3,063 research outputs found
Adaptive Multi-Rate Wavelet Method for Circuit Simulation
In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The ordinary circuit differential equations are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. Second, a semi-discretization by Rothe's method of the MPDEs results in a system of differential algebraic equations DAEs with periodic boundary conditions. These boundary value problems are solved by a Galerkin discretization using spline functions. An adaptive spline grid is generated, using spline wavelets for non-uniform grids. Moreover the instantaneous frequency is chosen adaptively to guarantee a smooth envelope resulting in large time steps and therefore high run time efficiency. Numerical tests on circuits exhibiting multi-rate behavior including mixers and PLL conclude the paper
Phonon-driven ultrafast exciton dissociation at donor-acceptor polymer heterojunctions
A quantum-dynamical analysis of phonon-driven exciton dissociation at polymer
heterojunctions is presented, using a hierarchical electron-phonon model
parameterized for three electronic states and 24 vibrational modes. Two
interfering decay pathways are identified: a direct charge separation, and an
indirect pathway via an intermediate bridge state. Both pathways depend
critically on the dynamical interplay of high-frequency C=C stretch modes and
low-frequency ring-torsional modes. The ultrafast, highly non-equilibrium
dynamics is consistent with time-resolved spectroscopic observations
Unquenched complex Dirac spectra at nonzero chemical potential: Two-colour QCD lattice data versus matrix model
We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses
Motivic Milnor fibre for nondegenerate function germs on toric singularities
We study function germs on toric varieties which are nondegenerate for their
Newton diagram. We express their motivic Milnor fibre in terms of their Newton
diagram. We extend a formula for the motivic nearby fibre to the case of a
toroidal degeneration. We illustrate this by some examples.Comment: 14 page
Wigner surmise for Hermitian and non-Hermitian Chiral random matrices
We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results
for zero and maximal non-Hermiticity in the microscopic large-N limit we find an excellent agreement, valid for a small number of exact zero-eigenvalues. New compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes, and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue
distributions are a useful tool in Lattice Gauge Theory and we illustrate this by showing that our new results can describe data from two-colour QCD simulations with chemical potential in the symplectic class
The extensive nature of group quality
We consider groups of interacting nodes engaged in an activity as many-body,
complex systems and analyse their cooperative behaviour from a mean-field point
of view. We show that inter-nodal interactions rather than accumulated
individual node strengths dominate the quality of group activity, and give rise
to phenomena akin to phase transitions, where the extensive relationship
between group quality and quantity reduces. The theory is tested using
empirical data on quantity and quality of scientific research groups, for which
critical masses are determined.Comment: 6 pages, 6 figures containing 13 plots. Very minor changes to
coincide with published versio
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