95 research outputs found
Two dimensional dynamical systems which admit Lie and Noether symmetries
We prove two theorems which relate the Lie point symmetries and the Noether
symmetries of a dynamical system moving in a Riemannian space with the special
projective group and the homothetic group of the space respectively. The
theorems are applied to classify the two dimensional Newtonian dynamical
systems, which admit a Lie point/Noether symmetry. Two cases are considered,
the non-conservative and the conservative forces. The use of the results is
demonstrated for the Kepler - Ermakov system, which in general is
non-conservative and for potentials similar to the H\`enon Heiles potential.
Finally it is shown that in a FRW background with no matter present, the only
scalar cosmological model which is integrable is the one for which 3-space is
flat and the potential function of the scalar field is exponential. It is
important to note that in all applications the generators of the symmetry
vectors are found by reading the appropriate entry in the relevant tables.Comment: 25 pages, 17 table
Quantum chemical investigation on the reaction mechanism of tertiary phosphines with unsaturated carboxylic acids: An insight into kinetic data
The structures of intermediates and transition states in the reaction of tertiary phosphines with unsaturated carboxylic acids have been calculated at the B3LYP level of theory using the 6-31+G(d,p) basis set. Analysis of the results shows that [1,3]-intramolecular migration of carboxylic proton to carbanionic center of generated zwitterionic intermediate is strongly kinetically unfavorable, and external proton-donor source is essential to complete quaternization. A molecular cluster of the intermediate with one molecule of water has been modeled for intermolecular reaction pathway, but even in this case, the proton transfer remains to be the rate-determining step that is in a good agreement with previous kinetic investigations on this reaction. The data obtained for this reaction have much in common with recent studies on the mechanisms of the Morita-Baylis-Hillman reaction and phosphine-catalyzed [3+2] cycloaddition, which revealed paramount importance of proton-transfer steps. Copyright © 2012 Wiley Periodicals, Inc
Quantum-chemical study of the effects of noncovalent interactions on the nuclear magnetic screening constants of pyrimidine base associates
The effects of weak noncovalent interactions on the nuclear magnetic screening (NMS) constants (σ 1H), (σ 13C) and charge distribution (q t ) on atoms in van der Waals model associates of unsubstituted and substituted pyrimidines and substituted uracil are considered. The NMS constants were calculated by the UB3LYP/6-31G(d,p) with GIAO functions. The correlation dependences of the 1H and 13C σ constants on the charge q on atoms whre constructed. It were shown that they can be represented as polynomials that include the terms that are linear and quadratic relative to the charge. The relations obtained in this way are similar in form and close in magnitude to the coefficients of the known Buckingham and Augspurger functions that describe the electric field effects on the nuclear magnetic screening constants. It was found that the coefficients in these polynomials have a definite physical sense in that they characterize nuclear magnetic screening and the "screening polarizability" tensor in the unperturbed molecule and associate, respectively. The NMS constants and charge distribution in pyrimidine base associates and accordingly the coefficients that reflect their values in polynomials depend on the form, size, and composition of the associate and can vary significantly depending on the position of the pyrimidine base in the associate. © 2007 Springer Science+Business Media, Inc
A quantum chemical study of an interaction between collagen fragments and calcium ions using calculations of model complexes
© 2015 Springer Science+Business Media New York. Quantum chemical calculations revealed that the complexation between proline-containing collagen fragments and calcium ions involves a preferential interaction between Ca2+ ions and the oxygen and nitrogen atoms of proline in the glycine - proline - alanine fragment of the amino acid sequence of collagen
Using the Noether symmetry approach to probe the nature of dark energy
We propose to use a model-independent criterion based on first integrals of
motion, due to Noether symmetries of the equations of motion, in order to
classify the dark energy models in the context of scalar field (quintessence or
phantom) FLRW cosmologies. In general, the Noether symmetries play an important
role in physics because they can be used to simplify a given system of
differential equations as well as to determine the integrability of the system.
