent dyes which are excited to fluoresce a spectrum characteristic of the particular particle. Photones are emitted adjacent at least one microchannel plate sensor to enable spatial and temporal coordinates to be assigned. The effect of comparing detected coordinates with predicted coordinates is to define a moving sample volume which effectively precludes the effects of background emissions.
Theoretical Investigations Regarding Single Molecules
DEFF Research Database (Denmark)
Pedersen, Kim Georg Lind
Neoclassical Valence Bond Theory, Quantum Transport, Quantum Interference, Kondo Effect, and Electron Pumping. Trap a single organic molecule between two electrodes and apply a bias voltage across this "molecular junction". When electrons pass through the molecule, the different electron paths can...... interfere destructively or constructively. Destructive interference effects in electron transport could potentially improve thermo-electrics, organic logic circuits and energy harvesting. We have investigated destructive interference in off-resonant transport through organic molecules, and have found a set...
Steady-state cerebral glucose concentrations and transport in the human brain
Gruetter, R.; Ugurbil, K.; Seaquist, E. R.
1998-01-01
Understanding the mechanism of brain glucose transport across the blood- brain barrier is of importance to understanding brain energy metabolism. The specific kinetics of glucose transport nave been generally described using standard Michaelis-Menten kinetics. These models predict that the steady- state glucose concentration approaches an upper limit in the human brain when the plasma glucose level is well above the Michaelis-Menten constant for half-maximal transport, K(t). In experiments wh...
Biofuels: from microbes to molecules
National Research Council Canada - National Science Library
Lu, Xuefeng
2014-01-01
.... The production of different biofuel molecules including hydrogen, methane, ethanol, butanol, higher chain alcohols, isoprenoids and fatty acid derivatives, from genetically engineered microbes...
Labelled molecules, modern research implements
International Nuclear Information System (INIS)
Pichat, L.; Langourieux, Y.
1974-01-01
Details of the synthesis of carbon 14- and tritium-labelled molecules are examined. Although the methods used are those of classical organic chemistry the preparation of carbon 14-labelled molecules differs in some respects, most noticeably in the use of 14 CO 2 which requires very special handling techniques. For the tritium labelling of organic molecules the methods are somewhat different, very often involving exchange reactions. The following are described in turn: the so-called Wilzbach exchange method; exchange by catalysis in solution; catalytic hydrogenation with tritium; reductions with borotritides. Some applications of labelled molecules in organic chemistry, biochemistry and pharmacology are listed [fr
Transport equation solving methods
International Nuclear Information System (INIS)
Granjean, P.M.
1984-06-01
This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr
Introduction to partial differential equations
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.
Growing interstellar molecules with ion-molecule reactions
International Nuclear Information System (INIS)
Bohme, D.K.
1989-01-01
Laboratory measurements of gas-phase ion-molecule reactions continue to provide important insights into the chemistry of molecular growth in interstellar environments. It is also true that the measurements are becoming more demanding as larger molecules capture our interest. While some of these measurements are motivated by current developments in chemical models of interstellar environments or by new molecular observations by astronomers, others explore novel chemistry which can lead to predictions of new interstellar molecules. Here the author views the results of some recent measurements, taken in the Ion Chemistry Laboratory at York University with the SIFT technique, which address some of the current needs of modellers and observers and which also provide some new fundamental insight into molecular growth, particularly when it occurs in the presence of large molecules such as PAH molecules which are now thought to have a major influence on the chemistry of interstellar environments in which they are present
Quadratic Diophantine equations
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.
Stochastic porous media equations
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.
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...
Numerical calculation of the cross section by the solution of the wave equation
International Nuclear Information System (INIS)
Drewko, J.
1982-01-01
A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)
Gas-evolution oscillators. 10. A model based on a delay equation
Energy Technology Data Exchange (ETDEWEB)
Bar-Eli, K.; Noyes, R.M. [Univ. of Oregon, Eugene, OR (United States)
1992-09-17
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas.
Gas-evolution oscillators. 10. A model based on a delay equation
International Nuclear Information System (INIS)
Bar-Eli, K.; Noyes, R.M.
1992-01-01
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas
Equations of mathematical physics
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
Iteration of adjoint equations
International Nuclear Information System (INIS)
Lewins, J.D.
1994-01-01
Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs
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....
Partial differential equations
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
Generalized estimating equations
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
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.
Analysis of wave equation in electromagnetic field by Proca equation
International Nuclear Information System (INIS)
Pamungkas, Oky Rio; Soeparmi; Cari
2017-01-01
This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Test equating methods and practices
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...
Enzyme Molecules in Solitary Confinement
Directory of Open Access Journals (Sweden)
Raphaela B. Liebherr
2014-09-01
Full Text Available Large arrays of homogeneous microwells each defining a femtoliter volume are a versatile platform for monitoring the substrate turnover of many individual enzyme molecules in parallel. The high degree of parallelization enables the analysis of a statistically representative enzyme population. Enclosing individual enzyme molecules in microwells does not require any surface immobilization step and enables the kinetic investigation of enzymes free in solution. This review describes various microwell array formats and explores their applications for the detection and investigation of single enzyme molecules. The development of new fabrication techniques and sensitive detection methods drives the field of single molecule enzymology. Here, we introduce recent progress in single enzyme molecule analysis in microwell arrays and discuss the challenges and opportunities.
Organizing and addressing magnetic molecules.
Gatteschi, Dante; Cornia, Andrea; Mannini, Matteo; Sessoli, Roberta
2009-04-20
Magnetic molecules ranging from simple organic radicals to single-molecule magnets (SMMs) are intensively investigated for their potential applications in molecule-based information storage and processing. The goal of this Article is to review recent achievements in the organization of magnetic molecules on surfaces and in their individual probing and manipulation. We stress that the inherent fragility and redox sensitivity of most SMM complexes, combined with the noninnocent role played by the substrate, ask for a careful evaluation of the structural and electronic properties of deposited molecules going beyond routine methods for surface analysis. Detailed magnetic information can be directly obtained using X-ray magnetic circular dichroism or newly emerging scanning probe techniques with magnetic detection capabilities.
Ion-Molecule Reaction Dynamics.
Meyer, Jennifer; Wester, Roland
2017-05-05
We review the recent advances in the investigation of the dynamics of ion-molecule reactions. During the past decade, the combination of single-collision experiments in crossed ion and neutral beams with the velocity map ion imaging detection technique has enabled a wealth of studies on ion-molecule reactions. These methods, in combination with chemical dynamics simulations, have uncovered new and unexpected reaction mechanisms, such as the roundabout mechanism and the subtle influence of the leaving group in anion-molecule nucleophilic substitution reactions. For this important class of reactions, as well as for many fundamental cation-molecule reactions, the information obtained with crossed-beam imaging is discussed. The first steps toward understanding micro-solvation of ion-molecule reaction dynamics are presented. We conclude with the presentation of several interesting directions for future research.
Boltzmann equations for a binary one-dimensional ideal gas.
Boozer, A D
2011-09-01
We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.
Indian Academy of Sciences (India)
The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
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 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. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Indian Academy of Sciences (India)
research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
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. Laplace transformation was used to solve the governing ...
Equational binary decision diagrams
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
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Structural Equation Model Trees
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…
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
African Journals Online (AJOL)
Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.
Indian Academy of Sciences (India)
However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...
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]…
Guiding center drift equations
International Nuclear Information System (INIS)
Boozer, A.H.
1979-03-01
The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
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
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C
Hanks, Thomas C.
2009-01-01
The diffusion equation is one of the three great partial differential equations of classical physics. It describes the flow or diffusion of heat in the presence of temperature gradients, fluid flow in porous media in the presence of pressure gradients, and the diffusion of molecules in the presence of chemical gradients. [The other two equations are the wave equation, which describes the propagation of electromagnetic waves (including light), acoustic (sound) waves, and elastic (seismic) waves radiated from earthquakes; and LaPlace’s equation, which describes the behavior of electric, gravitational, and fluid potentials, all part of potential field theory. The diffusion equation reduces to LaPlace’s equation at steady state, when the field of interest does not depend on t. Poisson’s equation is LaPlace’s equation with a source term.
Lectures on partial differential equations
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.
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)
Elements of partial differential equations
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
Single Molecule Electronics and Devices
Tsutsui, Makusu; Taniguchi, Masateru
2012-01-01
The manufacture of integrated circuits with single-molecule building blocks is a goal of molecular electronics. While research in the past has been limited to bulk experiments on self-assembled monolayers, advances in technology have now enabled us to fabricate single-molecule junctions. This has led to significant progress in understanding electron transport in molecular systems at the single-molecule level and the concomitant emergence of new device concepts. Here, we review recent developments in this field. We summarize the methods currently used to form metal-molecule-metal structures and some single-molecule techniques essential for characterizing molecular junctions such as inelastic electron tunnelling spectroscopy. We then highlight several important achievements, including demonstration of single-molecule diodes, transistors, and switches that make use of electrical, photo, and mechanical stimulation to control the electron transport. We also discuss intriguing issues to be addressed further in the future such as heat and thermoelectric transport in an individual molecule. PMID:22969345
On generalized fractional vibration equation
International Nuclear Information System (INIS)
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-01-01
Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.
Molecular Beam Chemistry: Reactions of Oxygen Atoms with Halogen Molecules.
1982-10-15
nonlinear one has s = 3, r = 1, and n = 3/2. In the "loose" complex the bending modes go over to free rotation of the product diatomit molecule; thus s...contains no adjustable parameters. All observable properties *l of the reaction may be predicted including product velocity and angular dis- tributions...example, P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill Book Co., New York, 1969). 65. Equation (3) is strictly
Theoretical aspects of electron transfer reactions of complex molecules
DEFF Research Database (Denmark)
Kuznetsov, A. M.; Ulstrup, Jens
2001-01-01
Features of electron transfer involving complex molecules are discussed. This notion presently refers to molecular reactants where charge transfer is accompanied by large molecular reorganization, and commonly used displaced harmonic oscillator models do not apply. It is shown that comprehensive...... theory of charge transfer in polar media offers convenient tools for the treatment of experimental data for such systems, with due account of large-amplitude strongly anharmonic intramolecular reorganization. Equations for the activation barrier and free energy relationships are provided, incorporating...
Electrode redox reactions with polarizable molecules
Matyushov, Dmitry V.
2018-04-01
A theory of redox reactions involving electron transfer between a metal electrode and a polarizable molecule in solution is formulated. Both the existence of molecular polarizability and its ability to change due to electron transfer distinguish this problem from classical theories of interfacial electrochemistry. When the polarizability is different between the oxidized and reduced states, the statistics of thermal fluctuations driving the reactant over the activation barrier becomes non-Gaussian. The problem of electron transfer is formulated as crossing of two non-parabolic free energy surfaces. An analytical solution for these free energy surfaces is provided and the activation barrier of electrode electron transfer is given in terms of two reorganization energies corresponding to the oxidized and reduced states of the molecule in solution. The new non-Gaussian theory is, therefore, based on two theory parameters in contrast to one-parameter Marcus formulation for electrode reactions. The theory, which is consistent with the Nernst equation, predicts asymmetry between the cathodic and anodic branches of the electrode current. They show different slopes at small electrode overpotentials and become curved at larger overpotentials. However, the curvature of the Tafel plot is reduced compared to the Marcus-Hush model and approaches the empirical Butler-Volmer form with different transfer coefficients for the anodic and cathodic currents.
Quantum Monte Carlo for vibrating molecules
International Nuclear Information System (INIS)
Brown, W.R.; Lawrence Berkeley National Lab., CA
1996-08-01
Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H 2 O and C 3 vibrational states, using 7 PES's, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H 2 O and C 3 . In order to construct accurate trial wavefunctions for C 3 , the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C 3 the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C 3 PES's suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies
Transport mirages in single-molecule devices
Gaudenzi, R.; Misiorny, M.; Burzurí, E.; Wegewijs, M. R.; van der Zant, H. S. J.
2017-03-01
Molecular systems can exhibit a complex, chemically tailorable inner structure which allows for targeting of specific mechanical, electronic, and optical properties. At the single-molecule level, two major complementary ways to explore these properties are molecular quantum-dot structures and scanning probes. This article outlines comprehensive principles of electron-transport spectroscopy relevant to both these approaches and presents a new, high-resolution experiment on a high-spin single-molecule junction exemplifying these principles. Such spectroscopy plays a key role in further advancing our understanding of molecular and atomic systems, in particular, the relaxation of their spin. In this joint experimental and theoretical analysis, particular focus is put on the crossover between the resonant regime [single-electron tunneling] and the off-resonant regime [inelastic electron (co)tunneling spectroscopy (IETS)]. We show that the interplay of these two processes leads to unexpected mirages of resonances not captured by either of the two pictures alone. Although this turns out to be important in a large fraction of the possible regimes of level positions and bias voltages, it has been given little attention in molecular transport studies. Combined with nonequilibrium IETS—four-electron pump-probe excitations—these mirages provide crucial information on the relaxation of spin excitations. Our encompassing physical picture is supported by a master-equation approach that goes beyond weak coupling. The present work encourages the development of a broader connection between the fields of molecular quantum-dot and scanning probe spectroscopy.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
equateIRT: An R Package for IRT Test Equating
Directory of Open Access Journals (Sweden)
Michela Battauz
2015-12-01
Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.
