Kinetic equations

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  • Within the framework of the Walecka model (QHD-I)[1] the renormalized effective Dirac equation and the kinetic equation for fermion are presented. In fact, the fermion propagator in the medium is dramatically different from that in the vacuum. The main feature is the treating of the fermion distribution in non equilibrium, which depends on the interaction rate involving temperature.

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  • Comprehensive manual embracing essentially all the classical and modern areas of chemical kinetics. Provides details of modern applications in chemistry, technology and biochemistry. Special sections of the book treat subjects not covered sufficiently in other manuals, including: modern methods of experimental determination of rate constants of reactions including laser pico- and femtochemistry, magnetochemistry, and ESR; and descriptions of advanced theories of elementary chemical processes.

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  • This textbook has evolved from part of the first-year graduate curriculum in the Department of Materials Science and Engineering at the Massachusetts Institute of Technology (MIT) . This curriculum includes four required semester-long subjects- “Materials at Equilibrium,” “Mechanical Properties of Materials,” “Electrical, Optical, and Magnetic Properties of Materials,” and “Kinetic Processes in Materials.

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  • In Section 1.5 of the textbook, Zak introduces the Lagrangian L = K − U , which is the difference between the kinetic and potential energy of the system. He then proceeds to obtain the Lagrange equations of motion in Cartesian coordinates for a point mass subject to conservative forces, namely, d dt ∂L ∂ xi ˙ − ∂L = 0 i = 1, 2, 3. ∂xi (1)

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  • The inner magnetosphere is an important region of space plasma because it is one of the “kitchens” for space weather effects. The scientific understanding of this region is important for predicting the interaction between space environmental conditions and human activities. The inner magnetospheric plasma is a unique composition of different plasma particles and waves. It covers a huge plasma energy range with spatial and time variations of many orders of magnitude.

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  • The following will be discussed in this chapter: Define rate constant, first order reaction, second order reaction and zero order reaction; define Vmax; define Km ; Michaelis-Menton equation defines the hyperbolic curve when [S] is plotted against initial velocity; know what the initial velocity and steady state assumptions mean;...

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  • The parametric transformation of acoustic and optical phonons in doped superlattices is theoretically studied by using a set of quantum kinetic equations for the phonons. The analytic expression of parametric transformation coefficient of acoustic and optical phonons in doped superlattices is obtained, that depends non-linear on the concentration of impurities. Numerical computations of theoretical results and graph are performed for GaAs:Si/GaAs:Be doped superlattices

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  • Investigations of kinetics of p-xylene deep oxidation on CuO/ -Al2O3 and CuO/ZSM-5 have been carried out. Specific surface area and pore size of catalyst samples as well as metallic state characteristics and catalytic properties of copper have been established. Catalyst CuO/ZSM-5 has been found to be more active than the first one, but it expressed lower stability because of less stable active form of Cu2+ on zeolite surface.

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  • The nonlinear absorption of a strong electromagnetic wave caused by confined electrons in cylindrical quantum wires is theoretically studied by using the quantum kinetic equation for electrons. The problem is considered in the case electron-acoustic phonon scattering. Analytic expressions for the dependence of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in rectangular quantum wires on the temperature T are obtained.

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  • Kinetic modelling of complex metabolic networks – a central goal of com-putational systems biology – is currently hampered by the lack of reliable rate equations for the majority of the underlying biochemical reactions and membrane transporters.

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  • Pharmacokinetics (t1/2) and the apparent volume of distribution Vapp (p. 28) by the equation: Vapp t1/2 = In 2 x –––– Cltot The smaller the volume of distribution or the larger the total clearance, the shorter is the half-life. In the case of drugs renally eliminated in unchanged form, the half-life of elimination can be calculated from the cumulative excretion in urine; the final total amount eliminated corresponds to the amount absorbed.

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  • Equating the total energy at the start and end (potential and kinetic) yields: (6.66) which is a quadratic in * and can be rearranged as follows: (6.67) Given the values of W = 5 lbs, h = 3.0 feet and k = 20 lbs/ft, *S = 5/20 = 0.25 ft. Substituting this in the above equation gives for the maximum deformation * = 1.5 feet or 6 *S. Drop Test Using a Spring Having Finite Weight Let us repeat the drop test, but now assume that the bar has appreciable mass, Wb, as shown in Fig. 6.41. The uniform bar-mass model is...

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  • A senior-level undergraduate course entitled “Vibration and Flutter” was taught for many years at Georgia Tech under the quarter system. This course dealt with elementary topics involving the static and/or dynamic behavior of structural ele- ments, both without and with the influence of a flowing fluid. The course did not discuss the static behavior of structures in the absence of fluid flow because this is typically considered in courses in structural mechanics.

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  • The adsorption of phenol over MCM-41 prepared from rice husk silica was investigated. MCM-41 material (RH-MCM-41) was synthesized using sodium silicate prepared from rice husk as a silica source and cetyltrimetylammoniumbromide (CTAB) as a surfactant with the following gel composition: 1SiO2: 0.106CTAB: 0.03NaOH: 150H2O. The obtained material was characterized by XRD and BET. RH-MCM-41 exhibits high surface area and highly ordered hexagonal mesoporous structures. The adsorption of phenol over RH-MCM-41 fit well to both Langmuir and Freundlich isothermers.

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  • Unstructured modelling growth of Lactobacillus acidophilus as a function of the temperature: We present modelling software developed under MATLAB in which parameter estimations are obtained by using non-linear regression techniques. The different parameters appear in a set of non-linear algebraic and differential equations representing the model of the process. From experimental data obtained in discontinuous cultures a representative mathematical model (unstructured kinetic model) of the macroscopic behaviour of Lactobacillus acidophilus has been developed.

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