Coping with the node problem in quantum hydrodynamics: the covering function method.

Dmytro Babyuk; Robert E Wyatt

doi:10.1063/1.1801211

Home/Archive/PubMed

PubMed · 15538843

Coping with the node problem in quantum hydrodynamics: the covering function method.

Dmytro Babyuk·Robert E Wyatt

View original source ↗Export metadata ↓

Abstract

A conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times t=1.2 ps. The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet.

Explore related subjects

Biophysics Chemistry, Physical Models, Statistical Models, Theoretical Normal Distribution Oscillometry Quantum Theory Water Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Dmytro Babyuk, Robert E Wyatt. 2004-11-15. Coping with the node problem in quantum hydrodynamics: the covering function method.. https://doi.org/10.1063/1.1801211

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2005

Probing protein-protein interactions by dynamic force correlation spectroscopy.

We develop a formalism for single molecule dynamic force spectroscopy to map the energy landscape of protein-protein complex (P(1)P(2)). The joint distribution P(tau(1),tau(2)) of unbinding lifetimes tau(1) and tau(2), measurable in a compression-tension cycle, which accounts for the internal relaxation dynamics of the proteins under tension, shows that the histogram of tau(1) is not Poissonian. The theory is applied to the forced unbinding of protein P1, modeled as a wormlike chain, from P(1)P(2). We propose a new class of experiments which can resolve the effect of internal protein dynamics on the unbinding lifetimes.

Biophysics↗

PubMed2005

A novel method for detergent concentration determination.

A fast and precise method for detergent concentration determination is presented. (Patent applications for the method described here have been submitted (EP05011904 and US60/702,261). Depending on the interest of the scientific community, the system will be commercialized. (For further information contact Hervé-W. Rémigy at the e-mail address below.) A small droplet of the detergent solution is deposited on a piece of Parafilm M and side views are recorded by two orthogonally arranged TV cameras. The droplet contours are then approximated by ellipses to determine the contact angles. Comparison of the observed contact angle values to calibrated standard curves of known detergent concentrations gives the concentration of the detergent assessed. A range of commonly used detergents was studied to demonstrate the reproducibility and precision of this simple method. As a first application, the detergent binding capacity of the Escherichia coli galactose/proton symporter (GalP) was assessed. Aggregation of GalP was observed when <260 +/- 5 dodecyl-beta,D-maltoside molecules were bound to one GalP molecule. These measurements document the efficacy of the drop-shape based detergent concentration determination described.

Biophysics↗

PubMed2005

Mechanical resistance of proteins explained using simple molecular models.

Recent experiments have demonstrated that proteins unfold when two atoms are mechanically pulled apart, and that this process is different to when heated or when a chemical denaturant is added to the solution. Experiments have also shown that the response of proteins to external forces is very diverse, some of them being "hard," and others "soft." Mechanical resistance originates from the presence of barriers on the energy landscape; together, experiment and simulation have demonstrated that unfolding occurs through alternative pathways when different pairs of atoms undergo mechanical extension. Here we use simulation to probe the mechanical resistance of six structurally diverse proteins when pulled in different directions. For this, we use two very different models: a detailed, transferable one, and a coarse-grained, structure-based one. The coarse-grained model gives results that are surprisingly similar to the detailed one and qualitatively agree with experiment; i.e., the mechanical resistance of different proteins or of a single protein pulled in different directions can be predicted by simulation. The results demonstrate the importance of pulling direction relative to the local topology in determining mechanical stability, and rationalize the effect of the location of importation/degradation tags on the rates of mitochondrial import or protein degradation in vivo.

Biophysics↗