Search results for "equation"
showing 10 items of 4219 documents
Polymer dynamics in time-dependent periodic potentials.
2008
Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we consider standard and modified Rubinstein-Duke polymers and calculate their mean drift and effective diffusion coefficient in the two-state non-symmetric flashing potential and symmetric traveling potential. Rich non-linear behavior of these observables is found. By varying the polymer length, we find cur…
Basic kinetic model for the reaction yielding linear polyurethanes. II
1995
On the basis of the gradual polyaddition kinetic model developed earlier, an attempt was made to provide a generalized mathematical model for the set of reactions yielding linear polyurethanes. The model is a system of first-order ordinary differential equations. It was assumed at the present stage of this model that the rate constants for the reaction considered do not change. The model developed was then solved numerically. Average molecular weight of the polymer and composition data for oligomers were calculated for a constant volume batch reactor and varied process parameters. The GPC method, which was tested for model urethane oligomers, was employed to verify the model developed. The …
Translocation dynamics of a short polymer driven by an oscillating force
2013
Under the terms of the Creative Commons Attribution 3.0 Unported License.
On the use of multi-parameter free energy relationships: the rearrangement of (Z)-arylhydrazones of 5-amino-3-benzoyl-1,2,4-oxadiazole into (2-aryl-5…
2010
Abstract By using a multi-parameter approach (a combination of Hammett/Ingold-Yukawa-Tsuno/Fujita-Nishioka free energy relationships) the mononuclear rearrangements of heterocycles (MRH) rates for five new ortho-substituted and ten new di-, tri-, or tetra-substituted (Z)-arylhydrazones of 5-amino-3-benzoyl-1,2,4-oxadiazole into the relevant (2-aryl-5-phenyl-2H-1,2,3-triazol-4-yl)ureas (in dioxane/water and in a large range of pS+ values) have been related to the electronic and proximity effects exerted by the present substituents, also considering previous results on some mono meta- and para-substituted (Z)-arylhydrazones. In every case, excellent correlation coefficients have been calculat…
Synthesis, crystal structures and magnetic properties of M(II)Cu(II) chains (M = Mn and Co) with sterically hindered alkyl-substituted phenyloxamate …
2011
A series of neutral oxamato-bridged heterobimetallic chains of general formula [MCu(L(x)2 (S)2] · p S · q H2O [p = 0-1, q = 0-2.5; L1 = N-2,6-dimethylphenyloxamate, S = DMF with M = Mn (1a) and Co (1b); L2 = N-2,6-diethylphenyloxamate, S = DMF with M = Mn (2a) and Co (2b) or S = DMSO with M = Mn (2c) and Co (2 d); L3 = N-2,6-diisopropylphenyloxamate, S = DMF with M = Mn (3a) and Co (3b) or S = DMSO with M = Mn (3c) and Co (3d)] were prepared by treating the corresponding anionic oxamatocopper(II) complexes [Cu(L(x))(2)]2- (x = 1-3) with M(2+) cations (M = Mn and Co) in DMF or DMSO as the solvent. The single-crystal X-ray structures of 2a and 3a reveal the occurrence of well-isolated, zigzag…
Experimental organic matter maturation at 2kbar: Heat-up effect to low temperatures on vitrinite reflectance
2012
Abstract An experimental study was performed to evaluate the effect of heat-up to various low temperatures on vitrinite reflectance ( VR ) at 2 kbar employing the same previously used heat-up procedures, starting material and apparatus. Heat-up is the isobaric experimental procedure consisting of the increase in temperature of the laboratory vitrinite maturation from room temperature to the desired run temperature T end of heat-up at which the isobaric-isothermal maturation starts. Experiments employed cold-seal pressure vessels with classical heat-up devices and were carried out on wet (water added) xylite of swamp cypress. Confined system maturation experiments were conducted at 2 kbar an…
Investigation on the indentation behavior of sandwich beams using crushable and hyperelastic foam cores
2010
In this work the indentation behaviour of sandwich beams is studied adopting the classical approach representing the core material as a Winkler-type foundation. It is shown how most of the proposed theories can be derived from a general fourth order linear differential equation expressing the equilibrium of the indented beam skin. Different assumptions on the supporting boundary constraints and materials constitutive behaviour, lead to simplifications of the general equation and to the prediction of different indentation features. An extension of the Segment-Wise approach recently proposed in the literature is in particular presented with potential to better simulate foam cores with markedl…
Comparison between the Kummer's transformation and Ewald method for the evaluation of the parallel plate Green's functions
2006
In this paper, we present a convergence and efficiency study of two different acceleration techniques for the evaluation of the parallel plate Green's functions. The first technique is based on the extraction of the asymptotic terms of the spectral representation of the parallel plate Green's functions by applying the Kummer's transformation. The second technique is a straightforward reformulation of the 2-D Green's functions for 1-D periodic structures to the parallel plate case. The PPW Green's functions calculated by the two methods have been successfully applied to the analysis of a practical inductive microwave filter containing metallic and dielectric posts. The filter analysis techni…
Concave Tetrathiafulvalene-Type Donors as Supramolecular Partners for Fullerenes
2007
The cap fits! A new class of concave π-extended tetrathiafulvalene (TTF) derivatives, truxene-TTFs, were prepared and characterized, and their self-assembly with fullerenes was investigated (see picture). Truxene-TTFs represent the first example of TTF-related electron donors that serve, without chemical modification, as monotopic receptors for fullerenes in solution. (Chemical Equation Presented). © 2007 Wiley-VCH Verlag GmbH & Co. KGaA.
Electrochemical Characterization of Corrosion Products in Leaded Bronze Sculptures Considering Ohmic Drop Effects on Tafel Analysis
2015
[EN] The characterization of corrosion products in leaded bronze based on the voltammetry of immobilized particles methodology is described. Voltammetric data, supported by Fourier transform infra-red spectroscopy, field emission scanning electron microscopy-energy dispersive X-ray microanalysis (FESEM-EDX) and scanning electrochemical microscopy (SECM) allow the identification of copper and lead corrosion materials. The mutual influence of such products is modeled upon considering uncompensated ohmic drops in the Tafel analysis of the rising portion of the respective voltammetric signals for their electrochemical reduction.