Calculation of a hydrogen molecule in the adiabatic approximation
International Nuclear Information System (INIS)
Vukajlovich, F.R.; Mogilevskij, O.A.; Ponomarev, L.I.
1979-01-01
The adiabatic approximation js used for calculating the energy levels of a hydrogen molecule, i.e. of the simplest four-body system with a Coulomb interaction. The aim of this paper is the investigation of the possible use of the adiabatic method in the molecular problems. The most effective regions of its application are discussed. An infinite system of integro-differential equations is constructed, which describes the hydrogen molecule in the adiabatic approximation with the effective potentials taking into account the corrections to the nuclear motion. The energy of the first three vibrational states of the hydrogen molecule is calculated and compared with the experimental data. The convergence of the method is discussed
Semiclassical theory of resonance inelastic electron-molecule collisions
International Nuclear Information System (INIS)
Kazanskij, A.K.
1986-01-01
Semiclassical approach to the theory of resonance electron-molecule collisions, unlocal with respect to interatomic distance was developed. Two problems were considered: modified adiabatic approach for sigle-pole approximation of R-matrix and Fano-Feshbach-Bardsley theory. It is shown that these problems are similar in semiclassical approximation. A simple equation system with coefficients expressed in quadratures was obtained. It enables to determine amplitudes of all processes (including dissociation adhesion, association ejection, free-free and free-bound transitions) in energetic representation with respect to nucleus vibrations in molecule with allowance for both descrete and continuous spectra of nucleus motion in molecule. Quantitative investigation of the system results to the notion of dynamic energy curve of intermediate state, generalizing the motion of such curve in boomerang theory
Kohn-Sham potentials for fullerenes and spherical molecules
International Nuclear Information System (INIS)
Pavlyukh, Y.; Berakdar, J.
2010-01-01
We present a procedure for the construction of accurate Kohn-Sham potentials of quasispherical molecules starting from the first-principles valence densities. The method is demonstrated for the case of icosahedral C 20 2+ and C 60 molecules. Provided the density is N representable the Hohenberg-Kohn theorem guarantees the uniqueness of the obtained potentials. The potential is iteratively built following the suggestion of R. van Leeuwen and E. J. Baerends [Phys. Rev. A 49, 2421 (1994)]. The high symmetry of the molecules allows a parametrization of the angular dependence of the densities and the potentials using a small number of symmetry-adapted spherical harmonics. The radial behavior of these quantities is represented on a grid and the density is reconstructed from the approximate potential by numerically solving the coupled-channel Kohn-Sham equations. Subsequently, the potential is updated and the procedure is continued until convergence is achieved.
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
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 modelthe 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...
Classical Diophantine equations
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, ...
Flavored quantum Boltzmann equations
International Nuclear Information System (INIS)
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Causal electromagnetic interaction equations
International Nuclear Information System (INIS)
Zinoviev, Yury M.
2011-01-01
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
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.
Spin tunneling in magnetic molecules
Kececioglu, Ersin
In this thesis, we will focus on spin tunneling in a family of systems called magnetic molecules such as Fe8 and Mn12. This is comparatively new, in relation to other tunneling problems. Many issues are not completely solved and/or understood yet. The magnetic molecule Fe 8 has been observed to have a rich pattern of degeneracies in its magnetic spectrum. We focus on these degeneracies from several points of view. We start with the simplest anisotropy Hamiltonian to describe the Fe 8 molecule and extend our discussion to include higher order anisotropy terms. We give analytical expressions as much as we can, for the degeneracies in the semi-classical limit in both cases. We reintroduce jump instantons to the instanton formalism. Finally, we discuss the effect of the environment on the molecule. Our results, for all different models and techniques, agree well with both experimental and numerical results.
Experimental decoherence in molecule interferometry
International Nuclear Information System (INIS)
Hackermueller, L.; Hornberger, K.; Stibor, A.; Zeilinger, A.; Arndt, M.; Kiesewetter, G.
2005-01-01
Full text: We present three mechanisms of decoherence that occur quite naturally in matter wave interferometer with large molecules. One way molecules can lose coherence is through collision with background gas particles. We observe a loss of contrast with increasing background pressure for various types of gases. We can understand this phenomenon quantitatively with a new model for collisional decoherence which corrects older models by a factor of 2 π;. The second experiment studies the thermal emission of photons related to the high internal energy of the interfering molecules. When sufficiently many or sufficiently short photons are emitted inside the interferometer, the fringe contrast is lost. We can continuously vary the temperature of the molecules and compare the loss of contrast with a model based on decoherence theory. Again we find good quantitative agreement. A third mechanism that influences our interference pattern is dephasing due to vibrations of the interference gratings. By adding additional vibrations we study this effect in more detail. (author)
Equations of multiparticle dynamics
International Nuclear Information System (INIS)
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Electroweak evolution equations
International Nuclear Information System (INIS)
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
Differential equations with Mathematica
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
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
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), ...
Analytic structure of solutions to multiconfiguration equations
Energy Technology Data Exchange (ETDEWEB)
Fournais, Soeren [Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, DK-8000 Arhus C (Denmark); Hoffmann-Ostenhof, Maria [Fakultaet fuer Mathematik, Universitaet Wien, Nordbergstrasse 15, A-1090 Vienna (Austria); Hoffmann-Ostenhof, Thomas [Institut fuer Theoretische Chemie, Waehringerstrasse 17, Universitaet Wien, A-1090 Vienna (Austria); Soerensen, Thomas Oestergaard [Department of Mathematics, Imperial College London, Huxley Building, 180 Queen' s Gate, London SW7 2AZ (United Kingdom)], E-mail: fournais@imf.au.dk, E-mail: Maria.Hoffmann-Ostenhof@univie.ac.at, E-mail: thoffman@esi.ac.at, E-mail: t.sorensen@imperial.ac.uk
2009-08-07
We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree-Fock) of Coulomb systems. We prove the following: let {l_brace}{psi}{sub 1}, ..., {psi}{sub M}{r_brace} be any solution to the rank-M multiconfiguration equations for a molecule with L fixed nuclei at R{sub 1},...,R{sub L} element of R{sup 3}. Then, for any j in {l_brace}1, ..., M{r_brace}, k in {l_brace}1, ..., L{r_brace}, there exists a neighborhood U{sub j,k} subset or equal R{sup 3} of R{sub k}, and functions {psi}{sup (1)}{sub j,k}, {psi}{sup (2)}{sub j,k}, real analytic in U{sub j,k}, such that {phi}{sub j}(x)={phi}{sub j,k}{sup (1)}(x)+|x-R{sub k}|{phi}{sub j,k}{sup (2)}(x), x element of U{sub j,k}. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo-Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schroedinger operator of atoms and molecules near two-particle coalescence points.
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.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
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
Photoionization of atoms and molecules
International Nuclear Information System (INIS)
Samson, J.A.R.
1976-01-01
A literature review on the present state of knowledge in photoionization is presented. Various experimental techniques that have been developed to study photoionization, such as fluorescence and photoelectron spectroscopy, mass spectroscopy, are examined. Various atoms and molecules were chosen to illustrate these techniques, specifically helium and xenon atoms and hydrogen molecules. Specialized photoionization such as in positive and negative ions, excited states, and free radicals is also treated. Absorption cross sections and ionization potentials are also discussed
Low pressure tritiation of molecules
International Nuclear Information System (INIS)
Moran, T.F.; Powers, J.C.; Lively, M.O.
1980-01-01
A method is described of tritiating sensitive biological molecules by depositing molecules of the substance to be tritiated on a supporting substrate in an evacuated vacuum chamber near, but not in the path of, an electron beam which traverses the chamber, admitting tritium gas into the chamber, and subjecting the tritium to the electron beam. Vibrationally excited tritium gas species are generated which collide and react with the substance thus incorporating tritium atoms into the substance. (U.K.)
Exact solutions of the generalized Lane–Emden equations of the ...
Indian Academy of Sciences (India)
the mutual attraction of its molecules and subject to the classical laws of thermodynamics. This equation was proposed ... was investigated for first integrals by Leach [31]. Moreover, transformation properties of a more general Emden–Fowler equation were considered in Mellin et al [5]. A review paper by Wong [32] contains ...
International Nuclear Information System (INIS)
Raghuraman, P.; Bossel, U.
1974-01-01
Under conditions typical for the extraction of nozzle beams from free jets the rarefied flow pattern in the expansion chamber containing skimming hardware components and background gas is studied using a free molecule solution to the Boltzmann equation
Computing generalized Langevin equations and generalized Fokker-Planck equations.
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.
FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...
African Journals Online (AJOL)
eobe
plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.
Thermal ion-molecule reactions in oxygen-containing molecules
International Nuclear Information System (INIS)
Kumakura, Minoru
1981-02-01
The energetics of ions and the thermal ion-molecule reactions in oxygen-containing molecules have been studied with a modified time-of-flight mass spectrometer. It was found that the translational energy of ion can be easily obtained from analysis of the decay curve using the time-of-flight mass spectrometer. The condensation-elimination reactions proceeded via cross- and homo-elimination mechanism in which the nature of intermediate-complex could be correlated with the nature of reactant ion. It was elucidated that behavior of poly-atomic oxygen-containing ions on the condensation-elimination reactions is considerably influenced by their oxonium ion structures having functional groups. In addition, the rate constants of the condensation-elimination reactions have affected with the energy state of reactant ion and the dipole moment and/or the polarizability of neutral molecule. It was clarified that the rate constants of the ion-molecule clustering reactions in poly-atomic oxygen-containing molecules such as cyclic ether of six member rings are very large and the cluster ions are stable owing to the large number of vibrational degree of freedom in the cluster ions. (author)
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
Auxiliary equation method for solving nonlinear partial differential equations
International Nuclear Information System (INIS)
Sirendaoreji,; Jiong, Sun
2003-01-01
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
The Molecule Cloud - compact visualization of large collections of molecules
Directory of Open Access Journals (Sweden)
Ertl Peter
2012-07-01
Full Text Available Abstract Background Analysis and visualization of large collections of molecules is one of the most frequent challenges cheminformatics experts in pharmaceutical industry are facing. Various sophisticated methods are available to perform this task, including clustering, dimensionality reduction or scaffold frequency analysis. In any case, however, viewing and analyzing large tables with molecular structures is necessary. We present a new visualization technique, providing basic information about the composition of molecular data sets at a single glance. Summary A method is presented here allowing visual representation of the most common structural features of chemical databases in a form of a cloud diagram. The frequency of molecules containing particular substructure is indicated by the size of respective structural image. The method is useful to quickly perceive the most prominent structural features present in the data set. This approach was inspired by popular word cloud diagrams that are used to visualize textual information in a compact form. Therefore we call this approach “Molecule Cloud”. The method also supports visualization of additional information, for example biological activity of molecules containing this scaffold or the protein target class typical for particular scaffolds, by color coding. Detailed description of the algorithm is provided, allowing easy implementation of the method by any cheminformatics toolkit. The layout algorithm is available as open source Java code. Conclusions Visualization of large molecular data sets using the Molecule Cloud approach allows scientists to get information about the composition of molecular databases and their most frequent structural features easily. The method may be used in the areas where analysis of large molecular collections is needed, for example processing of high throughput screening results, virtual screening or compound purchasing. Several example visualizations of large
Molecule-by-Molecule Writing Using a Focused Electron Beam
DEFF Research Database (Denmark)
Van Dorp, Willem F.; Zhang, Xiaoyan; Feringa, Ben L.
2012-01-01
atoms also be written with an electron beam? We verify this with focused electron-beam-induced deposition (FEBID), a direct-write technique that has the current record for the smallest feature written by (electron) optical lithography. We show that the deposition of an organometallic precursor...... on graphene can be followed molecule-by-molecule with FEBID. The results show that mechanisms that are inherent to the process inhibit a further increase in control over the process. Hence, our results present the resolution limit of (electron) optical lithography techniques. The writing of isolated...
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...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Partial differential equations
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.
Ordinary differential equations
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
Partial differential equations
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
Elliptic partial differential equations
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
dimensional Jaulent–Miodek equations
Indian Academy of Sciences (India)
(2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...
Equationally Noetherian property of Ershov algebras
Dvorzhetskiy, Yuriy
2014-01-01
This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.
Physics of Complex Polymeric Molecules
Kelly, Joshua Walter
The statistical physics of complex polymers with branches and circuits is the topic of this dissertation. An important motivation are large, single-stranded (ss) RNA molecules. Such molecules form complex ``secondary" and ``tertiary" structures that can be represented as branched polymers with circuits. Such structures are in part directly determined by the nucleotide sequence and in part subject to thermal fluctuations. The polymer physics literature on molecules in this class has mostly focused on randomly branched polymers without circuits while there has been minimal research on polymers with specific structures and on polymers that contain circuits. The dissertation is composed of three parts: Part I studies branched polymers with thermally fluctuating structure confined to a potential well as a simple model for the encapsidation of viral RNA. Excluded volume interactions were ignored. In Part II, I apply Flory theory to the study of the encapsidation of viral ss RNA molecules with specific branched structures, but without circuits, in the presence of excluded volume interaction. In Part III, I expand on Part II and consider complex polymers with specific structure including both branching and circuits. I introduce a method based on the mathematics of Laplacian matrices that allows me to calculate density profiles for such molecules, which was not possible within Flory theory.
