General Dynamic Approach Research Articles

Electron diffraction analysis for the molecules with multiple large-amplitude motions. 3-nitrostyrene--a molecule with two internal rotors.

Dynamic structural analysis of the molecules possessing large-amplitude degrees of freedom has been attempted by many researchers; however, so far, electron diffraction investigations involved only one large-amplitude coordinate (internal rotation or bending). The current state of computational facilities allows extending of the general dynamic approach to the systems possessing two or more large-amplitude motions. This paper presents the first practical implementation of the theoretical method developed previously by the authors for solving the dynamic-structural problem with two or more large-amplitude coordinates; the procedure is applied to a molecule of 3-nitrostyrene. The molecule is represented as a set of pseudoconformers built on a two-dimensional grid corresponding to both internal rotation coordinates present in the molecule (with 10-30° steps by each angle); altogether, up to 342 pseudoconformers were used. Structural analysis was based on the experimental electron diffraction data supported by quantum chemical calculations (at the MP2 and B3LYP levels of theory) and molecular spectroscopy data. Quantum chemistry predicts the planar structure of both syn- and anti- stable conformations with close energies and weak interaction between internal rotations of nitro and vinyl groups. The gas-phase electron diffraction experimental data are compatible with the quantum chemical predictions. The principal equilibrium geometry parameters of the molecule (syn- conformation) have been determined as follows: r(e)(C-C)(ring, avg.) = 1.391(1) Å, r(e)(C-C) = 1.477(5) Å, r(e)(C═C) = 1.333(7) Å, r(e)(C-N) = 1.463(5) Å, r(e)(N═O) = 1.227(3) Å, ∠e(O═N═O) = 124.3 (4)°. Experimental data for this molecule are insufficient to make estimates of the barrier heights of internal rotation; the population ratio of syn- and anti- conformations is evaluated as 50 ± 20%. Results of our investigation confirm the presence of significant internal rotations in the 3-nitrostyrene molecule.

Dynamics of quantum zeno and anti-zeno effects in an open system

We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature {\bf 405}, 546 (2000)). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly {\it enhanced} by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with {\it arbitrary} temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.

Measurement of Physical Quantities as the Formation of Their Analytical Metrological Images in Spaces of Linearly Independent Bases

The most general dynamic approach is proposed to measuring a physical quantity as a finite signal, based on analyzing the dynamics of the states of the sensitive element of the measuring instrument. It is shown that such an approach incorporates as a particular case the traditional static approach to measurement which consists in obtaining point estimates of the measured quantity utilizing scaling of the steady-state (static) conditions of the sensitive element of the measuring instrument.

Computer simulations and experimental investigations of X-ray multilayer mirrors

A general theory of the reflectivity by a perfect X-ray multilayer mirror based on the use of a recurrent relation is developed. The reflectivity is described by well-known Fresnel formulae which take into account jumps of susceptibility at the boundary between the layers. The analytical solution in the frame of a most general dynamical approach has been found and the conditions of application of the kinematical approximation are discussed. Experimental investigations of multilayer mirrors were carried out and the results were compared with the theory.

On the Theory of Reflectivity by an X‐Ray Multilayer Mirror

AbstractA general theory of reflectivity by a perfect X‐ray multilayer mirror based on the usage of a recurrent relation is developed. The reflectivity is described by the well‐known Fresnel formulae which take into account jumps of susceptibility at the boundary between the layers. The analytical solution in the frame of the most general dynamical approach is found and the condition of application of the kinematical approximation is discussed. Special attention is paid to the periodic multilayer structure containing two layers of different materials with more than one pair of these layers in the period.

A general dynamic model of 19th century US population change

The pattern of rural population growth in 23 northern states during the period 1790 to 1900 is examined using a general dynamic approach. The relationship between fertility, migration and population growth is analysed within a single settlement model and a control solution is produced which demonstrates that fertility and migration behaviour reacted to changes in land availability, eventually leading to population stability in rural areas.

The state of psychotherapy in British psychiatry.

Defining psychotherapy broadly as way of handling the experience of illness in which the therapist's personality becomes part of the healing process, the author traces its course in the history of British psychiatry. He points out that, although the older, organically oriented hospital psychiatry still occupies a formal position of strength, the National Health Service has prompted the evolution of a general dynamic approach to the treatment of the mentally ill, encompassing several of the previously isolated camps in psychiatry.