The generalized star product and the factorization of scattering matrices on graphs (2007)
ABSTRACT. In this article we continue our analysis of Schrodinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for...
Perturbation of spectra and spectral subspaces (2007)
Kostrykin, V., Makarov, K.A., Motovilov, A.K.
We consider the problem of variation of spectral subspaces for linear self-adjoint operators with emphasis on the case of off-diagonal perturbations. We prove a number of new optimal results on the...
On the existence of solutions to the operator Riccati equation and the tan Theta theorem (2005)
Kostrykin, V., Makarov, K.A., Motovilov, A.K.
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C. Under these assumptions we prove...
Approximate model for laser welding (2004)
Michel, J., Pfeiffer, S., Schulz, W., Nießen, M., Kostrykin, V.
The industrial application of laser welding implies a reliable and efficient production process. In order to facilitate this, modeling and simulation is used to reveal the crucial points of the...
Short-time dynamics in laser material processing (2004)
Kostrykin, V., Schulz, W., Nießen, M., Michel, J.
Material processings with laser radiation as cutting, welding, and drilling are established industrial processes. Their main advantages compared to conventional methods are the flexibility,...
Modeling and simulation of process monitoring and control in laser cutting (2004)
Schulz, W., Kostrykin, V., Michel, J., Niessen, M.
Laser cutting at moderate conditions is well established in industries. Both, high cutting speed for efficient machining and low cutting speed during contour cutting change the dynamical properties...
A random necklace model (2004)
We consider a Laplace operator on a random graph consisting of infinitely many loops joined symmetrically by intervals of unit length. The arc lengths of the loops are considered to be independent,...
Identification of dimension in phase space for cutting (2003)
Schulz, W., Eppelt, U., Heesen, H., Kostrykin, V., Michel, J., Niessen, M.
Laser cutting is an established separation process. Reliable machining at high productivity and quality as well as simplified machine operation are the actual goals in industries. This work describes...
Approximate model for laser welding (2003)
Michel, J., Pfeiffer, S., Schulz, W., Nießen, M., Kostrykin, V., Maier, C.
The industrial application of laser welding implies a reliable and efficient production process. Thus, modelling and simulation is used to reveal the crucial points of the welding process. The...
Quantum wires with magnetic fluxes (2003)
In the present article magnetic Laplacians on a graph are analyzed. We provide a complete description of the set of all operators which can be obtained from a given self-adjoint Laplacian by...
On a subspace perturbation problem (2003)
Kostrykin, V., Makarov, K.A., Motovilov, A.K.
We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let A and V be bounded self-adjoint operators. Assume that the spectrum of...
Statistical ensembles and density of states (2002)
We give a brief exposition of an approach to the statistical theory of small systems using the concept of integrated density of states familiar from the theory of random Schrodinger operators. The...
Energy transfer in scattering by rotating potentials (2002)
Enss, V., Kostrykin, V., Schrader, R.
Quantum mechanical scattering theory is studied for time-dependent Schrodinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at...
The generalized star product and the factorization of scattering matrices on graphs (2001)
In this article we continue our analysis of Schrodinger operators on arbitrary graphs given as certain Laplace operators. In the present article we give the proof of the composition rule for the...
Modelling, dynamical simulation and online monitoring in laser beam welding (2001)
Schulz, W., Michel, J., Niessen, M., Kostrykin, V., Abels, P., Kaierle, S.
Efficient and high quality processing requires identification of the underlying phenomena and on-line monitoring of the achieved performance. The reliability for prediction of the weld quality can be...
Microholes in zirconia coated Ni-superalloys for transpiration cooling of turbine blades (2000)
Horn, A., Weichenhain, R., Albrecht, S., Kreutz, E.W., Niessen, M., Michel, J., ...
Drillings in zirconia coated Ni-superalloys is done by melt extraction with pulsed laser radiation provided by a Nd:YAG slab laser with microsecond pulse duration. This laser system distinguishes...
. In this article we prove an upper bound for the Lyapunov exponent (E) and a two-sided bound for the integrated density of states N(E) at an arbitrary energy E > 0 of random Schrodinger operators...
Dynamics of ripple formation and melt flow in laser beam cutting (1999)
Schulz, W., Kostrykin, V., Niessen, M., Michel, J., Petring, D., Kreutz, E.W., ...
The dynamical behaviour of the laser beam fusion cutting process of metals is investigated. Integral methods such as the variational formulation are applied to the partial differential equations for...
Beam diagnosis and simulation for laser materials processing (1998)
Dahmen, M., Schulz, W., Kostrykin, V., Poprawe, R.
An important element of the processing chain of laser material processing is the laser beam. To ensure the process capability of this tool its spatial and temporal behavior as well as its effects on...
Kirchhoff's Rule for Quantum Wires (1998)
V. Kostrykin, Lehrstuhl Fur Lasertechnik, Rheinisch Westfalische, R. Schrader
In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator...
Ionization Probabilities through ultra-intense Fields in the extreme Limit (1997)
Fring, A., Kostrykin, V., Schrader, R.
We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we...
A free boundary problem related to laser beam fusion cutting. ODE approximation (1997)
Schulz, W., Kostrykin, V., Zefferer, H., Petring, D., Poprawe, R.
The laser beam fusion cutting process is described with a three-dimensional free boundary problem for the motion of one phase boundary. Its variational formulation is presented. An ODE approximation...
Ionization Probabilities through ultra-intense Fields in the extreme Limit (1997)
A. Fring, V. Kostrykin, R. Schrader
We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we...
Cluster Properties Of One Particle Schrödinger Operators. II (1997)
V. Kostrykin, Rheinisch Westfalische, R. Schrader
We continue the study of cluster properties of spectral and scattering characteristics of Schrodinger operators with potentials given as a sum of two wells, begun in our preceeding article [Rev....
On the absence of bound-state stabilization through short ultra-intense fields (1996)
Fring, A., Kostrykin, V., Schrader, R.
We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge...
On the Absence of Bound-State Stabilization Through Short Ultra-Intense Fields (1996)
Berlin Sfb, Preprint No, A. Fring, V. Kostrykin, R. Schrader
We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge...
Ionization of Rydberg Atoms by a Stark Kick (1994)
V. Enss, V. Kostrykin, R. Schrader
We provide a rigorous lower bound for the ionization probability of a Rydberg atom under the perturbation by a time-dependent electric field in the form of an ultrashort pulse idealized as a Dirac...