Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects

Using the variational cluster approach (VCA), we study the transition from the antiferromagnetic to the superconducting phase of the two-dimensional Hubbard model at zero temperature. Our calculations are based on a new method to evaluate the VCA grand potential which employs a modified Lanczos algorithm and avoids integrations over the real or imaginary frequency axis. Thereby, very accurate results are possible for cluster sizes not accessible to full diagonalization. This is important for an improved treatment of short-range correlations, including correlations between Cooper pairs in particular. We investigate the cluster-size dependence of the phase-separation tendency that has been proposed recently on the basis of calculations for smaller clusters. It is shown that the energy barrier driving the phase separation decreases with increasing cluster size. This supports the conjecture that the ground state exhibits microscopic inhomogeneities rather than macroscopic phase separation. The evolution of the single-particle spectum as a function of doping is studied in addtion and the relevance of our results for experimental findings is pointed out.Comment: 7 pages, 6 figures, published versio

The DVCS Measurement at HERA

The recent results of the studies of Deeply Virtual Compton Scattering (DVCS) events at HERA are presented. The possibility offered by this process to gain information about skewed parton distributions (SPD) is emphasized.Comment: Talk given at New Trends in HERA Physics 2001, Ringberg Castle, Tegernsee, Germany, 17-22 Jun 2001, 13 pages, 10 figures, recent ZEUS data discussed, references update

Some Characterizations and Properties of the "Distance to Ill-Posedness" and the Condition Measure of a Conic Linear System

A conic linear system is a system of the form P: find x that solves b- Ax E Cy, E Cx, where Cx and Cy are closed convex cones, and the data for the system is d = (A, b). This system is"well-posed" to the extent that (small) changes in the data (A, b) do not alter the status of the system (the system remains solvable or not). Intuitively, the more well-posed the system is, the easier it should be to solve the system or to demonstrate its infeasibility via a theorem of the alternative. Renegar defined the "distance to ill-posedness," p(d), to be the smallest distance of the data d = (A, b) to other data d = (A, b) for which the system P is "ill=posed," i.e., d = (A, b) is in the intersection of the closure of feasible and infeasible instances d' = (A', b') of P. Renegar also defined the "condition measure" of the data instance d as C(d) Alldll/p(d), and showed that this measure is a natural extension of the familiar condition measure associated with systems of linear equation. This study presents two categories of results related to p(d), the distance to ill-posedness, and C(d), the condition measure of d. The first category of results involves the approximation of p(d) as the optimal value of certain mathematical programs. We present ten different mathematical programs each of whose optimal values provides an approximation of p(d) to within certain constant factors, depending on whether P is feasible or not. The second category of results involves the existence of certain inscribed and intersecting balls involving the feasible region of P or the feasible region of its alternative system, in the spirit of the ellipsoid algorithm. These results roughly state that the feasible region of P (or its alternative system when P is not feasible) will contain a ball of radius r that is itself no more than a distance R from the origin, where the ratio R/r satisfies R/r _ ( -i) and R < O(n C(d)), where n is the dimension of the feasible region. Therefore the condition measure C(d) is a relevant tool in proving the existence of an inscribed ball in the feasible region of P that is not too far from the origin and whose radius is not too small

Prior Reduced Fill-In in Solving Equations in Interior Point Algorithms

The efficiency of interior-point algorithms for linear programming is related to the effort required to factorize the matrix used to solve for the search direction at each iteration. When the linear program is in symmetric form (i.e., the constraints are Ax b, x > 0 ), then there are two mathematically equivalent forms of the search direction, involving different matrices. One form necessitates factoring a matrix whose sparsity pattern has the same form as that of (A AT). The other form necessitates factoring a matrix whose sparsity pattern has the same form as that of (ATA). Depending on the structure of the matrix A, one of these two forms may produce significantly less fill-in than the other. Furthermore, by analyzing the fill-in of both forms prior to starting the iterative phase of the algorithm, the form with the least fill-in can be computed and used throughout the algorithm. Finally, this methodology can be applied to linear programs that are not in symmetric form, that contain both equality and inequality constraints

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Non-contact test set-up for aeroelasticity in a rotating turbomachine combining a novel acoustic excitation system with tip-timing

Due to trends in aero-design, aeroelasticity becomes increasingly important in modern turbomachines. Design requirements of turbomachines lead to the development of high aspect ratio blades and blade integral disc designs (blisks), which are especially prone to complex modes of vibration. Therefore, experimental investigations yielding high quality data are required for improving the understanding of aeroelastic effects in turbomachines. One possibility to achieve high quality data is to excite and measure blade vibrations in turbomachines. The major requirement for blade excitation and blade vibration measurements is to minimize interference with the aeroelastic effects to be investigated. Thus in this paper, a non-contact-and thus low interference-experimental set-up for exciting and measuring blade vibrations is proposed and shown to work. A novel acoustic system excites rotor blade vibrations, which are measured with an optical tip-timing system. By performing measurements in an axial compressor, the potential of the acoustic excitation method for investigating aeroelastic effects is explored. The basic principle of this method is described and proven through the analysis of blade responses at different acoustic excitation frequencies and at different rotational speeds. To verify the accuracy of the tip-timing system, amplitudes measured by tip-timing are compared with strain gage measurements. They are found to agree well. Two approaches to vary the nodal diameter (ND) of the excited vibration mode by controlling the acoustic excitation are presented. By combining the different excitable acoustic modes with a phase-lag control, each ND of the investigated 30 blade rotor can be excited individually. This feature of the present acoustic excitation system is of great benefit to aeroelastic investigations and represents one of the main advantages over other excitation methods proposed in the past. In future studies, the acoustic excitation method will be used to investigate aeroelastic effects in high-speed turbomachines in detail. The results of these investigations are to be used to improve the aeroelastic design of modern turbomachines.Siemens EnergyDFG/SFB/87

Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so

Community rotorcraft air transportation benefits and opportunities

Information about rotorcraft that will assist community planners in assessing and planning for the use of rotorcraft transportation in their communities is provided. Information useful to helicopter researchers, manufacturers, and operators concerning helicopter opportunities and benefits is also given. Three primary topics are discussed: the current status and future projections of rotorcraft technology, and the comparison of that technology with other transportation vehicles; the community benefits of promising rotorcraft transportation opportunities; and the integration and interfacing considerations between rotorcraft and other transportation vehicles. Helicopter applications in a number of business and public service fields are examined in various geographical settings

A low stray light, high current, low energy electron source

A design of an electron gun system is presented whose stray light emission is reduced by about three orders of magnitude compared to a regular low-energy electron diffraction gun. This is achieved by a combination of a BaO cathode run at rather low temperature and a 30° tandem parallel-plate analyzer used as an optical baffle. The system provides a high beam current of several microampers at 50 eV beam energy. The system can be used down to ∼10 eV

Screening of charged singularities of random fields

Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of plus or minus one. In random fields we can define a correlation function for the charge-weighted density of singularities. In many types of random fields, this correlation function satisfies an identity which shows that the singularities 'screen' each other perfectly: a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge, and vice-versa. This paper gives a simple and widely applicable derivation of this result. A counterexample where screening is incomplete is also exhibited.Comment: 12 pages, no figures. Minor revision of manuscript submitted to J. Phys. A, August 200