Quantum transport through organic molecules
International Nuclear Information System (INIS)
Maiti, Santanu K.
2007-01-01
We investigate the electronic transport for the model of benzene-1, 4-dithiolate (BDT) molecule and some other geometric models of benzene molecule attached with two semi-infinite metallic electrodes by the use of Green's function technique. An analytic approach for the electronic transport through the molecular bridges is presented, based on the tight-binding model. Transport of electrons in such molecular bridges is strongly affected by the geometry of the molecules and their coupling strength with the electrodes. Conductance (g) shows resonance peaks associated with the molecular energy eigenstates. In the weak molecule-to-electrodes coupling limit current (I) passing through the molecules shows staircase-like behavior with sharp steps, while, it varies quite continuously in the limit of strong molecular coupling with the applied bias voltage (V). In presence of the transverse magnetic field conductance gives oscillatory behavior with flux φ, threaded by the molecular ring, showing φ 0 ( = ch/e) flux-quantum periodicity. Though conductance changes with the application of transverse magnetic field, but the current-voltage characteristics remain same in presence of this magnetic field for these molecular bridge systems
Dissociation and decay of ultracold sodium molecules
International Nuclear Information System (INIS)
Mukaiyama, T.; Abo-Shaeer, J.R.; Xu, K.; Chin, J.K.; Ketterle, W.
2004-01-01
The dissociation of ultracold molecules was studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energies directly yielded the strength of the atom-molecule coupling. They showed nonlinear dependence on the ramp speed. This was explained by a Wigner threshold law which predicts that the decay rate of the molecules above threshold increases with the density of states. In addition, inelastic molecule-molecule and molecule-atom collisions were characterized
Flexible single molecule simulation of reaction-diffusion processes
International Nuclear Information System (INIS)
Hellander, Stefan; Loetstedt, Per
2011-01-01
An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.
International Nuclear Information System (INIS)
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
International Nuclear Information System (INIS)
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
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.)
International Nuclear Information System (INIS)
Kalinowski, M.W.; Szymanowski, L.
1982-03-01
A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)
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 ...
Small molecule fluoride toxicity agonists.
Nelson, James W; Plummer, Mark S; Blount, Kenneth F; Ames, Tyler D; Breaker, Ronald R
2015-04-23
Fluoride is a ubiquitous anion that inhibits a wide variety of metabolic processes. Here, we report the identification of a series of compounds that enhance fluoride toxicity in Escherichia coli and Streptococcus mutans. These molecules were isolated by using a high-throughput screen (HTS) for compounds that increase intracellular fluoride levels as determined via a fluoride riboswitch reporter fusion construct. A series of derivatives were synthesized to examine structure-activity relationships, leading to the identification of compounds with improved activity. Thus, we demonstrate that small molecule fluoride toxicity agonists can be identified by HTS from existing chemical libraries by exploiting a natural fluoride riboswitch. In addition, our findings suggest that some molecules might be further optimized to function as binary antibacterial agents when combined with fluoride. Copyright © 2015 Elsevier Ltd. All rights reserved.
Double photoionisation spectra of molecules
Eland, John
2017-01-01
This book contains spectra of the doubly charged positive ions (dications) of some 75 molecules, including the major constituents of terrestrial and planetary atmospheres and prototypes of major chemical groups. It is intended to be a new resource for research in all areas of molecular spectroscopy involving high energy environments, both terrestrial and extra-terrestrial. All the spectra have been produced by photoionisation using laboratory lamps or synchrotron radiation and have been measured using the magnetic bottle time-of-flight technique by coincidence detection of correlated electron pairs. Full references to published work on the same species are given, though for several molecules these are the first published spectra. Double ionisation energies are listed and discussed in relation to the molecular electronic structure of the molecules. A full introduction to the field of molecular double ionisation is included and the mechanisms by which double photoionisation can occur are examined in detail. A p...
Technetium-aspirin molecule complexes
International Nuclear Information System (INIS)
El-Shahawy, A.S.; Mahfouz, R.M.; Aly, A.A.M.; El-Zohry, M.
1993-01-01
Technetium-aspirin and technetium-aspirin-like molecule complexes were prepared. The structure of N-acetylanthranilic acid (NAA) has been decided through CNDO calculations. The ionization potential and electron affinity of the NAA molecule as well as the charge densities were calculated. The electronic absorption spectra of Tc(V)-Asp and Tc(V)-ATS complexes have two characteristic absorption bands at 450 and 600 nm, but the Tc(V)-NAA spectrum has one characteristic band at 450 nm. As a comparative study, Mo-ATS complex was prepared and its electronic absorption spectrum is comparable with the Tc-ATS complex spectrum. (author)
Exotic helium molecules; Molecules exotiques d'helium
Energy Technology Data Exchange (ETDEWEB)
Portier, M
2007-12-15
We study the photo-association of an ultracold cloud of magnetically trapped helium atoms: pairs of colliding atoms interact with one or two laser fields to produce a purely long range {sup 4}He{sub 2}(2{sup 3}S{sub 1}-2{sup 3}P{sub 0}) molecule, or a {sup 4}He{sub 2}(2{sup 3}S{sub 1}-2{sup 3}S{sub 1}) long range molecule. Light shifts in one photon photo-association spectra are measured and studied as a function of the laser polarization and intensity, and the vibrational state of the excited molecule. They result from the light-induced coupling between the excited molecule, and bound and scattering states of the interaction between two metastable atoms. Their analysis leads to the determination of the scattering length a = (7.2 {+-} 0.6) ruling collisions between spin polarized atoms. The two photon photo-association spectra show evidence of the production of polarized, long-range {sup 4}He{sub 2}(2{sup 3}S{sub 1}-2{sup 3}S{sub 1}) molecules. They are said to be exotic as they are made of two metastable atoms, each one carrying a enough energy to ionize the other. The corresponding lineshapes are calculated and decomposed in sums and products of Breit-Wigner and Fano profiles associated to one and two photon processes. The experimental spectra are fit, and an intrinsic lifetime {tau} = (1.4 {+-} 0.3) {mu}s is deduced. It is checked whether this lifetime could be limited by spin-dipole induced Penning autoionization. This interpretation requires that there is a quasi-bound state close to the dissociation threshold in the singlet interaction potential between metastable helium atoms for the theory to match the experiment. (author)
Exotic helium molecules; Molecules exotiques d'helium
Energy Technology Data Exchange (ETDEWEB)
Portier, M
2007-12-15
We study the photo-association of an ultracold cloud of magnetically trapped helium atoms: pairs of colliding atoms interact with one or two laser fields to produce a purely long range {sup 4}He{sub 2}(2{sup 3}S{sub 1}-2{sup 3}P{sub 0}) molecule, or a {sup 4}He{sub 2}(2{sup 3}S{sub 1}-2{sup 3}S{sub 1}) long range molecule. Light shifts in one photon photo-association spectra are measured and studied as a function of the laser polarization and intensity, and the vibrational state of the excited molecule. They result from the light-induced coupling between the excited molecule, and bound and scattering states of the interaction between two metastable atoms. Their analysis leads to the determination of the scattering length a = (7.2 {+-} 0.6) ruling collisions between spin polarized atoms. The two photon photo-association spectra show evidence of the production of polarized, long-range {sup 4}He{sub 2}(2{sup 3}S{sub 1}-2{sup 3}S{sub 1}) molecules. They are said to be exotic as they are made of two metastable atoms, each one carrying a enough energy to ionize the other. The corresponding lineshapes are calculated and decomposed in sums and products of Breit-Wigner and Fano profiles associated to one and two photon processes. The experimental spectra are fit, and an intrinsic lifetime {tau} = (1.4 {+-} 0.3) {mu}s is deduced. It is checked whether this lifetime could be limited by spin-dipole induced Penning autoionization. This interpretation requires that there is a quasi-bound state close to the dissociation threshold in the singlet interaction potential between metastable helium atoms for the theory to match the experiment. (author)
Differential equations extended to superspace
Energy Technology Data Exchange (ETDEWEB)
Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)
2003-07-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
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.
Differential equations extended to superspace
International Nuclear Information System (INIS)
Torres, J.; Rosu, H.C.
2003-01-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
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.
An equations of motion approach for open shell systems
International Nuclear Information System (INIS)
Yeager, D.L.; McKoy, V.
1975-01-01
A straightforward scheme is developed for extending the equations of motion formalism to systems with simple open shell ground states. Equations for open shell random phase approximation (RPA) are given for the cases of one electron outside of a closed shell in a nondegenerate molecular orbital and for the triplet ground state with two electrons outside of a closed shell in degenerate molecular orbitals. Applications to other open shells and extension of the open shell EOM to higher orders are both straightforward. Results for the open shell RPA for lithium atom and oxygen molecule are given
p-Euler equations and p-Navier-Stokes equations
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.
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)
Alternatives to the Dirac equation
International Nuclear Information System (INIS)
Girvin, S.M.; Brownstein, K.R.
1975-01-01
Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility
Wave Partial Differential Equation
Szöllös, Alexandr
2009-01-01
Práce se zabývá diferenciálními rovnicemi, jejich využitím při analýze vedení, experimenty s vedením a možnou akcelerací výpočtu v GPU s využitím prostředí nVidia CUDA. This work deals with diffrential equations, with the possibility of using them for analysis of the line and the possibility of accelerating the computations in GPU using nVidia CUDA. C
Gomez, Humberto
2016-06-01
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.
Scaling of differential equations
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...
Parabolized stability equations
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.
Pomeau, Yves; Piasecki, Jarosław
2017-11-01
The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.
Nucleic Acids as Information Molecules.
McInerney, Joseph D.
1996-01-01
Presents an activity that aims at enabling students to recognize that DNA and RNA are information molecules whose function is to store, copy, and make available the information in biological systems, without feeling overwhelmed by the specialized vocabulary and the minutia of the central dogma. (JRH)
Small Molecule PET-Radiopharmaceuticals
Elsinga, Philip H.; Dierckx, Rudi A. J. O.
This review describes several aspects required for the development of small molecule PET-tracers. Design and selection criteria are important to consider before starting to develop novel PET-tracers. Principles and latest trends in C-11 and F-18-radiochemistry are summarized. In addition an update
Hybrid molecule/superconductor assemblies
International Nuclear Information System (INIS)
McDevitt, J.T.; Haupt, S.G.; Riley, D.R.; Zhao, J.; Zhou, J.P., Jones, C.
1993-01-01
The fabrication of electronic devices from molecular materials has attracted much attention recently. Schottky diodes, molecular transistors, metal-insulator-semiconductor diodes, MIS field effect transistors and light emitting diodes have all been prepared utilizing such substances. The active elements in these devices have been constructed by depositing the molecular phase onto the surface of a metal, semiconductor or insulating substrate. With the recent discovery of high temperature superconductivity, new opportunities now exist for the study of molecule/superconductor interactions as well as for the construction of novel hybrid molecule/superconductor devices. In this paper, methods for preparing the initial two composite molecule/semiconductor devices will be reported. Consequently, light sensors based on dye-coated superconductor junctions as well as molecular switches fashioned from conductive polymer coated superconductor junctions as well as molecular switches fashioned from conductive polymer coated superconductor microbridges will be discussed. Moreover, molecule/superconductor energy and electron transfer phenomena will be illustrated also for the first time
Mass spectrometry of large molecules
International Nuclear Information System (INIS)
Facchetti, S.
1985-01-01
The lectures in this volume were given at a course on mass spectrometry of large molecules, organized within the framework of the Training and Education programme of the Joint Research Centre of the European Communities. Although first presented in 1983, most of the lectures have since been updated by their authors. (orig.)
African Journals Online (AJOL)
Temechegn
University of the Witwatersrand, Johannesburg, South Africa ... [African Journal of Chemical Education—AJCE 6(2), July 2016] ... understand science concepts: in essence these are macroscopic (phenomena), microscopic .... than the simple freeing up of already-existing smaller molecules: this implies a high melting point.
Fascinating Organic Molecules from Nature
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 5. Fascinating Organic Molecules from Nature - Using a Natural ... Road Banashankari 2nd Stage Bangalore 560 070, India. Department of Chemistry Sri Sathya Sai Institute of Higher Learning Brindavan Campus Bangalore 560 067, India.
Fascinating Organic Molecules from Nature
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 7. Fascinating Organic Molecules from Nature - Sweet Stimulants of ... Road Banashankari 2nd Stage Bangalore 560 070, India. Department of Chemistry Sri Sathya Sai Institute of Higher Learning Brindavan Campus Bangalore 560 067, India.
Energy Technology Data Exchange (ETDEWEB)
Sazonov, S. V., E-mail: sazonov.sergey@gmail.com [National Research Centre “Kurchatov Institute,” (Russian Federation); Ustinov, N. V., E-mail: n-ustinov@mail.ru [Moscow State University of Railways, Kaliningrad Branch (Russian Federation)
2017-02-15
The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.
Electron--molecule scattering in momentum space
International Nuclear Information System (INIS)
Ritchie, B.
