18,423 research outputs found
Coherent control of correlated nanodevices: A hybrid time-dependent numerical renormalization-group approach to periodic switching
The time-dependent numerical renormalization-group approach (TD-NRG),
originally devised for tracking the real-time dynamics of quantum-impurity
systems following a single quantum quench, is extended to multiple switching
events. This generalization of the TD-NRG encompasses the possibility of
periodic switching, allowing for coherent control of strongly correlated
systems by an external time-dependent field. To this end, we have embedded the
TD-NRG in a hybrid framework that combines the outstanding capabilities of the
numerical renormalization group to systematically construct the effective
low-energy Hamiltonian of the system with the prowess of complementary
approaches for calculating the real-time dynamics derived from this
Hamiltonian. We demonstrate the power of our approach by hybridizing the TD-NRG
with the Chebyshev expansion technique in order to investigate periodic
switching in the interacting resonant-level model. Although the interacting
model shares the same low-energy fixed point as its noninteracting counterpart,
we surprisingly find the gradual emergence of damped oscillations as the
interaction strength is increased. Focusing on a single quantum quench and
using a strong-coupling analysis, we reveal the origin of these
interaction-induced oscillations and provide an analytical estimate for their
frequency. The latter agrees well with the numerical results.Comment: 20 pager, Revtex, 10 figures, submitted to Physical Review
Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells
This article is an attempt to provide a self consistent picture, including
existence analysis and numerical solution algorithms, of the mathematical
problems arising from modeling photocurrent transients in Organic-polymer Solar
Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear
diffusion-reaction partial differential equations (PDEs) with electrostatic
convection, coupled to a kinetic ordinary differential equation (ODE). We
propose a suitable reformulation of the model that allows us to prove the
existence of a solution in both stationary and transient conditions and to
better highlight the role of exciton dynamics in determining the device turn-on
time. For the numerical treatment of the problem, we carry out a temporal
semi-discretization using an implicit adaptive method, and the resulting
sequence of differential subproblems is linearized using the Newton-Raphson
method with inexact evaluation of the Jacobian. Then, we use exponentially
fitted finite elements for the spatial discretization, and we carry out a
thorough validation of the computational model by extensively investigating the
impact of the model parameters on photocurrent transient times.Comment: 20 pages, 11 figure
Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator
In a Hilbert framework, we introduce continuous and discrete dynamical
systems which aim at solving inclusions governed by structured monotone
operators , where is the subdifferential of a
convex lower semicontinuous function , and is a monotone cocoercive
operator. We first consider the extension to this setting of the regularized
Newton dynamic with two potentials. Then, we revisit some related dynamical
systems, namely the semigroup of contractions generated by , and the
continuous gradient projection dynamic. By a Lyapunov analysis, we show the
convergence properties of the orbits of these systems.
The time discretization of these dynamics gives various forward-backward
splitting methods (some new) for solving structured monotone inclusions
involving non-potential terms. The convergence of these algorithms is obtained
under classical step size limitation. Perspectives are given in the field of
numerical splitting methods for optimization, and multi-criteria decision
processes.Comment: 25 page
Optimal control in ink-jet printing via instantaneous control
This paper concerns the optimal control of a free surface flow with moving
contact line, inspired by an application in ink-jet printing. Surface tension,
contact angle and wall friction are taken into account by means of the
generalized Navier boundary condition. The time-dependent differential system
is discretized by an arbitrary Lagrangian-Eulerian finite element method, and a
control problem is addressed by an instantaneous control approach, based on the
time discretization of the flow equations. The resulting control procedure is
computationally highly efficient and its assessment by numerical tests show its
effectiveness in deadening the natural oscillations that occur inside the
nozzle and reducing significantly the duration of the transient preceding the
attainment of the equilibrium configuration
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