Ferenc A. Bartha

Application of the many-body perturbation theory to normal saturated hydrocarbons in the localized representation

The second-order energy corrections are calculated for some normal saturated hydrocarbons by using the many body-perturbation theory (MBPT) based on localized orbitals. The correlation energies are expressed as the sum of contributions from virtual orbital pairs. We have found that these contributions are transferable and have interesting structural features: the trans-coplanar effects are relatively large. Partitioning the correlation energies according to the “order of neighbourhood” we have found that the zero order effects are the largest but the first and second neighbour contributions are also important.

Local stability implies global stability for the 2-dimensional Ricker map

In this study, we consider the difference equation where is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version of the equation, S. Levin and R. May conjectured in 1976 that local stability of the non-trivial equilibrium implies its global stability. Based on rigorous, computer-aided calculations and analytical tools, we prove the conjecture for d = 1.

An efficient method for using molecular symmetry: The presence of model geometries

Abstract In a series of papers a new method which uses the molecular symmetry for treatment of extended molecules is investigated. In this paper it is shown that in the presence of model geometries the method — on which a new ab initio program named SYCETY is based — is effective for calculation of large, related systems.

Acumen : an open-source testbed for cyber-physical systems research

Developing Cyber-Physical Systems requires methods and tools to support simulation and verification of hybrid (both continuous and discrete) models. The Acumen modeling and simulation language is an open source testbed for exploring the design space of what rigorous-but-practical next-generation tools can deliver to developers of Cyber-Physical Systems. Like verification tools, a design goal for Acumen is to provide rigorous results. Like simulation tools, it aims to be intuitive, practical, and scalable. However, it is far from evident whether these two goals can be achieved simultaneously. This paper explains the primary design goals for Acumen, the core challenges that must be addressed in order to achieve these goals, the “agile research method” taken by the project, the steps taken to realize these goals, the key lessons learned, and the emerging language design.

Accurate rigorous simulation should be possible for good designs

The development of Cyber-Physical Systems benefits from better methods and tools to support the simulation and verification of hybrid (continuous/discrete) models. Acumen is an open source testbed for exploring the design space of what rigorous-but-practical next-generation tools can deliver to developers. Central to Acumen is the notion of rigorous simulation. Like verification tools, rigorous simulation is intended to provide guarantees about the behavior of the system. Like traditional simulation tools, it is intended to be intuitive, practical, and scalable. Whether these two goals can be achieved simultaneously is an important, long-term challenge. This paper proposes a design principle that can play an important role in meeting this challenge. The principle addresses the criticism that accumulating numerical errors is a serious impediment to practical rigorous simulation. It is inspired by a twofold insight: one relating to the nature of systems engineered in the real world, and the other relating to how numerical errors in the simulation of a model can be recast as errors in the state or parameters of the model in the simulation. We present a suite of small, concrete benchmarks that can be used to assess the extent to which a rigorous simulator upholds the proposed principle. We also report on which benchmarks Acumens current rigorous simulator already succeeds and which ones remain challenging.

Fixed points of a destabilized Kuramoto-Sivashinsky equation

We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension u t + ? u x x x x + β u x x + γ u u x = α u for α, ? ? 0 and β , γ ? R . For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

Compile-Time Extensions to Hybrid ODEs

Reachability analysis for hybrid systems is an active area of development and has resulted in many promising prototype tools. Most of these tools allow users to express hybrid system as automata wi ...

Localized molecular orbitals of interacting molecular systems

We have studied the transferability of the localized molecular orbitals (LMOs) of interacting water molecules for distances around the intermolecular energy minimum. The Fock matrix elements (ε) and the “effective volumes”Vieff of the LMOs have been calculated and discussed. It was shown that for the valence shell LMOs the transferability is satisfied to a large extent, the deviation is less than 5 %. Due to this transferability the dispersion interaction energy can be calculated by using only the LMOs of the supermolecule and the BSSE can be neglected.