The Stern-Gerlach experiment and the effects of spin relaxation

The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.     

Long time missions and the fuel-optimal attitude maneuvering in a swinging mode

The problem of fuel-optimal attitude maneuvering of a space vehicle (SV) with non-fixed time is considered. The state constraint related to the maintenance of artificial gravitation is imposed. This problem is especially important for long-time space missions. The attitude of the space vehicle is controlled by means of a pair of reactive engines which produce a single control torque with fixed direction in the body-fixed frame. An optimal solution is obtained in the class of trajectories belonging to “swinging mode” two-periodic sliding cycling regimes. The solution is found in analytical form and optimal synthesis is obtained. The short conference version of this paper was published in Proceedings of the IFAC Workshop GSCP-04, Pereyslavl-Zalessky, Russia, September 21–29, 2004. This paper was presented as an invited lecture at the International Conference on Control and Optimization in honor of Professor Boris Polyak, Institute of Control Science RAN, Russia, Moscow, May 19–20, 2005.     

Fluorimetric determination of aldose reductased in small tissue samples

The assay is based on the consumption of NADPH catalyzed by the enzyme, with glucose as substrate, and measurement of the native NADPH fluorescence. This modification yields 10-fold higher sensitivity than the usual procedure based on absorbance measurements at 340 nm. The method is applied to tissue samples weighing 0.1–2 mg.     

Line shapes in CP/MAS (13)C NMR spectra of cellulose I

The CP/MAS (13)C NMR line shape of cellulose I has been qualitatively analyzed by direct simulations using the Ornstein-Uhlenbeck stochastic process and the Kubo model. Both approaches describe a anhydroglucose C4 carbon as a oscillator with fluctuating Larmor frequency. The NMR resonance frequency is written omega=omega +omega(t), where the fluctuating part with zero mean was modelled as a stationary Markov diffusion process. The simulation results both motivates the use of multiple line shapes when fitting CP/MAS (13)C NMR spectra recorded on cellulose I and gives some insights into why signals from crystalline cellulose I give rise to Lorentzian line shapes.     

Minimum Mixed Time–Energy Trajectory Planning of a Nonlinear Vehicle Subject to 2D Disturbances

Journal of Optimization Theory and Applications - The problem of a planar vehicle moving on a surface, such as aerial drones or small naval vessels, can be treated as a series of trajectory...     

On-line microdialysis for enhanced resolution and sensitivity during electrospray mass spectrometry of non-covalent complexes and competitive binding studies

Many proteins and macromolecules easily form metal adduct ions which impairs their analysis by mass spectrometry. The present study describes how the formation of undesired adducts can be minimized by on-line microdialysis for non-covalent binding studies of macromolecules with low molecular mass ligands with electrospray ionization mass spectrometry (ESI-MS). The technique was indispensable for protein-ligand studies due to reduction of unwanted adduct ions, and thus gave excellent resolution and a sensitivity improvement of at least 5 times. The core of the analytical system was a modified microdialysis device, which was operated in countercurrent mode. A novel technique based on microdialysis for competitive binding studies is also presented. The non-covalent complex between a protein and a ligand was formed in the sample vial prior to analysis. The complex was injected into an on-line microdialysis system where a competitive ligand was administered in the dialysis buffer outside of the fiber. The second ligand competitively displaced the first ligand through transport via the wall of the dialysis fiber, and the intact complexes were detected by ESI-MS.     

Electrospray ionization mass spectrometry as a tool for determination of drug binding sites to human serum albumin by noncovalent interaction

Most proteins in blood plasma bind ligands. Human serum albumin (HSA) is the main transport protein with a very high capacity for binding of endogenous and exogenous compounds in plasma. Many pharmacokinetic properties of a drug depend on the level of binding to plasma proteins. This work reports studies of noncovalent interactions by means of nanoelectrospray ionization mass spectrometry (nanoESI-MS) for determination of the specific binding of selected drug candidates to HSA. Warfarin, iopanoic acid and digitoxin were chosen as site-specific probes that bind to the main sites of HSA. Two drug candidates and two known binders to HSA were analyzed using a competitive approach. The drugs were incubated with the target protein followed by addition of site-specific probes, one at a time. The drug candidates showed predominant affinity to site I (warfarin site). Naproxen and glyburide showed affinity to both sites I and II. The advantages of nanoESI-MS for these studies are the sensitivity, the absence of labeled molecules and the short method development time.     

A Fourier transform infrared study of the lamellar liquid crystalline phase of dimethyldodecyl amineoxide-water and dimethyldodecyl amineoxide-gramicidin-D-water systems

The overall conformational order of the alkyl tail of the lyotropic lamellar phase of the dimethyldodecyl amineoxide, (CH₃)₂ON⁺(CH₂)₁₁CH₃ (DDAO)---H₂O system (75.7 wt.%) has been studied by using Fourier transform infrared spectroscopy. The spectral region 1000–1400 cm⁻¹, covering the CH₂ wagging modes and the methyl umbrella modes of DDAO, has been recorded in the temperature interval 3–60°C and at different mole fractions of gramicidin-D with respect to DDAO (X_g = 0.03, 0.05 and 0.1) for both DDAO-H₂O and DDAO-D₂O systems. It has been shown that the DDAO amphiphile molecules of the lamellar phase reorganise in a phase-like transition near 25–30°C. The DDAO-water system does not show any significant bands corresponding to a double gauche conformation at 1355 cm⁻¹ nor to a gauche-transgauche (kinked) conformation at 1367 cm⁻¹. These bands are probably present but hidden in the broad low-frequency side of the CH₃ umbrella band at 1377 cm⁻¹. Upon incorporation of gramicidin into the lamellar phase both head group and acyl chain spectra of the lipid change in such a way as to indicate a decreased “ordering” of the molecules, as judged by comparison with spectra of the same molecule in a micellar environment, and with increased fluidity of the acyl chains.     

The use of partitioning technique in the solution of operator equations for ionizations and excitations

An inhomogeneous operator equation is associated with the equations of motion for ionization- and excitation operators. The partitioning technique is applied to solve the equation. Formal expressions for the ionization- and excitation operators are obtained and examples of approximations to these are given.