ЭФФЕКТ ПОВЫШЕНИЯ АДСОРБЦИОННОЙ АКТИВНОСТИ ХОЛЕСТЕРИЧЕСКИХ ЖИДКОКРИСТАЛЛИЧЕСКИХ СОЕДИНЕНИЙ В ПРОЦЕССЕ ТРЕНИЯ ТВЕРДЫХ ТЕЛ

It is found that, when solid bodies are in static contact with liquid lubricants containing surfactants and cholesteric liquid-crystal compounds, the behavior of their adsorption depends on the adsorbent nature and chemical composition. When copper, steel and glass powders are in long contact with oleic acid solutions in Vaseline oil, the additive concentration decreases, and in the case of solutions of cholesteric liquid–crystal compounds, their concentration in oil increases. When metals (friction pair steel–steel) are in dynamic contact, adsorption processes involving solutions of liquid crystal compounds occur by other mechanisms. The increase in the adsorption activity of cholesteric liquid-crystal compounds in the friction of solids is established. It is found that changing the concentration of liquid-crystal additives in the used oil due to the adsorption tribo-activity in the process of dynamic contact correlates with a decrease and a subsequent stabilization of the friction coefficient of the steel–steel pair.Установлено, что при статическом контакте твердых тел с жидкими смазочными материалами, содержащими поверхностно-активные вещества и холестерические жидкокристаллические соединения, закономерности их адсорбции зависят от природы и химического состава адсорбента. При длительном контактировании порошков меди, стали и стекла с растворами олеиновой кислоты в вазелиновом масле концентрация присадки уменьшается, а в случае растворов жидкокристаллических соединений холестерического типа их концентрация в масле увеличивается. При динамическом контакте металлов (пара трения сталь-сталь) адсорбционные процессы с участием растворов жидкокристаллических соединений протекают по иным механизмам. Обнаружено увеличение адсорбционной активности холестерических жидкокристаллических соединений при трении твердых тел. Установлено, что изменение концентрации жидкокристаллической присадки в отработанном масле за счет трибоактивируемой адсорбции в процессе динамического контакта коррелирует со снижением и последующей стабилизацией коэффициента трения пары сталь-сталь

Novel integrated tunable laser using filtered feedback for simple and very fast tuning

We present a novel integrated tunable laser based on filtered feedback, which combines a simple tuning method with ns switching speed

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible

Integrated filtered-feedback tunable laser with enhanced control of feedback phase

Recently we presented a novel discretely tunable laser that consists of a Fabry-Perot laser which was forced to operate in single-mode condition by applying on-chip filtered feedback. The laser switches extremely fast (3 ns) and requires simple on/off control currents to switch the wavelength. In these first devices it was not possible to control the phase of the feedback light independently from the feedback intensity. In was solved by adding an extra electrode allowing us to control the phase separately. In this paper we present the new device and study the effect of the control ofthefeedbackphase in order to improve the performance ofthe original tunable laser concept

Integrated filtered-feedback tunable laser with enhanced control of feedback phase

Recently we presented a novel discretely tunable laser that consists of a Fabry-Perot laser which was forced to operate in single-mode condition by applying on-chip filtered feedback. The laser switches extremely fast (3 ns) and requires simple on/off control currents to switch the wavelength. In these first devices it was not possible to control the phase of the feedback light independently from the feedback intensity. In was solved by adding an extra electrode allowing us to control the phase separately. In this paper we present the new device and study the effect of the control ofthefeedbackphase in order to improve the performance ofthe original tunable laser concept

Generalizing the autonomous Kepler Ermakov system in a Riemannian space

We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov dynamical system to three dimensions using the sl(2,R) invariance of Noether symmetries and determine all three dimensional autonomous Hamiltonian Kepler Ermakov dynamical systems which are Liouville integrable via Noether symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in a Riemannian space which admits a gradient homothetic vector by the requirements (a) that it admits a first integral (the Riemannian Ermakov invariant) and (b) it has sl(2,R) invariance. We consider both the non-Hamiltonian and the Hamiltonian systems. In each case we compute the Riemannian Ermakov invariant and the equations defining the dynamical system. We apply the results in General Relativity and determine the autonomous Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman Robertson Walker spacetime. We consider a locally rotational symmetric (LRS) spacetime of class A and discuss two cosmological models. The first cosmological model consists of a scalar field with exponential potential and a perfect fluid with a stiff equation of state. The second cosmological model is the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both applications the gravitational field equations reduce to those of the generalized autonomous Riemannian Kepler Ermakov dynamical system which is Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page

Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered

Resonant enhancement of the jump rate in a double-well potential

We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate.Comment: Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figure

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries