Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self-excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.     

The Theory of Kairons

In relativistic quantum mechanics wave functions of particles satisfy field equations that have initial data on a space-like hypersurface. We propose a dual field theory of “wavicles” that have their initial data on a time-like worldline. Propagation of such fields is superluminal, even though the Hilbert space of the solutions carries a unitary representation of the Poincaré group of mass zero. We call the objects described by these field equations “Kairons”. The paper builds the field equations in a general relativistic framework, allowing for a torsion. Kairon fields are section of a vector bundle over space-time. The bundle has infinite-dimensional fibres.     

Ultrafast dynamics of metal complexes of tetrasulphonated phthalocyanines

A promising material in medicine, electronics, optoelectronics, electrochemistry, catalysis, and photophysics, tetrasulphonated aluminum phthalocyanine (AlPcS(4)), is investigated by means of steady-state and time-resolved pump-probe spectroscopies. Absorption and steady-state fluorescence spectroscopy indicate that AlPcS(4) is essentially monomeric. Spectrally resolved pump-probe data are recorded on time scales ranging from femtoseconds to nanoseconds. The nature of these fast processes and pathways of the competing relaxation processes from the initially excited electronic states in aqueous and organic (dimethyl sulfoxide) solutions are discussed. The decays and bleaching recovery have been fitted in the ultrafast window (0-10 ps) and later time window extending to nanoseconds (0-1 ns). While the excited-state dynamics have been found to be sensitive to the solvent environment, we were able to show that the fast dynamics is described by three time constants in the ranges of 115-500 fs, 2-25 ps, and 150-500 ps. We were able to ascribe these three time constants to different processes. The shortest time constants have been assigned to vibrational wavepacket dynamics. The few picosecond components have been assigned to vibrational relaxation in the excited electronic states. Finally, the 150-500 ps components represent the decay from S(1) to the ground state. The experimental and theoretical treatment proposed in this paper provides a basis for a substantial revision of the commonly accepted interpretation of the Soret transition (B transition) that exists in the literature.     

Construction of a porous homochiral coordination polymer with two types of Cu(n)I(n) alternating units linked by quinine: a solvothermal and a mechanochemical approach

The polymer network: The reaction of quinine (QN) with CuI under solvothermal, as well as liquid-assisted grinding, conditions afforded a unique 1D homochiral coordination polymer {[Cu(4)(μ(3)-I)(4)(QN)(2)][Cu(3)(μ(3)-I)(2)(μ(2)-I)(QN)(2)](2)}(n), containing both triangular Cu(3)I(3) and cubane Cu(4)I(4) clusters as connecting nodes (see scheme). Van der Waals interactions between the adjacent 1D polymer chains lead to an extended quasi-honeycomb homochiral pillared 3D network with solvent-free 1D channels.     

Numerical simulation of two-stage combustion in SI engine with prechamber

Burning lean mixture in spark ignition (SI) engine leads to decrease in temperature of combustion process and is one of the methods of limiting nitric oxide emission and increasing the engine efficiency. The two-stage combustion system of stratified mixture (engine with prechamber) can be an effective method of lean mixture combustion. The paper presents the results of three-dimensional modeling of fuel mixture preparation and combustion in SI engine with sectional combustion chamber powered by liquefied fuel. Three dimensional modeling was performed in KIVA-3V code. The modeling results were compared with results obtained from the analysis of experimental measurements of two-stage combustion test engine operating at the Institute of Internal Combustion Engines and Control Engineering (Czestochowa University of Technology). The performed simulations of the combustion process provided data concerning the spatial and temporal distributions of turbulent kinetic energy, pressure, temperature and nitric oxides concentration in the combustion chambers of the engine. The engine model with two-stage combustion system properly represents the real processes which occur in the combustion chambers of the test engine. Pressure and temperature courses in function of CA obtained from the experiment and modeling were in good qualitative and quantitative consistence. Comparison of modeled and measured nitric oxide emissions revealed relatively significant discrepancies. In case of λ = 1.4, the measured values of NO_x concentration were 1.75 times higher than the modeled values. In case of λ = 2.0, the modeled and measured values were close to each other and were within the range of measurement error.     

Application of semi-permeable membrane dialysis/ion trap mass spectrometry technique to determine polybrominated diphenyl ethers and polychlorinated biphenyls in milk fat

Polychlorinated biphenyls (PCBs) and polybrominated diphenyl ethers (PBDEs) are hazardous food contaminants, their maximum legally allowable levels in food and environment are in the low pg g⁻¹ range. Therefore some highly selective and sensitive analytical methods must be used to determine them. The 96/23/EC Directive implemented by EC Decision of 12 August 2002 requires recovery rate of an analyte at a concentration below 1 ng g⁻¹ within the 50–120% range at relative standard deviation (RSD) as low as possible.     

Bands of Localized Electromagnetic Waves in 3D Random Media

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed electric dipoles. Spectra of certain random matrices are investigated and the possibility of appearance of the continuous band of localized waves emerging in the limit of an infinite medium is indicated. It is shown that localization could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated.     

Fundamental Geometric Structures for the Dirac Equation in General Relativity

We present an axiomatic approach to Dirac's equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory.