Search results for "Equations"
showing 10 items of 955 documents
A nonstandard Volterra integral equation on time scales
2019
Abstract This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.
Determinants of the Effectiveness of Using Renewable Resource Management-Based Simulations in the Development of Critical Thinking: An Application of…
2019
The twenty-first century&rsquo
Effect of the junction angle on turbulent flow at a hydraulic confluence
2018
Despite the existing knowledge concerning the hydrodynamic processes at river junctions, there is still a lack of information regarding the particular case of low width and discharge ratios, which are the typical conditions of mountain river confluences. Aiming at filling this gap, laboratory and numerical experiments were conducted, comparing the results with literature findings. Ten different confluences from 45 ∘ to 90 ∘ were simulated to study the effects of the junction angle on the flow structure, using a numerical code that solves the 3D Reynolds Averaged Navier-Stokes (RANS) equations with the k- ϵ turbulence closure model. The results showed that the higher the junction angle, the …
Hydrolysis of (CH3)Hg+ in Different Ionic Media: Salt Effects and Complex Formation
1998
The hydrolysis of monomethylmercury(II) was studied potentiometrically, in NaNO3, Na2SO4, and NaCl aqueous solution, in a wide range of ionic strengths (NaNO3, 0 ≤ I ≤ 3.25; Na2SO4, 0 ≤ I ≤ 1; NaCl, 0 ≤ I ≤ 3 mol dm-3) and at t = 25 °C. For the reaction (CH3)Hg+ = (CH3)Hg(OH)° + H+, we found log K1 = −4.528 (I = 0 mol dm-3). The species [(CH3)Hg]2(OH)+ was also found, with log β2 = −2.15. Monomethylmercury(II) forms quite strong complexes with Cl- (log K = 5.45, I = 0 mol dm-3) and SO42- (log K = 2.64, I = 0 mol dm-3). The dependence on ionic strength of formation constants was considered by using a Debye−Huckel type equation. Hydrolysis and complex formation constants (at different ionic s…
Fabrication of Single Cylindrical Au-Coated Nanopores with Non-Homogeneous Fixed Charge Distribution Exhibiting High Current Rectifications
2014
We have designed and characterized a cylindrical nanopore that exhibits high electrochemical current rectification ratios at low and intermediate electrolyte concentrations. For this purpose, the track-etched single cylindrical nanopore in polymer membrane is coated with a gold (Au) layer via electroless plating technique. Then, a non-homogeneous fixed charge distribution inside the Au-coated nanopore is obtained by incorporating thiol-terminated uncharged poly(N-isopropylacrylamide) (PNIPAM) chains in series to poly(4-vinyl pyridine) (PVP) chains, which are positively charged at acidic pH values. The functionalization reaction is checked by measuring the current–voltage (I–V) curves prior …
Hybrid Lattice Boltzmann/Dynamic Self-Consistent Field Simulations of Microphase Separation and Vesicle Formation in Block Copolymer Systems
2011
We present a hybrid numerical method to introduce hydrodynamics in dynamic self-consistent field (SCF) studies of inhomogeneous polymer systems. It solves a set of coupled dynamical equations: The ...
Testing of a constitutive equation for entangled networks by elongational and shear data of polymer melts
1973
An entangled network such as a polymer melt or a concentrated solution is here described by a set of two simultaneous equations. One of them is a balance of entanglements, the other gives the stress in the classical form of aMaxwell equation.
Double-quantum nutations in a two-level spin system
1986
The transient oscillatory behavior of the nonlinear response of a two-level electron-spin system is experimentally investigated in a sample of glassy silica with ${E}_{1}^{\mathcal{'}}$ centers (S=(1/2)) at microwave frequency at T=4.2 K. The transient regime, excited by an intense step-modulated radiation tuned to double-quantum (DQ) resonance, is monitored by revealing the second-harmonic (SH) wave radiated by the spins undergoing DQ transitions. Time- and frequency-domain results show that the emitted SH wave has two components: the former, which vanishes at the DQ resonance, exhibits an overdamped transient regime, the latter consists of damped oscillations at a frequency which depends …
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…
Temperature dependence of η / s of strongly interacting matter: Effects of the equation of state and the parametric form of ( η / s ) ( T )
2020
We investigate the temperature dependence of the shear viscosity to entropy density ratio η/s using a piecewise linear parametrization. To determine the optimal values of the parameters and the associated uncertainties, we perform a global Bayesian model-to-data comparison on Au+Au collisions at √sNN=200 GeV and Pb+Pb collisions at 2.76 TeV and 5.02 TeV, using a 2+1D hydrodynamical model with the Eskola-Kajantie-Ruuskanen-Tuominen (EKRT) initial state. We provide three new parametrizations of the equation of state (EoS) based on contemporary lattice results and hadron resonance gas, and use them and the widely used s95p parametrization to explore the uncertainty in the analysis due to the c…