1979-01-01
We examine the Fourier transform of the Schroedinger equation for electron--molecule scattering, treated as potential scattering from a multicenter distribution of charged fixed in space. When the angle theta between R,the internuclear vector of a diatomic target, and q, the momentum transfer, is held fixed during the collision, then the directions of incidence and scattering are fixed relative to R. The process is then described as having a dynamical dependence on the magnitude of q, q, from which the scattering angle is determined, and a parametric dependence on q's direction relative to R. This approximation is used routinely at high energies in the calculation of the Born amplitude. Fixed--nuclei coordinate--space studies suggest that this approximation can be extended to low energies, provided the amplitude is taken from the solution of the integral equation of momentum space rather than from its inhomogeneity, proportional to the Born amplitude. We constrain R to be in the same direction relative to q', a virtual momentum transfer belonging to the kernel, as it is to q.Calculations are performed for the e, H 2 scattering in the static approximation, and cross sections averaged over theta/sub R/ are shown to be in good agreement with cross sections calculated by use of coupled spherical and coupled spheroidal partial wave theories. The angular distribution in the static approximation is also calculated at an incident energy close to 7 eV, where exchange is relatively unimportant. This result is in reasonably good agreement with that of R matrix theory in the static--exchange approximation. The extension of the theory to treat exchange is formulated and discussed. Also its extension to treat more complicated molecular targets is discussed
Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
Bernhoff, Niclas
2018-05-01
An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.
Isotope separation using vibrationally excited molecules
International Nuclear Information System (INIS)
Woodroffe, J.A.; Keck, J.C.
1979-01-01
Vibrational excitation of molecules having components of a selected isotope type is used to produce a conversion from vibrational to translational excitation of the molecules by collision with the molecules of a heavy carrier gas. The resulting difference in translaton between the molecules of the selected isotope type and all other molecules of the same compound permits their separate collection. When applied to uranium enrichment, a subsonic cryogenic flow of molecules of uranium hexafluoride in combination with an argon carrier gas is directed through a cooled chamber that is illuminated by laser radiaton tuned to vibrationally excite the uranium hexafluoride molecules of a specific uranium isotope. The excited molecules collide with carrier gas molecules, causing a conversion of the excitation energy into a translation of the excited molecule, which results in a higher thermal energy or diffusivity than that of the other uranium hexafluoride molecules. The flowing molecules including the excited molecules directly enter a set of cryogenically cooled channels. The higher thermal velocity of the excited molecules increases the probability of their striking a collector surface. The molecules which strike this surface immediately condense. After a predetermined thickness of molecules is collected on the surface, the flow of uranium hexafluoride is interrupted and the chamber heated to the point of vaporization of the collected hexafluoride, permitting its removal. (LL)
Molecules in strong laser fields. In depth study of H{sub 2} molecule
Energy Technology Data Exchange (ETDEWEB)
Awasthi, Manohar
2009-10-29
A method for solving the time-dependent Schroedinger equation (TDSE) describing the electronic motion of the molecules exposed to very short intense laser pulses has been developed. The time-dependent electronic wavefunction is expanded in terms of a superposition of field-free eigenstates. The field-free eigenstates are calculated in two ways. In the first approach, which is applicable to two electron systems like H{sub 2}, fully correlated field-free eigenstates are obtained in complete dimensionality using configuration-interaction calculation where the one-electron basis functions are built from B splines. In the second approach, which is even applicable to larger molecules, the field-free eigenstates are calculated within the single-active-electron (SAE) approximation using density functional theory. In general, the method can be divided into two parts, in the first part the field-free eigenstates are calculated and then in the second part a time propagation for the laser pulse parameters is performed. The H{sub 2} molecule is the testing ground for the implementation of both the methods. The reliability of the configuration interaction (CI) based method for the solution of TDSE (CI-TDSE) is tested by comparing results in the low-intensity regime to the prediction of lowest-order perturbation theory. Another test for the CI-TDSE method is in the united atom limit for the H{sub 2} molecule. By selecting a very small value of the internuclear distance close to zero for the H{sub 2} molecule, Helium atom is obtained. Once the functionality and the reliability of the method is established, it is used for obtaining accurate results for molecular hydrogen exposed to intense laser fields. The results for the standard 800 nm Titanium-Sapphire laser and its harmonics at 400 nm and 266 nm are shown. The results for a scan over a wide range of incident photon energies as well as dependence on the internuclear distance are presented. The photoelectron spectra including
Molecules in strong laser fields. In depth study of H2 molecule
International Nuclear Information System (INIS)
Awasthi, Manohar
2009-01-01
A method for solving the time-dependent Schroedinger equation (TDSE) describing the electronic motion of the molecules exposed to very short intense laser pulses has been developed. The time-dependent electronic wavefunction is expanded in terms of a superposition of field-free eigenstates. The field-free eigenstates are calculated in two ways. In the first approach, which is applicable to two electron systems like H 2 , fully correlated field-free eigenstates are obtained in complete dimensionality using configuration-interaction calculation where the one-electron basis functions are built from B splines. In the second approach, which is even applicable to larger molecules, the field-free eigenstates are calculated within the single-active-electron (SAE) approximation using density functional theory. In general, the method can be divided into two parts, in the first part the field-free eigenstates are calculated and then in the second part a time propagation for the laser pulse parameters is performed. The H 2 molecule is the testing ground for the implementation of both the methods. The reliability of the configuration interaction (CI) based method for the solution of TDSE (CI-TDSE) is tested by comparing results in the low-intensity regime to the prediction of lowest-order perturbation theory. Another test for the CI-TDSE method is in the united atom limit for the H 2 molecule. By selecting a very small value of the internuclear distance close to zero for the H 2 molecule, Helium atom is obtained. Once the functionality and the reliability of the method is established, it is used for obtaining accurate results for molecular hydrogen exposed to intense laser fields. The results for the standard 800 nm Titanium-Sapphire laser and its harmonics at 400 nm and 266 nm are shown. The results for a scan over a wide range of incident photon energies as well as dependence on the internuclear distance are presented. The photoelectron spectra including above
Preparation of translationally cold neutral molecules.
Di Domenicantonio, Giulia; Bertsche, Benjamin; Osterwalder, Andreas
2011-01-01
Efforts at EPFL to obtain translationally cold neutral molecules are described. Active deceleration of polar molecules is performed by confining the molecules in moving three-dimensional electrostatic traps, and by appropriately choosing the velocity of those traps. Alternatively, cold molecules can be obtained by velocity filtering. Here, the velocity of the molecules is not changed, but instead the cold molecules are extracted from a thermal sample by using the competition between the electrostatic force and the centrifugal force inside a bent electrostatic guide for polar molecules.
Ichikawa, Kazuhisa; Suzuki, Takashi; Murata, Noboru
2010-11-30
Molecular events in biological cells occur in local subregions, where the molecules tend to be small in number. The cytoskeleton, which is important for both the structural changes of cells and their functions, is also a countable entity because of its long fibrous shape. To simulate the local environment using a computer, stochastic simulations should be run. We herein report a new method of stochastic simulation based on random walk and reaction by the collision of all molecules. The microscopic reaction rate P(r) is calculated from the macroscopic rate constant k. The formula involves only local parameters embedded for each molecule. The results of the stochastic simulations of simple second-order, polymerization, Michaelis-Menten-type and other reactions agreed quite well with those of deterministic simulations when the number of molecules was sufficiently large. An analysis of the theory indicated a relationship between variance and the number of molecules in the system, and results of multiple stochastic simulation runs confirmed this relationship. We simulated Ca²(+) dynamics in a cell by inward flow from a point on the cell surface and the polymerization of G-actin forming F-actin. Our results showed that this theory and method can be used to simulate spatially inhomogeneous events.
Atoms - molecules - nuclei. Vol. 1
International Nuclear Information System (INIS)
Otter, G.; Honecker, R.
1993-01-01
This first volume covers the following topics: Wave-particle dualism, classical atomic physics; the Schroedinger equation, angular momentum in quantum physics, one-electron atoms and many-electron atoms with atomic structure, atomic spectra, exotic atoms, influence of electric and magnetic fields
Introduction to partial differential equations
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.
Analytic solutions of hydrodynamics equations
International Nuclear Information System (INIS)
Coggeshall, S.V.
1991-01-01
Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions
On matrix fractional differential equations
Directory of Open Access Journals (Sweden)
Adem Kılıçman
2017-01-01
Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.
Differential equations methods and applications
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. .
Integral equations and their applications
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...
Stochastic partial differential equations
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 ...
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.
Quantum Monte Carlo for atoms and molecules
International Nuclear Information System (INIS)
Barnett, R.N.
1989-11-01
The diffusion quantum Monte Carlo with fixed nodes (QMC) approach has been employed in studying energy-eigenstates for 1--4 electron systems. Previous work employing the diffusion QMC technique yielded energies of high quality for H 2 , LiH, Li 2 , and H 2 O. Here, the range of calculations with this new approach has been extended to include additional first-row atoms and molecules. In addition, improvements in the previously computed fixed-node energies of LiH, Li 2 , and H 2 O have been obtained using more accurate trial functions. All computations were performed within, but are not limited to, the Born-Oppenheimer approximation. In our computations, the effects of variation of Monte Carlo parameters on the QMC solution of the Schroedinger equation were studied extensively. These parameters include the time step, renormalization time and nodal structure. These studies have been very useful in determining which choices of such parameters will yield accurate QMC energies most efficiently. Generally, very accurate energies (90--100% of the correlation energy is obtained) have been computed with single-determinant trail functions multiplied by simple correlation functions. Improvements in accuracy should be readily obtained using more complex trial functions
A radial distribution function-based open boundary force model for multi-centered molecules
Neumann, Philipp
2014-06-01
We derive an expression for radial distribution function (RDF)-based open boundary forcing for molecules with multiple interaction sites. Due to the high-dimensionality of the molecule configuration space and missing rotational invariance, a computationally cheap, 1D approximation of the arising integral expressions as in the single-centered case is not possible anymore. We propose a simple, yet accurate model invoking standard molecule- and site-based RDFs to approximate the respective integral equation. The new open boundary force model is validated for ethane in different scenarios and shows very good agreement with data from periodic simulations. © World Scientific Publishing Company.
International Nuclear Information System (INIS)
Markovic, M. I.; Radunovic, J. B.
1976-01-01
Determination of spatial distribution of neutron flux in water, most frequently used moderator in thermal reactors, demands microscopic scattering kernels dependence on cosine of thermal neutrons scattering angle when solving the Boltzmann equation. Since spatial orientation of water molecules influences this dependence it is necessary to perform orientation averaging or rotation-vibrational intermediate scattering function for water molecules. The calculations described in this paper and the obtained results showed that methods of orientation averaging do not influence the anisotropy of thermal neutrons scattering on water molecules, but do influence the inelastic scattering
Effects of molecular orientation in the laser ionization of molecules
International Nuclear Information System (INIS)
Xinhua Xie; Gerald Jordan; Christopher Ede; Armin Scrinzi
2006-01-01
Complete test of publication follows. Time-dependent electron momentum distributions are calculated during ionization of linear molecules by a strong laser pulse and upon recollision. For typical experimental laser parameters, we find a strong influence of molecular orientation and initial state symmetry on the total ionization rates and also on momentum distributions, compared to which the effect of electron correlation is less important for simple molecules. The dynamics of electron release and subsequent recollision with the parent ion largely determines the time-frequency structure of harmonic radiation, which underlies the generation of attosecond XUV pulses and the time-resolved imaging techniques for the electronic structure of molecules. In the present work, the effects of orientation and initial orbital symmetry are investigated by solving the time-dependent Schroedinger equation for a two-dimensional diatomic molecule in the single-active electron approximation. As in the presence of strong external fields recolliding electrons cannot be easily separated from bound electrons, the electron wave packet is probed at some distance from where all electrons can be safety considered as detached. We find that momentum distributions strongly depend on molecular size, orientation of the molecular axis, and node structure of the initial state. In order to determine the momentum spectra at the time of electron release and upon recollision, we classically propagate the Wigner distributions of probed wavepackets backward and forward in time, respectively. We find that the times of peak recollision current can vary strongly with the orientation of the molecule. Moreover, correlation effects on the electron spectra are included using the multi-configuration time-dependent Hartree-Fock method. The calculations are performed in three spatial dimensions with the restriction to cylindrical symmetry, where the molecule is aligned with the laser field. Correlation is studied
Wetterich, C.
2018-06-01
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.
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.
Supersymmetric two-particle equations
International Nuclear Information System (INIS)
Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.
1986-01-01
In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found
Introduction to ordinary differential equations
Rabenstein, Albert L
1966-01-01
Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutio
On matrix fractional differential equations
Adem Kılıçman; Wasan Ajeel Ahmood
2017-01-01
The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...
Observing electron motion in molecules
International Nuclear Information System (INIS)
Chelkowski, S; Yudin, G L; Bandrauk, A D
2006-01-01
We study analytically the possibility for monitoring electron motion in a molecule using two ultrashort laser pulses. The first prepares a coherent superposition of two electronic molecular states whereas the second (attosecond pulse) photoionizes the molecule. We show that interesting information about electron dynamics can be obtained from measurement of the photoelectron spectra as a function of the time delay between two pulses. In particular, asymmetries in photoelectron angular distribution provide a simple signature of the electron motion within the initial time-dependent coherently coupled two molecular states. Both asymmetries and electron spectra show very strong two-centre interference patterns. We illustrate these effects using as an example a dissociating hydrogen molecular ion probed by the attosecond pulses
Tunneling Ionization of Diatomic Molecules
DEFF Research Database (Denmark)
Svensmark, Jens Søren Sieg
2016-01-01
When a molecule is subject to a strong laser field, there is a probability that an electron can escape, even though the electrons are bound by a large potential barrier. This is possible because electrons are quantum mechanical in nature, and they are therefore able to tunnel through potential...... barriers, an ability classical particles do not possess. Tunnelling is a fundamental quantum mechanical process, a process that is distinctly non-classical, so solving this tunnelling problem is not only relevant for molecular physics, but also for quantum theory in general. In this dissertation the theory...... of tunneling ionizaion of molecules is presented and the results of numerical calculations are shown. One perhaps surprising result is, that the frequently used Born-Oppenheimer approximation breaks down for weak fields when describing tunneling ionization. An analytic theory applicable in the weak-field limit...
