Search results for "equation"
showing 10 items of 4219 documents
Symmetry-based canonical dressing of a bidimensionally trapped and laser-driven ion
2001
Abstract We present a detailed and exact construction of a unitary operator accomplishing the diagonalization of an effective quadratic radiation-matter interaction model describing a bidimensionally trapped and appropriately laser-driven ion. The possibility of applying the same mathematical method to other effective radiation-matter interaction model is briefly put into evidence.
Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
2006
We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. The model problem we refer to is the following (1){ut−div(α(u)∇u)=β(u)|∇u|2+f(x,t),in Ω×]0,T[;u(x,t)=0,on ∂Ω×]0,T[;u(x,0)=u0(x),in Ω. Here Ω is a bounded open set in RN, T>0. The unknown function u=u(x,t) depends on x∈Ω and t∈]0,T[. The symbol ∇u denotes the gradient of u with respect to x. The real functions α, β are continuous; moreover α is positive, bounded and may vanish at ±∞. As far as the data are concerned, we require the following assumptions: ∫ΩΦ(u0(x))dx<∞ where Φ is a convenient function which …
Unitary decoupling treatment of a quadratic bimodal cavity quantum electrodynamics model
2013
We consider a two-photon quantum model of radiation–matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system, the explicit construction of two collective radiation modes, one of which is freely evolving and the other one quadratically coupled to the matter subsystem, is reported. The meaning and advantages of such a decoupling treatment are carefully discussed.
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets
2004
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
Quadratically Tight Relations for Randomized Query Complexity
2020
In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R(f). The certificate complexity C(f) is such a complexity measure for the zero-error randomized query complexity R0(f): C(f) ≤R0(f) ≤C(f)2. In the first part of the paper we introduce a new complexity measure, expectational certificate complexity EC(f), which is also a quadratically tight bound on R0(f): EC(f) ≤R0(f) = O(EC(f)2). For R(f), we prove that EC2/3 ≤R(f). We then prove that EC(f) ≤C(f) ≤EC(f)2 and show that there is a quadratic separation between the two, thus EC(f) gives a tighter upper bound for R0(f). The measure is also related to the fractional…
Quasilinear elliptic equations with singular quadratic growth terms
2011
In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.
Stability of thin polymer films: influence of solvents.
2004
The interface and surface properties and the wetting behavior of polymer-solvent mixtures are investigated using Monte Carlo simulations and self-consistent field calculations. We carry out Monte Carlo simulations in the framework of a coarse-grained bead-spring model using short chains (oligomers) of N(P)=5 beads and a monomeric solvent, N(S)=1. The self-consistent field calculations are based on a simple phenomenological equation of state for compressible binary mixtures and we employ Gaussian chain model. The bulk behavior of the polymer-solvent mixture belongs to type III in the classification of van Konynenburg and Scott [Phil. Trans. R. Soc. London, Ser. A 298, 495 (1980)]. It is char…
Monte Carlo simulation of a lattice model for ternary polymer mixtures
1988
Monte Carlo studies of symmetrical polymer mixturesAB, modelled by selfavoiding walks withNA=NB=N steps on a simple cubic lattice, are presented for arbitrary concentrations of vacanciesφv in the range fromφv=0.2 toφv=0.8 and chain lengthsN≤64. We obtained the phase diagrams and the equation of state for three choices of the ratio ∈ / ∈AB (∈ being the energy between monomers of the same kind, ∈AB being the energy between different monomers). Flory-Huggins theory provides only a qualitative understanding of these results. If the equation of state is “fitted” with an effective Flory-Huggins parameterχeff, the latter turns out to be strongly dependent on both concentration and temperature.
Towards the Quantitative Prediction of the Phase Behavior of Polymer Solutions by Computer Simulation
2009
The phase diagram of polymer solutions (cf. e.g. alkanes dissolved in supercritical carbon dioxide) is complicated, since there are four control parameters (temperature, pressure, monomer volume fraction, chain length of the polymer) and due to the interplay of liquid-vapor transitions and fluid-fluid unmixing. As a result I very intricate phase diagram topologies can result. An attempt to develop coarse-1 grained models that can deal with this task will be described. As usual, the polymers I will be modelled as off-lattice bead-spring chains, where several chemical monomers I are integrated into one effective bond, torsional degrees of freedom being dis-I regarded. But also a coarse-graine…
Effect of the phase behaviour of the solvent–antisolvent systems on the gas–antisolvent-crystallisation of paracetamol
2005
Abstract The influence of the phase behaviour of the solvent–antisolvent system on the process conditions for the gas–antisolvent process is investigated. The two fluids are modelled by the Peng–Robinson equation of state while the dissolved solid is described by a Clapeyron-type approach. Based on the correlation of the ternary system, a liquid–liquid immiscibility region has been found which hinders the proper crystallisation of the solute. A thorough investigation of the binary solvent–antisolvent system by the global phase diagram methods yields a criterion for the proper choice of the solvent. The crucial property turns out to be the distance of the solvent–antisolvent system from the …