Dynamical Casimir effect in a periodically changing domain: A dynamical systems approach

We study the problem of the behavior of a quantum massless scalar field in the space between two parallel infinite perfectly conducting plates, one of them stationary, the other moving periodically. We reformulate the physical problem into a problem about the asymptotic behavior of the iterates of a map of the circle, and then apply results from theory of dynamical systems to study the properties of the map. Many of the general mathematical properties of maps of the circle translate into properties of the field in the cavity. For example, we give a complete classification of the possible resonances in the system, and show that small enough perturbations do not destroy the resonances. We use some mathematical identities to give transparent physical interpretation of the processes of creation and amplification of the quantum field due to the motion of the boundary and to elucidate the similarities and the differences between the classical and quantum fields in domains with moving boundaries.Comment: 19 pages, 7 figure

Reaction-Diffusion Modeling ERK- and STAT-Interaction Dynamics

<p/> <p>The modeling of the dynamics of interaction between ERK and STAT signaling pathways in the cell needs to establish the biochemical diagram of the corresponding proteins interactions as well as the corresponding reaction-diffusion scheme. Starting from the verbal description available in the literature of the cross talk between the two pathways, a simple diagram of interaction between ERK and STAT5a proteins is chosen to write corresponding kinetic equations. The dynamics of interaction is modeled in a form of two-dimensional nonlinear dynamical system for ERK&#8212;and STAT5a &#8212;protein concentrations. Then the spatial modeling of the interaction is accomplished by introducing an appropriate diffusion-reaction scheme. The obtained system of partial differential equations is analyzed and it is argued that the possibility of Turing bifurcation is presented by loss of stability of the homogeneous steady state and forms dissipative structures in the ERK and STAT interaction process. In these terms, a possible scaffolding effect in the protein interaction is related to the process of stabilization and destabilization of the dissipative structures (pattern formation) inherent to the model of ERK and STAT cross talk.</p

Energy Dissipation in Fractal-Forced Flow

The rate of energy dissipation in solutions of the body-forced 3-d incompressible Navier-Stokes equations is rigorously estimated with a focus on its dependence on the nature of the driving force. For square integrable body forces the high Reynolds number (low viscosity) upper bound on the dissipation is independent of the viscosity, consistent with the existence of a conventional turbulent energy cascade. On the other hand when the body force is not square integrable, i.e., when the Fourier spectrum of the force decays sufficiently slowly at high wavenumbers, there is significant direct driving at a broad range of spatial scales. Then the upper limit for the dissipation rate may diverge at high Reynolds numbers, consistent with recent experimental and computational studies of "fractal-forced'' turbulence.Comment: 14 page

Qualitative Modelling of Quasi-homogeneous Effects in ERK and STAT Interaction Dynamics

On the basis of qualitative analysis of author's model published in previous paper, the stability and temporal behaviour of quasi-homogeneous distributions of ERK-protein concentrations are analyzed in terms of corresponding reaction-diffusion problem. The stable quasi-homogeneous distributions are treated as a dynamical basis of pathway compartmentalization. It is also shown, that a crowding effect exists in the form of loss of pathway stability. An experimentally verifiable issue for possible existence of protein scaffolding mechanism is derived on the basis of its qualitative correspondence with the pattern formation and molecular crowding effects inherent to the considered model. Moreover, it is demonstrated, that the predicted ERK and STAT pathway instability can be interpreted as traveling wave propagation of molecular concentration drop and jump from the nucleus membrane to the cell one and vice versa

Eustachian tube function test as a predictor of middle ear barotrauma

Background: Most of the cases of middle ear barotrauma in divers are due to the impassability of the Eustachian tube. The aim of our study is to compare the results of tympanometry and Valsalva part of Eustachian Tube Function test (ЕТF-test) with the ability of divers to compensate for the change in ambient pressure in a hyperbaric chamber. Material and methods: The study included 35 professional divers undergoing annual medical examination. For all subjects is measured first intratympanal pressure at rest, then after the maneuver of Valsalva with impedancemeter. Then a barofunction test (BFT) was performed to assess the diving fitness and the passability of the Eustachian tubes. It consists of divers compressing and decompressing in a hyperbaric chamber to a pressure of 2.2 ATA for 1 minute. Based on results from previous studies we are using a 20 DaPa cutoff point on the ETF test to predict Eustachian tube passability and a successful barofunction test. Results: In the current study 24 divers have ETF test results higher than 20 DaPa. 3 divers have ETF test values lower than 20 DaPa in both ears, but none of them displayed difficulties in the BFT. 8 divers have ETF values lower than 20 DaPa in one ear and higher than 20 DaPa in the other. 7 of the last group displayed difficulties with the BFT in the ear with poor ETF result. Conclusions: We consider that the ETF test can be used to assess diving fitness as a screening method before performing a BFT, as values above 20 DaPa guarantee Eustachian tube function sufficient for diving activities. Values of 20 DaPa and less are not a definite predictor of the BFT results. The results of the ETF test can also be used in the usual work of an otorhinolaryngologist to evaluate Eustachian function in cases of unilateral disease of middle ear

New Market Segmentation Knowledge in the Function of Bioeconomy Development in Serbia

Sustainability of companies in modern market conditions greately depends on the knowledge. In order to improve their business processes and satisfy the needs of their customers, managers have to rely on new marketing knowledge, especially in new sectors such as bioeconomy. The aim of this paper is to investigate potential added value to Serbian organic food market segmentation researches (belonging to preconditions of further bioeconomy development) when implementing new marketing knowledge – food-related lifestyle market segmentation and scales’ testings. The results point out to adventurous consumers as the most important current and future market for organic food. Besides being the most educated (what was already established for consumers accepting organic food well in previous domestic researches), it is the first time that consumers accepting organic food in larger extent are brought in connection to their inclusion of the whole family in the preparation of meals and acceptance of novelties in cooking. It is also the first time to identify that there is a segment in domestic conditions for which price is not the greatest obstacle for increasing organic food consumption. That can be of the great importance for all actors (both national and foreign) operating at domestic food market