Physics of atoms and molecules
International Nuclear Information System (INIS)
Bransden, B.H.; Joachain, C.J.
1983-01-01
This book presents a unified account of the physics of atoms and molecules at a level suitable for second- and third-year undergraduate students of physics and physical chemistry. Following a brief historical introduction to the subject the authors outline the ideas and approximation methods of quantum mechanics to be used later in the book. Six chapters look at the structure of atoms and the interactions between atoms and electromagnetic radiation. The authors then move on to describe the structure of molecules and molecular spectra. Three chapters deal with atomic collisions, the scattering of electrons by atoms and the scattering of atoms by atoms. The concluding chapter considers a few of the many important applications of atomic physics within astrophysics, laser technology, and nuclear fusion. Problems are given at the end of each chapter, with hints at the solutions in an appendix. Other appendices include various special topics and derivations together with useful tables of units. (author)
Electrondriven processes in polyatomic molecules
Energy Technology Data Exchange (ETDEWEB)
McKoy, Vincent [California Inst. of Technology (CalTech), Pasadena, CA (United States)
2017-03-20
This project developed and applied scalable computational methods to obtain information about low-energy electron collisions with larger polyatomic molecules. Such collisions are important in modeling radiation damage to living systems, in spark ignition and combustion, and in plasma processing of materials. The focus of the project was to develop efficient methods that could be used to obtain both fundamental scientific insights and data of practical value to applications.
Intersystem crossing in complex molecules
International Nuclear Information System (INIS)
Pappalardo, R.G.
1980-01-01
The general question of singlet-triplet intersystem crossing is addressed in the context of large organic molecules, i.e., ''complex'' molecules capable of self-relaxation in the absence of collisions. Examples of spectral properties of such molecules in the vapor phase are discussed, relying on extensive Russian literature in this area. Formal expressions for the relaxation rate in the electronic excited states are derived on the basis of the formalism of collision theory, and are applied to the specific case of intersystem crossing. The derivation of the ''energy-gap'' law for triplet-singlet conversion in aromatic hydrocarbons is briefly outlined. The steep rise of internal conversion rates as a function of excess excitation energy, and its competition with the intersystem crossing process, are reviewed for the case of naphthalene vapor. A general expression for the spin-orbit interaction Hamiltonian in molecular systems is outlined. Experimental observations on singlet-triplet conversion rates and the factors that can drastically affect such rates are discussed, with emphasis on the ''in- ternal'' and ''external'' heavy-atom effects. Basic relations of ESR spectroscopy and magnetophotoselection are reviewed. Technological implications of the singlet-triplet crossing in complex molecules are discussed in the context of chelate lasers, dye lasers and luminescent displays. Effects related to singlet-triplet crossing, and generally to excited-state energy-transfer in biological systems, are exemplified by the role of aromatic amino-acids in the phosphorescence of proteins, by some recent studies of energy-transfer in models of biomembranes, and by the clustering of triplet-energy donor-acceptor pairs in micelles
Cellular Adhesion and Adhesion Molecules
SELLER, Zerrin
2014-01-01
In recent years, cell adhesion and cell adhesion molecules have been shown to be important for many normal biological processes, including embryonic cell migration, immune system functions and wound healing. It has also been shown that they contribute to the pathogenesis of a large number of common human disorders, such as rheumatoid arthritis and tumor cell metastasis in cancer. In this review, the basic mechanisms of cellular adhesion and the structural and functional features of adhes...
Electron interactions with polar molecules
International Nuclear Information System (INIS)
Garrett, W.R.
1981-01-01
A description is given of a number of the features of discrete and continuous spectra of electrons interacting with polar molecules. Attention is focused on the extent to which theoretical predictions concerning cross sections, resonances, and bound states are strongly influenced by the various approximations that are so ubiquitous in the treatment of such problems. Similarly, threshold scattering and photodetachment processes are examined for the case of weakly bound dipole states whose higher members overlap the continuum
Electronic representation of wave equation
Energy Technology Data Exchange (ETDEWEB)
Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)
2016-06-08
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Generalized Lorentz-Force equations
International Nuclear Information System (INIS)
Yamaleev, R.M.
2001-01-01
Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles
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.)
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.
The Dirac equation for accountants
International Nuclear Information System (INIS)
Ord, G.N.
2006-01-01
In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics
Elbing, Mark; Ochs, Rolf; Koentopp, Max; Fischer, Matthias; von Hänisch, Carsten; Weigend, Florian; Evers, Ferdinand; Weber, Heiko B.; Mayor, Marcel
2005-01-01
We have designed and synthesized a molecular rod that consists of two weakly coupled electronic π -systems with mutually shifted energy levels. The asymmetry thus implied manifests itself in a current–voltage characteristic with pronounced dependence on the sign of the bias voltage, which makes the molecule a prototype for a molecular diode. The individual molecules were immobilized by sulfur–gold bonds between both electrodes of a mechanically controlled break junction, and their electronic transport properties have been investigated. The results indeed show diode-like current–voltage characteristics. In contrast to that, control experiments with symmetric molecular rods consisting of two identical π -systems did not show significant asymmetries in the transport properties. To investigate the underlying transport mechanism, phenomenological arguments are combined with calculations based on density functional theory. The theoretical analysis suggests that the bias dependence of the polarizability of the molecule feeds back into the current leading to an asymmetric shape of the current–voltage characteristics, similar to the phenomena in a semiconductor diode. PMID:15956208
The largest molecules in space
International Nuclear Information System (INIS)
Greenberg, J.M.
1983-01-01
The bulk of complex molecules in the space between the stars is shown to be in the small frozen particles of interstellar dust. Each dust grain typically contains some 10 9 atoms of oxygen, carbon and nitrogen in an amorphous molecular mixture. As a result of chemical processing of the particles by ultraviolet photons over times spanning proportional10 8 -10 9 years a substantial portion of each dust grain is converted into complex organic molecules whose maximum molecular weight is limited only by the size of the grain. Laboratory studies of evolution of analog grain materials shows that molecular weights of the order of 500 are readily created and that there is an excellent probability of much more complex molecules being produced. The organic dust component constitutes about one tenth of a percent of the total mass of the Milky Way and far outweighs any estimates of the total mass of all the planets. A planet like the earth is continually accreting matter from space and there was a high probability that in the first five hundred million years after its crust formed it passed through several dark clouds and accreted from a hundred million to ten thousand million tonnes of the organic material of the interstellar dust during each passage. It is suggested that this rain of material could have provided the molecular templates for the origin of life. (orig.)
Electric moments in molecule interferometry
International Nuclear Information System (INIS)
Eibenberger, Sandra; Gerlich, Stefan; Arndt, Markus; Tuexen, Jens; Mayor, Marcel
2011-01-01
We investigate the influence of different electric moments on the shift and dephasing of molecules in a matter wave interferometer. Firstly, we provide a quantitative comparison of two molecules that are non-polar yet polarizable in their thermal ground state and that differ in their stiffness and response to thermal excitations. While C 25 H 20 is rather rigid, its larger derivative C 49 H 16 F 52 is additionally equipped with floppy side chains and vibrationally activated dipole moment variations. Secondly, we elucidate the role of a permanent electric dipole momentby contrasting the quantum interference pattern of a (nearly) non-polar and a polar porphyrin derivative. We find that a high molecular polarizability and even sizeable dipole moment fluctuations are still well compatible with high-contrast quantum interference fringes. The presence of permanent electric dipole moments, however, can lead to a dephasing and rapid degradation of the quantum fringe pattern already at moderate electric fields. This finding is of high relevance for coherence experiments with large organic molecules, which are generally equipped with strong electric moments.
Unconventional superfluids of fermionic polar molecules in a bilayer system
Energy Technology Data Exchange (ETDEWEB)
Boudjemâa, Abdelâali, E-mail: a.boudjemaa@univhb-chlef.dz
2017-05-25
We study unconventional superfluids of fermionic polar molecules in a two-dimensional bilayer system with dipoles are head-to-tail across the layers. We analyze the critical temperature of several unconventional pairings as a function of different system parameters. The peculiar competition between the d- and the s-wave pairings is discussed. We show that the experimental observation of such unconventional superfluids requires ultralow temperatures, which opens up new possibilities to realize several topological phases. - Highlights: • Investigation of novel superfluids of fermionic polar molecules in a bilayer geometry. • Solving the gap equation and the l-wave interlayer scattering problem. • Calculation of the critical temperature of several competing pairings using the BCS approach.
Structures and potential energy functions of Pu3 molecule
International Nuclear Information System (INIS)
Meng Daqiao; Jiang Gang; Liu Xiaoya; Luo Deli; Zhu Zhenghe
2001-01-01
Density functional (B3LYP) method with relativistic effective core potential (RECP) has been used to optimize the structures of Pu 2 and Pu 3 molecules. The results show that the ground states of Pu 2 and Pu 3 molecules are of D ∞h and D 3h symmetry, and of 13 and 19 fold, respectively. The spectral constants of Pu 2 , ω e = 52.3845 cm -1 and ω e x e = 0.0201 cm -1 , and the harmonic frequencies of Pu 3 , ν 1 = 56.9007 cm -1 , ν 2 = 57.1816 cm - '1 and ν 3 = 64.0785 cm -1 , have also been obtained on the B3LYP/RECP level. The potential energy functions of Pu 2 and Pu 3 have been derived, for the first time so far as known, from normal equation fitting and the many-body expansion theory
Collision of hydrogen molecules interacting with two grapheme sheets
Directory of Open Access Journals (Sweden)
Malivuk-Gak Dragana
2017-01-01
Full Text Available It have been performed the computational experiments with two hydrogen molecules and two graphene sheets. Hydrogen - hydrogen and hydrogen - carbon interactions are described by Lennard - Jones potential. Equations of motion of the wave packet centre are solved numerically. The initial molecule velocity was determined by temperature and collisions occur in central point between two sheets. The molecules after collision stay near or get far away of graphene sheets. Then one can find what temperatures, graphene sheet sizes and their distances are favourable for hydrogen storage. It is found that quantum corrections of the molecule classical trajectories are not significant here. Those investigations of possibility of hydrogen storage by physisorption are of interest for improvement of the fuel cell systems. The main disadvantages of computational experiments are: (1 it cannot compute with very large number of C atoms, (2 it is assumed that carbon atoms are placed always in their equilibrium positions and (3 the changes of wave packet width are not considered.
Improved alternating gradient transport and focusing of neutral molecules
International Nuclear Information System (INIS)
Kalnins, Juris; Lambertson, Glen; Gould, Harvey
2001-01-01
Polar molecules, in strong-field seeking states, can be transported and focused by an alternating sequence of electric field gradients that focus in one transverse direction while defocusing in the other. We show by calculation and numerical simulation, how one may greatly improve the alternating gradient transport and focusing of molecules. We use a new optimized multipole lens design, a FODO lattice beam transport line, and lenses to match the beam transport line to the beam source and the final focus. We derive analytic expressions for the potentials, fields, and gradients that may be used to design these lenses. We describe a simple lens optimization procedure and derive the equations of motion for tracking molecules through a beam transport line. As an example, we model a straight beamline that transports a 560 m/s jet-source beam of methyl fluoride molecules 15 m from its source and focuses it to 2 mm diameter. We calculate the beam transport line acceptance and transmission, for a beam with velocity spread, and estimate the transmitted intensity for specified source conditions. Possible applications are discussed
Surface single-molecule dynamics controlled by entropy at low temperatures
Gehrig, J. C.; Penedo, M.; Parschau, M.; Schwenk, J.; Marioni, M. A.; Hudson, E. W.; Hug, H. J.
2017-02-01
Configuration transitions of individual molecules and atoms on surfaces are traditionally described using an Arrhenius equation with energy barrier and pre-exponential factor (attempt rate) parameters. Characteristic parameters can vary even for identical systems, and pre-exponential factors sometimes differ by orders of magnitude. Using low-temperature scanning tunnelling microscopy (STM) to measure an individual dibutyl sulfide molecule on Au(111), we show that the differences arise when the relative position of tip apex and molecule changes by a fraction of the molecule size. Altering the tip position on that scale modifies the transition's barrier and attempt rate in a highly correlated fashion, which results in a single-molecular enthalpy-entropy compensation. Conversely, appropriately positioning the STM tip allows selecting the operating point on the compensation line and modifying the transition rates. The results highlight the need to consider entropy in transition rates of single molecules, even at low temperatures.
Difference equations theory, applications and advanced topics
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...
Differential equations a dynamical systems approach ordinary differential equations
Hubbard, John H
1991-01-01
This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.
On the non-stationary generalized Langevin equation
Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja
2017-12-01
In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.
Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function
Durmus, Aysen
2018-03-01
The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.
