Search results for "equation"
showing 10 items of 4219 documents
Unequal rapidity correlators in the dilute limit of the JIMWLK evolution
2019
We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution in the color glass condensate effective field theory. We discuss a diagrammatic interpretation of the long-range con elators. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a Balitsky-Fadin…
Nucleon localization function in rotating nuclei
2020
Background: An electron localization function was originally introduced to visualize bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules and solids. In nuclear physics, a nucleon localization function (NLF) has been used to characterize clusters in light nuclei, fragment formation in fission and pasta phases in the inner crust of neutron stars. Purpose: We use the NLF to study the nuclear response to fast rotation. Methods: We generalize the NLF to the case of nuclear rotation. The extended expressions involve both time-even and time-odd local densities. Since current density and density gradient contribute to the NLF primarily at th…
Quantum interference and the time-dependent radiation of nanojunctions
2021
Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.
Modelling Cd(II) removal from aqueous solutions by adsorption on a highly mineralized peat. Batch and fixed-bed column experiments
2006
This paper evaluates the potential use of a locally available organic soil amendment as a low-cost adsorbent. The removal of cadmium from aqueous solutions was studied by means of kinetic, batch and fixed-bed experiments. Batch experiments were conducted to evaluate the process kinetics and the removal equilibrium over a broad pH range. Pseudo-second-order kinetics and Freundlich equilibrium parameters were obtained. Six column experiments were carried out at different flow-rates and feed concentrations. Breakthrough curves showed higher metal retention than expected from the batch adsorption isotherms. Column modelling assuming rate-controlled pore diffusion was successfully performed. The…
Effect of pH, cation concentration and sorbent concentration on cadmium and copper removal by a granular activated carbon
1999
The single adsorption of cadmium and copper from aqueous solutions has been investigated on Darco 12-20 mesh granular activated carbon for a wide range of experimental conditions: pH, metal concentration and carbon concentration. The results showed the efficiency of the activated carbon as sorbent for both metals. Metal removal increases on raising pH and carbon concentration, and decreases on raising the initial metal concentration. The adsorption processes have been modelled using the surface complex formation (SCF) Triple Layer Model (TLM) with a single surface bidentate species or with an overall surface species with fractional stoichiometry. Bidentate stoichiometry considering pH, meta…
Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement
2020
We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.
Well-posedness and singularity formation for the Camassa-Holm equation
2006
We prove the well-posedness of Camassa--Holm equation in analytic function spaces both locally and globally in time, and we investigate numerically the phenomenon of singularity formation for particular initial data.
Rate Theory for Electrocatalytic Systems: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron Transfer Reactions
2019
Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro) canonical ensemble are gene…
Unified Rate Theory of Electrochemistry and Electrocatalysis: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron…
2019
Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro)canonical ensemble are gener…