Search results for " solution"
showing 10 items of 3084 documents
Synthesis, crystal and molecular-electronic structure, and kinetic investigation of two new sterically hindered isomeric forms of the dimethyl[methyl…
2017
Two new structural isomers – 2,4-dimethyl-5-[methyl(phenylsulfonyl)amino]benzenesulfonyl chloride (1) and 2,4-dimethyl-3-[methyl(phenylsulfonyl)amino]benzenesulfonyl chloride (2) were synthesized by interaction of N-(2,4-dimethylphenyl)-N-methyl-benzenesulfonamide or N-(2,6-dimethylphenyl)-N-methylbenzenesulfonamide with chlorosulfonic acid. Both compounds have been structurally characterized by X-ray single crystal diffraction at 100 K. The crystals of 1 are triclinic: space group View the MathML source, a = 8.1542(2), b = 11.0728(3), c = 11.2680(3) Å, α = 116.557(3), β = 95.155(2), γ = 108.258(2)°, V = 831.97(4) Å3, Z = 2, R = 0.0251 for 2429 reflections; the crystals of 2 are monoclinic:…
Stochastic Differential Equations
2020
Stochastic differential equations describe the time evolution of certain continuous n-dimensional Markov processes. In contrast with classical differential equations, in addition to the derivative of the function, there is a term that describes the random fluctuations that are coded as an Ito integral with respect to a Brownian motion. Depending on how seriously we take the concrete Brownian motion as the driving force of the noise, we speak of strong and weak solutions. In the first section, we develop the theory of strong solutions under Lipschitz conditions for the coefficients. In the second section, we develop the so-called (local) martingale problem as a method of establishing weak so…
Higher order matrix differential equations with singular coefficient matrices
2015
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.
A paradigm of extreme rainfall pluvial floods in complex urban areas: the flood event of 15 July 2020 in Palermo (Italy)
2021
Abstract. In the last few years, some regions of the Mediterranean area have witnessed a progressive increase in extreme events, such as urban and flash floods, as a response to the increasingly frequent and severe extreme rainfall events, which are often exacerbated by the ever-growing urbanization. In such a context, the urban drainage systems may not be sufficient to convey the rainwater, thus increasing the risk deriving from the occurrence of such events. This study focuses on a particularly intense urban flood that occurred in Palermo (Italy) on 15 July 2020; it represents a typical pluvial flood due to extreme rainfall on a complex urban area that many cities have experienced in rece…
Molecular recognition processes at functionalized lipid surfaces: a neutron reflectivity study
1992
The specific binding of proteins to functionalized monolayers on aqueous subphases has been characterized by neutron reflectivity measurements. As a model for the investigation of a recognition process on a molecular length scale, streptavidin (SA) and biotin were chosen because of the high specific affinity between them. Reflectivities from the aqueous (NaCl/H2O or NaCl/D2O) surfaces covered with the biotin-lipid monolayers before and after the adsorption of proteins were collected with a novel, fixed wavelength liquid surface neutron reflectometer. In quantitative terms, binding was found to occur at a biotin surface concentration as low as 1 molecule/1250 A2 (compare to ∼ 1 molecule/40 A…
Influence of surface chemistry on the structural organization of monomolecular protein layers adsorbed to functionalized aqueous interfaces.
1993
The molecular organization of streptavidin (SA) bound to aqueous surface monolayers of biotin-functionalized lipids and binary lipid mixtures has been investigated with neutron reflectivity and electron and fluorescence microscopy. The substitution of deuterons (2H) for protons (1H), both in subphase water molecules and in the alkyl chains of the lipid surface monolayer, was utilized to determine the interface structure on the molecular length scale. In all cases studied, the protein forms monomolecular layers underneath the interface with thickness values of approximately 40 A. A systematic dependence of the structural properties of such self-assembled SA monolayers on the surface chemistr…
Specific Protein Binding to Functionalized Interfaces
1992
We report on the characterization of specific binding reactions between streptavidin and biotinylated model membrane surfaces. Self-assembly techniques as well as the Langmuir-Blodgett-Kuhn method were employed to prepare reactive, functionalized surfaces on various solid supports in contact with the aqueous protein solution. Plasmon surface polaritons optical measurements as well as atomic force microscopy and studies with the surface forces apparatus give rather detailed information as to the streptavidin monolayer formation, the kinetics of this process (either binding site- or diffusion limited), the selectivity of the reaction at laterally heterogeneous membranes, and the involved inte…
Stress induced grain boundary migration in very soluble brittle salt
1999
Abstract Grain boundary migration (GBM) was studied in-situ at room temperature, atmospheric pressure and an applied diffmfwerential stress of ∼9.5 MPa under the optical microscope, in a wet aggregate of an elastic-brittle salt (sodium chlorate). The aggregate was previously deformed predominantly by a combination of grain boundary sliding, pressure solution and cataclastic solution creep. After deformation, but when the sample was still under differential stress, undeformed, fracture-free grains were observed to grow at the cost of deformed, intensely fractured grains. GMB rates typically fell in the range 2--10 μm/day. GBM took place only as long as the sample was under stress. Boundaries…
The structure of reactive grain-boundaries under stress containing confined fluids
2006
We present numerical experiments on structure development in grain-boundaries during dissolution–precipitation creep. Two solids that are represented by an elastic spring configuration are pressed together with a compressible fluid in the grain-boundary. The solid can dissolve or precipitate depending on elastic and surface energy as well as fluid pressure and concentration of dissolved material in the fluid. We perform a number of numerical experiments with different starting configurations that represent a large-scale island-channel interface with solid–solid contacts across the islands, a rough grain-boundary interface with a fluid along the whole interface and a smooth thin-film interfa…
Effect of microcracking on pressure-solution strain rate: The Gratz grain-boundary model
1998
Different, but reasonable and well-accepted assumptions made about grain-boundary structure during pressure-solution (PS) creep may easily have an effect of more than 10 orders of magnitude on the calculated PS deformation rate. Understanding of grain-boundary structure during PS creep is therefore extremely important. Experimental evidence is presented in support of a grain-boundary model previously proposed by A. J. Gratz on the basis of observations on naturally deformed rocks. In this model, boundaries are assumed to have a static island-channel network structure. Channels are located where microcracks intersect the boundary. The rate of material transport is governed by thin-film diffu…