Decoupling the Arrhenius equation via mechanochemistry.
Andersen, Joel M; Mack, James
2017-08-01
Mechanochemistry continues to reveal new possibilities in chemistry including the opportunity for "greening" reactions. Nevertheless, a clear understanding of the energetic transformations within mechanochemical systems remains elusive. We employed a uniquely modified ball mill and strategically chosen Diels-Alder reactions to evaluate the role of several ball-milling variables. This revealed three different energetic regions that we believe are defining characteristics of most, if not all, mechanochemical reactors. Relative to the locations of a given ball mill's regions, activation energy determines whether a reaction is energetically easy (Region I), challenging (Region II), or unreasonable (Region III) in a given timeframe. It is in Region II, that great sensitivity to mechanochemical conditions such as vial material and oscillation frequency emerge. Our unique modifications granted control of reaction vessel temperature, which in turn allowed control of the locations of Regions I, II, and III for our mill. Taken together, these results suggest envisioning vibratory mills (and likely other mechanochemical methodologies) as molecular-collision facilitating devices that act upon molecules occupying a thermally-derived energy distribution. This unifies ball-milling energetics with solution-reaction energetics via a common tie to the Arrhenius equation, but gives mechanochemistry the unique opportunity to influence either half of the equation. In light of this, we discuss a strategy for translating solvent-based reaction conditions to ball milling conditions. Lastly, we posit that the extra control via frequency factor grants mechanochemistry the potential for greater selectivity than conventional solution reactions.
About of the quantum theory of the molecules
International Nuclear Information System (INIS)
Born M; Oppenheimer, R
1998-01-01
It is shown that the parts of molecular spectral terms corresponding to electronic motion, nuclear rotational and nuclear vibration energies mar be obtained systematically as members of a power series development on the fourth root of the ratio between the electron mass and the average nuclear mass. Such procedure leads to rotational equations, which represent a generalization of the Kramers and Pauli hypotheses (about a top with intrinsic angular momentum). Furthermore, justifications of the Franck and Condon considerations about the band intensities are given. This is shown for diatomic molecules
Continuum simulations of water flow past fullerene molecules
DEFF Research Database (Denmark)
Popadic, A.; Praprotnik, M.; Koumoutsakos, P.
2015-01-01
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently by continuum flow...
Tunneling anisotropic magnetoresistance in single-molecule magnet junctions
Xie, Haiqing; Wang, Qiang; Jiao, Hujun; Liang, J.-Q.
2012-08-01
We theoretically investigate quantum transport through single-molecule magnet (SMM) junctions with ferromagnetic and normal-metal leads in the sequential regime. The current obtained by means of the rate-equation gives rise to the tunneling anisotropic magnetoresistance (TAMR), which varies with the angle between the magnetization direction of ferromagnetic lead and the easy axis of SMM. The angular dependence of TAMR can serve as a probe to determine experimentally the easy axis of SMM. Moreover, it is demonstrated that both the magnitude and the sign of TAMR are tunable by the bias voltage, suggesting a new spin-valve device with only one magnetic electrode in molecular spintronics.
Alignment of symmetric top molecules by short laser pulses
DEFF Research Database (Denmark)
Hamilton, Edward; Seideman, Tamar; Ejdrup, Tine
2005-01-01
-resolved photofragment imaging. Using methyliodide and tert-butyliodide as examples, we calculate and measure the alignment dynamics, focusing on the temporal structure and intensity of the revival patterns, including their dependence on the pulse duration, and their behavior at long times, where centrifugal distortion......Nonadiabatic alignment of symmetric top molecules induced by a linearly polarized, moderately intense picosecond laser pulse is studied theoretically and experimentally. Our studies are based on the combination of a nonperturbative solution of the Schrodinger equation with femtosecond time...
Vortex molecule in a nanoscopic square superconducting plate
International Nuclear Information System (INIS)
Suematsu, Hisataka; Kato, Masaru; Ishida, Takekazu; Koyama, Tomio; Machida, Masahiko
2010-01-01
Using the finite element method and solving the Bogoliubov-de Gennes equation, we have investigated magnetic field dependence of the stable vortex structures in a mesoscopic superconducting plate at low temperature (T = 0.1T c ). Because of the compactness of vortex configuration, there is interference between bound states around vortices and such quasi-particle structure affects the vortex configuration. Especially in two-vortices state, vortices form a molecule-like state, where bound states of each vortex form molecular orbital like bonding and anti-bonding states. The vortex configuration is different from that, which is expected from the repulsive interaction between vortices. (author)
International Nuclear Information System (INIS)
Collins, L.A.; Schneider, B.I.
1984-01-01
The linear algebraic, separable potential approach is applied to the electronic excitation of atoms and molecules by electron impact. By representing the exchange and off-diagonal direct terms on a basis, the standard set of coupled inelastic equations is reduced to a set of elastic inhomogeneous equations. The procedure greatly simplifies the formulation by allowing a large portion of the problem to be handled by standard bound-state techniques and by greatly reducing the order of the scattering equations that must be solved. Application is made to the excitation of atomic hydrogen in the three-state close-coupling (1s, 2s, 2p) approximation. (author)
Spectroscopy, scattering, and KK molecules
Energy Technology Data Exchange (ETDEWEB)
Weinstein, J. [Univ. of Mississippi, University, MS (United States)
1994-04-01
The author presents a pedagogical description of a new theoretical technique, based on the multichannel Schroedinger equation, for simultaneously applying the quark model to both meson spectroscopy and meson-meson scattering. This is an extension of an earlier analysis which led to the prediction that the f{sub o}(975) and a{sub o}(980) scalar mesons are K{bar K} molecular states.
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
On Degenerate Partial Differential Equations
Chen, Gui-Qiang G.
2010-01-01
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...
Differential equations a concise course
Bear, H S
2011-01-01
Concise introduction for undergraduates includes, among other topics, a survey of first order equations, discussions of complex-valued solutions, linear differential operators, inverse operators and variation of parameters method, the Laplace transform, Picard's existence theorem, and an exploration of various interpretations of systems of equations. Numerous clearly stated theorems and proofs, examples, and problems followed by solutions.
Differential equations and finite groups
Put, Marius van der; Ulmer, Felix
2000-01-01
The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois
Saturation and linear transport equation
International Nuclear Information System (INIS)
Kutak, K.
2009-03-01
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)
Lie symmetries in differential equations
International Nuclear Information System (INIS)
Pleitez, V.
1979-01-01
A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt
Introduction to nonlinear dispersive equations
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...
Students' Understanding of Quadratic Equations
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…
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.
Generalized Fermat equations: A miscellany
Bennett, M.A.; Chen, I.; Dahmen, S.R.; Yazdani, S.
2015-01-01
This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q, r), including a number of infinite families, for which the equation has been solved to date, detailing
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...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...
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.)
Higher order field equations. II
International Nuclear Information System (INIS)
Tolhoek, H.A.
1977-01-01
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)
Olariu, Victor; Manesso, Erica; Peterson, Carsten
2017-06-01
Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis-Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming.
Energetics of glucose metabolism: a phenomenological approach to metabolic network modeling.
Diederichs, Frank
2010-08-12
A new formalism to describe metabolic fluxes as well as membrane transport processes was developed. The new flux equations are comparable to other phenomenological laws. Michaelis-Menten like expressions, as well as flux equations of nonequilibrium thermodynamics, can be regarded as special cases of these new equations. For metabolic network modeling, variable conductances and driving forces are required to enable pathway control and to allow a rapid response to perturbations. When applied to oxidative phosphorylation, results of simulations show that whole oxidative phosphorylation cannot be described as a two-flux-system according to nonequilibrium thermodynamics, although all coupled reactions per se fulfill the equations of this theory. Simulations show that activation of ATP-coupled load reactions plus glucose oxidation is brought about by an increase of only two different conductances: a [Ca(2+)] dependent increase of cytosolic load conductances, and an increase of phosphofructokinase conductance by [AMP], which in turn becomes increased through [ADP] generation by those load reactions. In ventricular myocytes, this feedback mechanism is sufficient to increase cellular power output and O(2) consumption several fold, without any appreciable impairment of energetic parameters. Glucose oxidation proceeds near maximal power output, since transformed input and output conductances are nearly equal, yielding an efficiency of about 0.5. This conductance matching is fulfilled also by glucose oxidation of β-cells. But, as a price for the metabolic mechanism of glucose recognition, β-cells have only a limited capability to increase their power output.
Minkiewicz, Piotr; Darewicz, Malgorzata; Iwaniak, Anna
2018-01-01
A simple equation to calculate the oxidation states (oxidation numbers) of individual atoms in molecules and ions may be introduced instead of rules associated with words alone. The equation includes two of three categories of bonds, classified as proposed by Goodstein: number of bonds with more electronegative atoms and number of bonds with less…
Single Molecule Nano-Metronome
Buranachai, Chittanon; McKinney, Sean A.; Ha, Taekjip
2006-01-01
We constructed a DNA-based nano-mechanical device called the nano-metronome. Our device is made by introducing complementary single stranded overhangs at the two arms of the DNA four-way junction. The ticking rates of this stochastic metronome depend on ion concentrations and can be changed by a set of DNA-based switches to deactivate/reactivate the sticky end. Since the device displays clearly distinguishable responses even with a single basepair difference, it may lead to a single molecule ...
Single Molecule Nano-Metronome
Buranachai, Chittanon; McKinney, Sean A.; Ha, Taekjip
2008-01-01
We constructed a DNA-based nano-mechanical device called the nano-metronome. Our device is made by introducing complementary single stranded overhangs at the two arms of the DNA four-way junction. The ticking rates of this stochastic metronome depend on ion concentrations and can be changed by a set of DNA-based switches to deactivate/reactivate the sticky end. Since the device displays clearly distinguishable responses even with a single basepair difference, it may lead to a single molecule sensor of minute sequence differences of a target DNA. PMID:16522050
XUV ionization of aligned molecules
Energy Technology Data Exchange (ETDEWEB)
Kelkensberg, F.; Siu, W.; Gademann, G. [FOM Institute AMOLF, Science Park 104, NL-1098 XG Amsterdam (Netherlands); Rouzee, A.; Vrakking, M. J. J. [FOM Institute AMOLF, Science Park 104, NL-1098 XG Amsterdam (Netherlands); Max-Born-Institut, Max-Born Strasse 2A, D-12489 Berlin (Germany); Johnsson, P. [FOM Institute AMOLF, Science Park 104, NL-1098 XG Amsterdam (Netherlands); Department of Physics, Lund University, Post Office Box 118, SE-221 00 Lund (Sweden); Lucchini, M. [Department of Physics, Politecnico di Milano, Istituto di Fotonica e Nanotecnologie CNR-IFN, Piazza Leonardo da Vinci 32, 20133 Milano (Italy); Lucchese, R. R. [Department of Chemistry, Texas A and M University, College Station, Texas 77843-3255 (United States)
2011-11-15
New extreme-ultraviolet (XUV) light sources such as high-order-harmonic generation (HHG) and free-electron lasers (FELs), combined with laser-induced alignment techniques, enable novel methods for making molecular movies based on measuring molecular frame photoelectron angular distributions. Experiments are presented where CO{sub 2} molecules were impulsively aligned using a near-infrared laser and ionized using femtosecond XUV pulses obtained by HHG. Measured electron angular distributions reveal contributions from four orbitals and the onset of the influence of the molecular structure.
''Crown molecules'' for separating cesium
International Nuclear Information System (INIS)
Dozol, J.F.; Lamare, V.
2002-01-01
After the minor actinides, the second category of radionuclides that must be isolated to optimize nuclear waste management concerns fission products, especially two cesium isotopes. If the cesium-135 isotope could be extracted, it could subsequently be transmuted or conditioned using a tailor-made process. Eliminating the 137 isotope from reprocessing and nuclear facility-dismantling waste would allow to dispose of most of this waste in near-surface facilities, and simply process the small remaining quantity containing long-lived elements. CEA research teams and their international partners have thought up crown molecules that could be used to pick out the cesium and meet these objectives. (authors)
XUV ionization of aligned molecules
International Nuclear Information System (INIS)
Kelkensberg, F.; Siu, W.; Gademann, G.; Rouzee, A.; Vrakking, M. J. J.; Johnsson, P.; Lucchini, M.; Lucchese, R. R.
2011-01-01
New extreme-ultraviolet (XUV) light sources such as high-order-harmonic generation (HHG) and free-electron lasers (FELs), combined with laser-induced alignment techniques, enable novel methods for making molecular movies based on measuring molecular frame photoelectron angular distributions. Experiments are presented where CO 2 molecules were impulsively aligned using a near-infrared laser and ionized using femtosecond XUV pulses obtained by HHG. Measured electron angular distributions reveal contributions from four orbitals and the onset of the influence of the molecular structure.
The neural cell adhesion molecule
DEFF Research Database (Denmark)
Berezin, V; Bock, E; Poulsen, F M
2000-01-01
During the past year, the understanding of the structure and function of neural cell adhesion has advanced considerably. The three-dimensional structures of several of the individual modules of the neural cell adhesion molecule (NCAM) have been determined, as well as the structure of the complex...... between two identical fragments of the NCAM. Also during the past year, a link between homophilic cell adhesion and several signal transduction pathways has been proposed, connecting the event of cell surface adhesion to cellular responses such as neurite outgrowth. Finally, the stimulation of neurite...