The Noether symmetries are computed for nine distinct accelerating cosmological
scenarios that contain a homogeneous scalar field associated with different
types of potentials. We verify that all the scalar field potentials, presented
here, admit the trivial first integral namely energy conservation, as they
should. We also find that the exponential potential inspired from scalar field
cosmology, as well as some types of hyperbolic potentials, include extra
Noether symmetries. This feature suggests that these potentials should be
preferred along the hierarchy of scalar field potentials. Finally, using the
latter potentials, in the framework of either quintessence or phantom scalar
field cosmologies that contain also a non-relativistic matter(dark matter)
component, we find that the main cosmological functions, such as the scale
factor of the universe, the scalar field, the Hubble expansion rate and the
metric of the FRLW space-time, are computed analytically. Interestingly, under
specific circumstances the predictions of the exponential and hyperbolic scalar
field models are equivalent to those of the CDM model, as far as the
global dynamics and the evolution of the scalar field are concerned. The
present analysis suggests that our technique appears to be very competitive to
other independent tests used to probe the functional form of a given potential
and thus the associated nature of dark energy.Comment: Accepted for publication in Physical Review D (13 pages
Deformation quantization of linear dissipative systems
A simple pseudo-Hamiltonian formulation is proposed for the linear
inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics,
our approach is based on the use of non-stationary Poisson brackets, i.e.
corresponding Poisson tensor is allowed to explicitly depend on time. Starting
from this pseudo-Hamiltonian formulation we develop a consistent deformation
quantization procedure involving a non-stationary star-product and an
``extended'' operator of time derivative , differentiating
the -product. As in the usual case, the -algebra of physical
observables is shown to admit an essentially unique (time dependent) trace
functional . Using these ingredients we construct a complete and
fully consistent quantum-mechanical description for any linear dynamical system
with or without dissipation. The general quantization method is exemplified by
the models of damped oscillator and radiating point charge.Comment: 14 pages, typos correcte
Production method of nanostructured wood-polymer composition with microwave application
ABSTRACT: Introduction. Currently, wood-polymer compositions (WPC) are widely used in the national economy and construction. The composition of WPC varies widely depending on the further purpose. Improving the binding quality in the wood-polymer
system is one of the promising areas for enhancing operational characteristics. Organic and inorganic substrates nanostructured with
individual substances, including metal particles, are used as binding components. In the petrochemical industry, most high-capacity
productions use catalysts based on active carriers like heavy metals when developing targeted products for various purposes. After
several stages of regeneration, recovering these heavy metals becomes impossible. Consequently, spent catalysts accumulate in
sedimentation tanks and sludge collectors, lacking an efficient method for disposal and secondary use. One of the components
included in the composition of spent catalysts is chromium (+6), which belongs to carcinogenic metals. Numerous disposal methods
are currently inadequate for neutralizing this metal on an industrial scale, which is of interest for research. Methods and materials.
The study is aimed at converting carcinogenic chromium (+6) into non-carcinogenic chromium (+3) by ultrahigh frequency exposure
(microwave), which will open up opportunities for its use as a chromium-containing nanocomplex binding a tree-polymer. Results
and discussions. The ultrahigh-frequency effect on the mixture of wood-polymer composition and spent chromium (+6) causes an
increase in the penetration depth of high–frequency waves, characterized by a uniform distribution of energy over the entire area
of the composite, which is explained by the reduction of chromium (VI) oxide into chromium (III) oxide, and there is also a change
in the color of the nanostructured wood-polymer composition (WP – compositions) from yellow to malachite. Conclusion. This
study, which consists in the application of microwave exposure to the wood-nanoparticle-polymer system, confirms the receipt of
a durable construction product and its use in the construction of roofs, facade boards, sidewalks, piers, port facilities, et
Conditional linearizability criteria for a system of third-order ordinary differential equations
We provide linearizability criteria for a class of systems of third-order
ordinary differential equations (ODEs) that is cubically semi-linear in the
first derivative, by differentiating a system of second-order quadratically
semi-linear ODEs and using the original system to replace the second
derivative. The procedure developed splits into two cases, those where the
coefficients are constant and those where they are variables. Both cases are
discussed and examples given
Constraints and analytical solutions of theories of gravity using Noether symmetries
We perform a detailed study of the modified gravity models in the
light of the basic geometrical symmetries, namely Lie and Noether point
symmetries, which serve to illustrate the phenomenological viability of the
modified gravity paradigm as a serious alternative to the traditional scalar
field approaches. In particular, we utilize a model-independent selection rule
based on first integrals, due to Noether symmetries of the equations of motion,
in order to identify the viability of models in the context of flat FLRW
cosmologies. The Lie/Noether point symmetries are computed for six modified
gravity models that include also a cold dark matter component. As it is
expected, we confirm that all the proposed modified gravity models admit the
trivial first integral namely energy conservation. We find that only the
model, which generalizes the concordance
cosmology, accommodates extra Lie/Noether point symmetries. For this
model the existence of non-trivial Noether (first) integrals can be used to
determine the integrability of the model. Indeed within this context we solve
the problem analytically and thus we provide for the first time the evolution
of the main cosmological functions such as the scale factor of the universe and
the Hubble expansion rate.Comment: Accepted for publication in Physical Review D (10 pages), typos
corrected and some new references include
- …