Koch, Norbert; Wee, Andrew Thye Shen
2013-01-01
Reviewing recent progress in the fundamental understanding of the molecule-metal interface, this useful addition to the literature focuses on experimental studies and introduces the latest analytical techniques as applied to this interface.The first part covers basic theory and initial principle studies, while the second part introduces readers to photoemission, STM, and synchrotron techniques to examine the atomic structure of the interfaces. The third part presents photoelectron spectroscopy, high-resolution UV photoelectron spectroscopy and electron spin resonance to study the electroni
Positron creation in superheavy quasi-molecules
International Nuclear Information System (INIS)
Mueller, B.
1976-01-01
The review of positron creation in superheavy quasi-molecules includes spontaneous positron emission from superheavy atoms, supercritical quasi-molecules, background effects, and some implications of the new ground state. 66 references
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…
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
Characterization of Interstellar Organic Molecules
International Nuclear Information System (INIS)
Gencaga, Deniz; Knuth, Kevin H.; Carbon, Duane F.
2008-01-01
Understanding the origins of life has been one of the greatest dreams throughout history. It is now known that star-forming regions contain complex organic molecules, known as Polycyclic Aromatic Hydrocarbons (PAHs), each of which has particular infrared spectral characteristics. By understanding which PAH species are found in specific star-forming regions, we can better understand the biochemistry that takes place in interstellar clouds. Identifying and classifying PAHs is not an easy task: we can only observe a single superposition of PAH spectra at any given astrophysical site, with the PAH species perhaps numbering in the hundreds or even thousands. This is a challenging source separation problem since we have only one observation composed of numerous mixed sources. However, it is made easier with the help of a library of hundreds of PAH spectra. In order to separate PAH molecules from their mixture, we need to identify the specific species and their unique concentrations that would provide the given mixture. We develop a Bayesian approach for this problem where sources are separated from their mixture by Metropolis Hastings algorithm. Separated PAH concentrations are provided with their error bars, illustrating the uncertainties involved in the estimation process. The approach is demonstrated on synthetic spectral mixtures using spectral resolutions from the Infrared Space Observatory (ISO). Performance of the method is tested for different noise levels.
Double-valence-fluctuating molecules and superconductivity
International Nuclear Information System (INIS)
Hirsch, J.E.; Scalapino, D.J.
1985-01-01
We discuss the possibility of ''double-valence-fluctuating'' molecules, having two ground-state configurations differing by two electrons. We propose a possible realization of such a molecule, and experimental ways to look for it. We argue that a weakly coupled array of such molecules should give rise to a strong-coupling Shafroth-Blatt-Butler superconductor, with a high transition temperature
Trapping molecules in two and three dimensions
International Nuclear Information System (INIS)
Pinkse, PW.H.; Junglen, T.; Rieger, T.; Rangwala, S.A.; Windpassinger, P.; Rempe, G.
2005-01-01
Full text: Cold molecules offer a new testing ground for quantum-physical effects in nature. For example, producing slow beams of large molecules could push experiments studying the boundary between quantum interference and classical particles up towards ever heavier particles. Moreover, cold molecules, in particular YbF, seem an attractive way to narrow down the constraints on the value of the electron dipole moment and finally, quantum information processing using chains of cold polar molecules or vibrational states in molecules have been proposed. All these proposals rely on advanced production and trapping techniques, most of which are still under development. Therefore, novel production and trapping techniques for cold molecules could offer new possibilities not found in previous methods. Electric traps hold promise for deep trap potentials for neutral molecules. Recently we have demonstrated two-dimensional trapping of polar molecules in a four-wire guide using electrostatic and electrodynamic trapping techniques. Filled from a thermal effusive source, such a guide will deliver a beam of slow molecules, which is an ideal source for interferometry experiments with large molecules, for instance. Here we report about the extension of this work to three-dimensional trapping. Polar molecules with a positive Stark shift can be trapped in the minimum of an electrostatic field. We have successfully tested a large volume electrostatic trap for ND3 molecules. A special feature of this trap is that it can be loaded continuously from an electrostatic guide, at a temperature of a few hundred mK. (author)
Artificial Enzymes, "Chemzymes"
DEFF Research Database (Denmark)
Bjerre, Jeannette; Rousseau, Cyril Andre Raphaël; Pedersen, Lavinia Georgeta M
2008-01-01
Enzymes have fascinated scientists since their discovery and, over some decades, one aim in organic chemistry has been the creation of molecules that mimic the active sites of enzymes and promote catalysis. Nevertheless, even today, there are relatively few examples of enzyme models that successf......Enzymes have fascinated scientists since their discovery and, over some decades, one aim in organic chemistry has been the creation of molecules that mimic the active sites of enzymes and promote catalysis. Nevertheless, even today, there are relatively few examples of enzyme models...... that successfully perform Michaelis-Menten catalysis under enzymatic conditions (i.e., aqueous medium, neutral pH, ambient temperature) and for those that do, very high rate accelerations are seldomly seen. This review will provide a brief summary of the recent developments in artificial enzymes, so called...... "Chemzymes", based on cyclodextrins and other molecules. Only the chemzymes that have shown enzyme-like activity that has been quantified by different methods will be mentioned. This review will summarize the work done in the field of artificial glycosidases, oxidases, epoxidases, and esterases, as well...
Modeling the drug transport in the anterior segment of the eye.
Avtar, Ram; Tandon, Deepti
2008-10-02
The aim of the present work is the development of a simple mathematical model for the time course concentration profile of topically administered drugs in the anterior chamber aqueous humor and investigation of the effects of various model parameters on the aqueous humor concentration of lipophilic and hydrophilic drugs. A simple pharmacokinetic model for the transient drug transport in the anterior segment has been developed by using the conservation of mass in the precorneal tear film, Fick's law of diffusion and Michaelis-Menten kinetics of drug metabolism in cornea, and the conservation of mass in the anterior chamber. An analytical solution describing the drug concentration in the anterior chamber has been obtained. The model predicts that an increase in the drug metabolic (consumption) rate in the corneal epithelium reduces the drug concentration in the anterior chamber for both lipophilic and hydrophilic molecules. A decrease in the clearance rate and distribution volume of the drug in the anterior chamber raises the aqueous humor concentration significantly. It is also observed that decay rate of drug concentration in the anterior chamber is higher for lipophilic molecules than that for hydrophilic molecules. The bioavailability of drugs applied topically to the eye may be improved by a rise in the precorneal tear volume, diffusion coefficient in corneal epithelium and distribution coefficient across the endothelium anterior chamber interface, and by reducing the drug metabolism, drug clearance rate and distribution volume in anterior chamber.
Zhao, Qingying; Li, Min; Luo, Jun
2017-12-04
In nanomachine applications towards targeted drug delivery, drug molecules released by nanomachines propagate and chemically react with tumor cells in aqueous environment. If the nanomachines release drug molecules faster than the tumor cells react, it will result in loss and waste of drug molecules. It is a potential issue associated with the relationship among reaction rate, release rate and efficiency. This paper aims to investigate the relationship among reaction rate, release rate and efficiency based on two drug reception models. We expect to pave a way for designing a control method of drug release. We adopted two analytical methods that one is drug reception process based on collision with tumors and another is based on Michaelis Menten enzymatic kinetics. To evaluate the analytical formulations, we used the well-known simulation framework N3Sim to establish simulations. The analytical results of the relationship among reaction rate, release rate and efficiency is obtained, which match well with the numerical simulation results in a 3-D environment. Based upon two drug reception models, the results of this paper would be beneficial for designing a control method of nanomahine-based drug release.
Approximate solutions to Mathieu's equation
Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.
2018-06-01
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Soliton equations and Hamiltonian systems
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
Galois theory of difference equations
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.
Integral equation methods for electromagnetics
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
Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation
Wang, D.
2017-12-01
The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.
Reformulation of Maxwell's equations to incorporate near-solute solvent structure.
Yang, Pei-Kun; Lim, Carmay
2008-09-04
Maxwell's equations, which treat electromagnetic interactions between macroscopic charged objects in materials, have explained many phenomena and contributed to many applications in our lives. Derived in 1861 when no methods were available to determine the atomic structure of macromolecules, Maxwell's equations assume the solvent to be a structureless continuum. However, near-solute solvent molecules are highly structured, unlike far-solute bulk solvent molecules. Current methods cannot treat both the near-solute solvent structure and time-dependent electromagnetic interactions in a macroscopic system. Here, we derive "microscopic" electrodynamics equations that can treat macroscopic time-dependent electromagnetic field problems like Maxwell's equations and reproduce the solvent molecular and dipole density distributions observed in molecular dynamics simulations. These equations greatly reduce computational expense by not having to include explicit solvent molecules, yet they treat the solvent electrostatic and van der Waals effects more accurately than continuum models. They provide a foundation to study electromagnetic interactions between molecules in a macroscopic system that are ubiquitous in biology, bioelectromagnetism, and nanotechnology. The general strategy presented herein to incorporate the near-solute solvent structure would enable studies on how complex cellular protein-ligand interactions are affected by electromagnetic radiation, which could help to prevent harmful electromagnetic spectra or find potential therapeutic applications.
Iterative Splitting Methods for Differential Equations
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
Nonlinear integrodifferential equations as discrete systems
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.
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)
Theoretical femtosecond physics atoms and molecules in strong laser fields
Grossmann, Frank
2013-01-01
Theoretical investigations of atoms and molecules interacting with pulsed or continuous wave lasers up to atomic field strengths on the order of 10^16 W/cm² are leading to an understanding of many challenging experimental discoveries. This book deals with the basics of femtosecond physics and goes up to the latest applications of new phenomena. The book presents an introduction to laser physics with mode-locking and pulsed laser operation. The solution of the time-dependent Schrödinger equation is discussed both analytically and numerically. The basis for the non-perturbative treatment of laser-matter interaction in the book is the numerical solution of the time-dependent Schrödinger equation. The light field is treated classically, and different possible gauges are discussed. Physical phenonema, ranging from Rabi-oscillations in two-level systems to the ionization of atoms, the generation of high harmonics, the ionization and dissociation of molecules as well as the control of chemical reactions are pre...
Electron attachment to indole and related molecules
Energy Technology Data Exchange (ETDEWEB)
Modelli, Alberto, E-mail: alberto.modelli@unibo.it [Dipartimento di Chimica “G. Ciamician”, Universitá di Bologna, via Selmi 2, 40126 Bologna (Italy); Centro Interdipartimentale di Ricerca in Scienze Ambientali (CIRSA), Universitá di Bologna, via S. Alberto 163, 48123 Ravenna (Italy); Jones, Derek, E-mail: d.jones@isof.cnr.it [ISOF, Istituto per la Sintesi Organica e la Fotoreattività, C.N.R., via Gobetti 101, 40129 Bologna (Italy); Pshenichnyuk, Stanislav A., E-mail: sapsh@anrb.ru [Institute of Molecule and Crystal Physics, Ufa Research Centre, Russian Academy of Sciences, Prospekt Oktyabrya 151, 450075 Ufa (Russian Federation)
2013-11-14
Gas-phase formation of temporary negative ion states via resonance attachment of low-energy (0–6 eV) electrons into vacant molecular orbitals of indoline (I), indene (II), indole (III), 2-methylen-1,3,3-trimethylindoline (IV), and 2,3,3-trimethyl-indolenine (V) was investigated for the first time by electron transmission spectroscopy (ETS). The description of their empty-level structures was supported by density functional theory and Hartree-Fock calculations, using empirically calibrated linear equations to scale the calculated virtual orbital energies. Dissociative electron attachment spectroscopy (DEAS) was used to measure the fragment anion yields generated through dissociative decay channels of the parent molecular anions of compounds I-V, detected with a mass filter as a function of the incident electron energy in the 0–14 eV energy range. The vertical and adiabatic electron affinities were evaluated at the B3LYP/6-31+G(d) level as the anion/neutral total energy difference. The same theoretical method is also used for evaluation of the thermodynamic energy thresholds for production of the negative fragments observed in the DEA spectra. The loss of a hydrogen atom from the parent molecular anion ([M-H]{sup −}) provides the most intense signal in compounds I-IV. The gas-phase DEAS data can provide support for biochemical reaction mechanisms in vivo involving initial hydrogen abstraction from the nitrogen atom of the indole moiety, present in a variety of biologically important molecules.
Elbing, Mark; Ochs, Rolf; Koentopp, Max; Fischer, Matthias; von Hänisch, Carsten; Weigend, Florian; Evers, Ferdinand; Weber, Heiko B.; Mayor, Marcel
2005-06-01
We have designed and synthesized a molecular rod that consists of two weakly coupled electronic π -systems with mutually shifted energy levels. The asymmetry thus implied manifests itself in a current-voltage characteristic with pronounced dependence on the sign of the bias voltage, which makes the molecule a prototype for a molecular diode. The individual molecules were immobilized by sulfur-gold bonds between both electrodes of a mechanically controlled break junction, and their electronic transport properties have been investigated. The results indeed show diode-like current-voltage characteristics. In contrast to that, control experiments with symmetric molecular rods consisting of two identical π -systems did not show significant asymmetries in the transport properties. To investigate the underlying transport mechanism, phenomenological arguments are combined with calculations based on density functional theory. The theoretical analysis suggests that the bias dependence of the polarizability of the molecule feeds back into the current leading to an asymmetric shape of the current-voltage characteristics, similar to the phenomena in a semiconductor diode. Author contributions: F.E., H.B.W., and M.M. designed research; M.E., R.O., M.K., M.F., F.E., H.B.W., and M.M. performed research; M.E., R.O., M.K., M.F., C.v.H., F.W., F.E., H.B.W., and M.M. contributed new reagents/analytic tools; M.E., R.O., M.K., C.v.H., F.E., H.B.W., and M.M. analyzed data; and F.E., H.B.W., and M.M. wrote the paper.This paper was submitted directly (Track II) to the PNAS office.Abbreviations: A, acceptor; D, donor; MCB, mechanically controlled break junction.Data deposition: The atomic coordinates have been deposited in the Cambridge Structural Database, Cambridge Crystallographic Data Centre, Cambridge CB2 1EZ, United Kingdom (CSD reference no. 241632).
Integral equation for Coulomb problem
International Nuclear Information System (INIS)
Sasakawa, T.
1986-01-01
For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems
Geophysical interpretation using integral equations
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...
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.
Kinetic equations in dirty superconductors
International Nuclear Information System (INIS)
Kraehenbuehl, Y.
1981-01-01
Kinetic equations for superconductors in the dirty limit are derived using a method developed for superfluid systems, which allows a systematic expansion in small parameters; exact charge conservation is obeyed. (orig.)
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)
Solving Differential Equations in R
Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...
Wave-equation dispersion inversion
Li, Jing; Feng, Zongcai; Schuster, Gerard T.
2016-01-01
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
International Nuclear Information System (INIS)
Jannussis, A.; Streclas, A.; Sourlas, D.; Vlachos, K.
1977-01-01
Using the theorem of the derivative of a function of operators with respect to any parameter, we can find the equation of motion of a system in classical mechanics, in canonical as well as in non-canonical mechanics
Quantum-statistical kinetic equations
International Nuclear Information System (INIS)
Loss, D.; Schoeller, H.
1989-01-01
Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived
Lorentz Covariance of Langevin Equation
International Nuclear Information System (INIS)
Koide, T.; Denicol, G.S.; Kodama, T.
2008-01-01
Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...
A mathematical model of phosphorylation AKT in Acute Myeloid Leukemia
Adi, Y. A.; Kusumo, F. A.; Aryati, L.; Hardianti, M. S.
2016-04-01
In this paper we consider a mathematical model of PI3K/AKT signaling pathways in phosphorylation AKT. PI3K/AKT pathway is an important mediator of cytokine signaling implicated in regulation of hematopoiesis. Constitutive activation of PI3K/AKT signaling pathway has been observed in Acute Meyloid Leukemia (AML) it caused by the mutation of Fms-like Tyrosine Kinase 3 in internal tandem duplication (FLT3-ITD), the most common molecular abnormality associated with AML. Depending upon its phosphorylation status, protein interaction, substrate availability, and localization, AKT can phosphorylate or inhibite numerous substrates in its downstream pathways that promote protein synthesis, survival, proliferation, and metabolism. Firstly, we present a mass action ordinary differential equation model describing AKT double phosphorylation (AKTpp) in a system with 11 equations. Finally, under the asumtion enzyme catalyst constant and steady state equilibrium, we reduce the system in 4 equation included Michaelis Menten constant. Simulation result suggested that a high concentration of PI3K and/or a low concentration of phospatase increased AKTpp activation. This result also indicates that PI3K is a potential target theraphy in AML.
International Nuclear Information System (INIS)
Winkler, E.
1991-01-01
If nonlinear biological processes are investigated by means of tracer experiments they can be modelled with linear kinetic equations (compartment equations) as long as the total system is in a stationary state. But if nonstationary behaviour is included considerations on the kinetics of the individual processes are necessary. Within the range of biological and agricultural investigations especially first order reactions (constant fraction processes), zero order reactions (constant amount process) and saturation reactions (Michaelis-Menten-kinetics) are to be taken into account. A rigorous treatment of data based on system theory can be preceeded by graphic-algebraic procedure which may be more or less uncertain in its results but which can easily be handled. An example is given of methodological considerations concerning the combination of evaluation procedures and the discrimination between different reaction mechanisms. It treats protein turnover in 2 different parts of growing wheat plants investigated by means of an 15 N-tracer experiment. Whereas in a stationary system (upper stalk section) linear tracer equations were sufficient irrespective of the true reaction mechanism, for protein synthesis in the upper leaf as a nonstationary system it was necessary to decide between the hypotheses of a zero order and a first order reaction. In accordance with statements in the literature the unambiguous result was a combination of protein synthesis as a zero order process and of protein degradation as a first order process. (orig.) [de
A mathematical model of phosphorylation AKT in Acute Myeloid Leukemia
Energy Technology Data Exchange (ETDEWEB)
Adi, Y. A., E-mail: yudi.adi@math.uad.ac.id [Department of Mathematic Faculty of MIPA Universitas Ahmad Dahlan (Indonesia); Department of Mathematic Faculty of MIPA Universitas Gadjah Mada (Indonesia); Kusumo, F. A.; Aryati, L. [Department of Mathematic Faculty of MIPA Universitas Gadjah Mada (Indonesia); Hardianti, M. S. [Department of Internal Medicine, Faculty of Medicine, Universitas Gadjah Mada (Indonesia)
2016-04-06
In this paper we consider a mathematical model of PI3K/AKT signaling pathways in phosphorylation AKT. PI3K/AKT pathway is an important mediator of cytokine signaling implicated in regulation of hematopoiesis. Constitutive activation of PI3K/AKT signaling pathway has been observed in Acute Meyloid Leukemia (AML) it caused by the mutation of Fms-like Tyrosine Kinase 3 in internal tandem duplication (FLT3-ITD), the most common molecular abnormality associated with AML. Depending upon its phosphorylation status, protein interaction, substrate availability, and localization, AKT can phosphorylate or inhibite numerous substrates in its downstream pathways that promote protein synthesis, survival, proliferation, and metabolism. Firstly, we present a mass action ordinary differential equation model describing AKT double phosphorylation (AKTpp) in a system with 11 equations. Finally, under the asumtion enzyme catalyst constant and steady state equilibrium, we reduce the system in 4 equation included Michaelis Menten constant. Simulation result suggested that a high concentration of PI3K and/or a low concentration of phospatase increased AKTpp activation. This result also indicates that PI3K is a potential target theraphy in AML.
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.)
Hidden Statistics of Schroedinger Equation
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.
Feynman integrals and difference equations
Energy Technology Data Exchange (ETDEWEB)
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
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 {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Dissociation Energies of Diatomic Molecules
International Nuclear Information System (INIS)
Qun-Chao, Fan; Wei-Guo, Sun
2008-01-01
Molecular dissociation energies of 10 electronic states of alkali molecules of KH, 7 LiD, 7 LiH, 6 LiH, NaK, NaLi and NaRb are studied using the highest three accurate vibrational energies of each electronic state, and an improved parameter-free analytical formula which is obtained starting from the LeRoy–Bernstein vibrational energy expression near the dissociation limit. The results show that as long as the highest three vibrational energies are accurate, the current analytical formula will give accurate theoretical dissociation energies D e theory , which are in excellent agreement with the experimental dissociation energies D e expt . (atomic and molecular physics)
Optoelectronics of Molecules and Polymers
Moliton, André
2006-01-01
Optoelectronic devices are being developed at an extraordinary rate. Organic light emitting diodes, photovoltaic devices and electro-optical modulators are pivotal to the future of displays, photosensors and solar cells, and communication technologies. This book details the theories underlying the relevant mechanisms in organic materials and covers, at a basic level, how the organic components are made. The first part of this book introduces the fundamental theories used to detail ordered solids and localised energy levels. The methods used to determine energy levels in perfectly ordered molecular and macromolecular systems are discussed, making sure that the effects of quasi-particles are not missed. The function of excitons and their transfer between two molecules are studied, and the problems associated with interfaces and charge injection into resistive media are presented. The second part details technological aspects such as the fabrication of devices based on organic materials by dry etching. The princ...
Sagar, Sunil
2014-04-17
Derivatives of plumbagin can be selectively cytotoxic to breast cancer cells. Derivative `A` (Acetyl Plumbagin) has emerged as a lead molecule for testing against estrogen positive breast cancer and has shown low hepatotoxicity as well as overall lower toxicity in nude mice model. The toxicity of derivative `A` was determined to be even lower than vehicle control (ALT and AST markers). The possible mechanism of action identified based on the microarray experiments and pathway mapping shows that derivative `A` could be acting by altering the cholesterol-related mechanisms. The low toxicity profile of derivative `A` highlights its possible role as future anti-cancer drug and/or as an adjuvant drug to reduce the toxicity of highly toxic chemotherapeutic drugs
Sagar, Sunil; Kaur, Mandeep; Esau, Luke E.
2014-01-01
Derivatives of plumbagin can be selectively cytotoxic to breast cancer cells. Derivative `A` (Acetyl Plumbagin) has emerged as a lead molecule for testing against estrogen positive breast cancer and has shown low hepatotoxicity as well as overall lower toxicity in nude mice model. The toxicity of derivative `A` was determined to be even lower than vehicle control (ALT and AST markers). The possible mechanism of action identified based on the microarray experiments and pathway mapping shows that derivative `A` could be acting by altering the cholesterol-related mechanisms. The low toxicity profile of derivative `A` highlights its possible role as future anti-cancer drug and/or as an adjuvant drug to reduce the toxicity of highly toxic chemotherapeutic drugs
Hydride Molecules towards Nearby Galaxies
Monje, Raquel R.; La, Ngoc; Goldsmith, Paul
2018-06-01
Observations carried out by the Herschel Space Observatory revealed strong spectroscopic signatures from light hydride molecules within the Milky Way and nearby active galaxies. To better understand the chemical and physical conditions of the interstellar medium, we conducted the first comprehensive survey of hydrogen fluoride (HF) and water molecular lines observed through the SPIRE Fourier Transform Spectrometer. By collecting and analyzing the sub-millimeter spectra of over two hundred sources, we found that the HF J = 1 - 0 rotational transition which occurs at approximately 1232 GHz was detected in a total of 39 nearby galaxies both in absorption and emission. The analysis will determine the main excitation mechanism of HF in nearby galaxies and provide steady templates of the chemistry and physical conditions of the ISM to be used in the early universe, where observations of hydrides are more scarce.
Modelling of energetic molecule-surface interactions
International Nuclear Information System (INIS)
Kerford, M.
2000-09-01
This thesis contains the results of molecular dynamics simulations of molecule-surface interactions, looking particularly at fullerene molecules and carbon surfaces. Energetic impacts of fullerene molecules on graphite create defect craters. The relationship between the parameters of the impacting molecule and the parameters of the crater axe examined and found to be a function of the energy and velocity of the impacting molecule. Less energetic fullerene molecules can be scattered from a graphite surface and the partitioning of energy after a scattering event is investigated. It is found that a large fraction of the kinetic energy retained after impact is translational energy, with a small fraction of rotational energy and a number of vibrational modes. At impact energies where the surface is not broken and at normal incidence, surface waves axe seen to occur. These waves axe used to develop a method of desorbing molecules from a graphite surface without damage to either the surface or the molecules being desorbed. A number of fullerene molecules are investigated and ways to increase the desorption yield are examined. It is found that this is a successful technique for desorbing large numbers of intact molecules from graphite. This technique could be used for desorbing intact molecules into a gas phase for mass spectrometric analysis. (author)
Observation of pendular butterfly Rydberg molecules
Niederprüm, Thomas; Thomas, Oliver; Eichert, Tanita; Lippe, Carsten; Pérez-Ríos, Jesús; Greene, Chris H.; Ott, Herwig
2016-01-01
Engineering molecules with a tunable bond length and defined quantum states lies at the heart of quantum chemistry. The unconventional binding mechanism of Rydberg molecules makes them a promising candidate to implement such tunable molecules. A very peculiar type of Rydberg molecules are the so-called butterfly molecules, which are bound by a shape resonance in the electron–perturber scattering. Here we report the observation of these exotic molecules and employ their exceptional properties to engineer their bond length, vibrational state, angular momentum and orientation in a small electric field. Combining the variable bond length with their giant dipole moment of several hundred Debye, we observe counter-intuitive molecules which locate the average electron position beyond the internuclear distance. PMID:27703143
A Mott-like State of Molecules
International Nuclear Information System (INIS)
Duerr, S.; Volz, T.; Syassen, N.; Bauer, D. M.; Hansis, E.; Rempe, G.
2006-01-01
We prepare a quantum state where each site of an optical lattice is occupied by exactly one molecule. This is the same quantum state as in a Mott insulator of molecules in the limit of negligible tunneling. Unlike previous Mott insulators, our system consists of molecules which can collide inelastically. In the absence of the optical lattice these collisions would lead to fast loss of the molecules from the sample. To prepare the state, we start from a Mott insulator of atomic 87Rb with a central region, where each lattice site is occupied by exactly two atoms. We then associate molecules using a Feshbach resonance. Remaining atoms can be removed using blast light. Our method does not rely on the molecule-molecule interaction properties and is therefore applicable to many systems
Numerical solution of Boltzmann's equation
International Nuclear Information System (INIS)
Sod, G.A.
1976-04-01
The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig