Lorentzian Equations Research Articles

Effects of self- and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators

We describe spontaneous symmetry breaking in the powers of two optical modes coupled into a ring resonator, using a pair of coupled Lorentzian equations, featuring tunable self- and cross-phase modulation terms. We investigate a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self-/cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalised description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.

Grain colonization by fumonisin-producing Fusarium spp. and fumonisin synthesis in South African commercial maize in relation to prevailing weather conditions

Fumonisins are mycotoxins produced primarily by Fusarium verticillioides and F. proliferatum on maize. These mycotoxins are secondary, carcinogenic metabolites with a worldwide distribution. This study was performed to evaluate the relationship between weather variables, the colonization of grain by F. verticillioides and resultant fumonisin contamination. Grain colonization by Fusarium spp. was determined using quantitative real-time PCR (qPCR) and contamination with fumonisins using HPLC analysis. Results indicated high natural infection by fumonisin-producing Fusarium spp. and fumonisin concentrations in warmer production areas such as Northern Cape, North West and Free State Provinces. Site-specific weather data, including temperature, radiation, humidity, rainfall and evapo-transpiration were provided by the ARC-Institute for Soil Water and Climate's meteorology office. Stepwise multiple regression analysis selected the variables mean maximum temperature and mean minimum humidity (days 1–14 post-silking) as having significant relationships with colonization of maize kernels by fumonisin-producing Fusarium spp.. Further relationships were calculated using the non-linear, 3-dimensional Lorentzian equation (Sigmaplot 10.0). The optimum temperature for colonization of maize by Fusarium spp. were 28.97, 32.14 and 30.40 °C and the optimum minimum humidities were calculated at 27.29, 31.86 and 29.74% respectively over the three recorded seasons. The application of correlation analysis and stepdown multiple regression analysis on sequential means of weather data and the inclusion of observed fungal biomass as a variable, suggested two phases in the development of fumonisins in maize kernels i.e. colonization of maize tissues during the early post-silking stage, followed by fumonisin production during the dough stage of grain fill. Based on this statistical model it would appear that fumonisin production by a specific biomass of fumonisin producing Fusarium spp. on grain was influenced largely by temperature and less so by rainfall. Optimum fumonisin concentrations were obtained with fungal biomasses of 39.94 pg during 2007, 47.65 pg during 2008 and 90.69 pg during 2009. Optimum temperatures for fumonisin production were 30.33, 31.12 and 29.80 °C for 2007–2009, respectively.Although these statistical models were not consistent over seasons with regard to actual prediction values, they were consistent regarding time of fungal infection and fumonisin production. It is evident that additional driving variables need to be identified.

Theory for spiralling ions for 2D FT-ICR and comparison with precessing magnetization vectors in 2D NMR.

Two-dimensional (2D) Fourier transform ion cyclotron resonance (FT-ICR) offers an approach to mass spectrometry (MS) that pursuits similar objectives as MS/MS experiments. While the latter must focus on one ion species at a time, 2D FT ICR can examine all possible correlations due to ion fragmentation in a single experiment: correlations between precursors, charged and neutral fragments. We revisited the original 2D FT-ICR experiment that has hitherto fallen short of stimulating significant analytical applications, probably because it is technically demanding. These shortcomings can now be overcome by improved FT-ICR instrumentation and computer hard- and software. We seek to achieve a better understanding of the intricacies of the behavior of ions during a basic two-dimensional ICR sequence comprising three simple monochromatic pulses. Through simulations based on Lorentzian equations, we have mapped the ion trajectories for different pulse durations and phases.

Effects of dilution with PMMA and network formation on fluorescence from benzimidazolylphenylenes linked to PMMA network

AbstractN,N′‐5‐(2‐benzimidazolyl)‐1,3‐phenylenebis(methacrylamide) (BIPBMA) was synthesized and copolymerized with methyl methacrylate (MMA) by changing feed BIPBMA/MMA molar ratio. The swelling experiments suggest that these cross‐linked copolymers (c‐copolymers) have a polymer network structure. To compare with c‐copolymers, synthesized 3‐(2‐benzimidazolyl) phenylmethacrylamide (BIPMA) was copolymerized with MMA by changing feed BIPMA/MMA molar ratio. These linear copolymers (l‐copolymers) were dissolved in N,N‐dimethylacetamide (DMA). The fluorescence spectra of c‐copolymers were well fitted by trial‐and‐error contraction with sums of five or less of Lorentzian equations. The fluorescence spectra of l‐copolymers were so distributed that only the initial peak was fitted to a single Lorentzian equation. The fluorescence spectra of BIPBMA/DMA solutions with various concentrations were also fitted to sums of five or less of Lorentzian equations. The fitted coefficients were used to quantify dilution effect. The fluorescence intensity of c‐copolymers is higher than that of l‐copolymers in a same chromophore concentration. A relation between the intensity and the chromophore concentration shows a concentration quenching owing to chromophore aggregating for c‐copolymer, l‐copolymer, and the solution. A critical concentration point before which the intensity increases appeared in the plots of intensity against concentration for the c‐copolymer and the solution. The critical point of the c‐copolymer is higher than that of the solution and that of the l‐copolymer (if observed). This suggests that the network formation and the dilution break up the chromophore aggregates. The fluorescence spectra of c‐copolymers (1/200) adjusted by varying AIBN concentrations suggest that the fluorescence is independent of the extent of cross‐linking. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Ruch unieruchomiony

This article discusses the problem of movement. The meaning of the term “movement” has undergone more changes in the course of history than any other term. The main change has been the immobilizing of movement. To show this, the author briefly presents the vicissitudes of its development from antiquity to the present. The relation between force and movement is also considered. In this matter the author follows the approach of Fr. John Dorda SJ, who proves that forces are not efficient causes, but rather formal causes. The fields of forces do not influence movement generally, but only its shape and trajectory. To illustrate this, four cases are presented and the Lorentzian equation is adduced. The problem of the ontological status of movement has been discussed at some length. It is argued that movement cannot be reduced to geometrical relations alone.

Study of crystalline orientation in drawn ultra‐high–molecular weight polyethylene films

AbstractA wide‐angle x‐ray diffraction (WAXD) study of the development of molecular orientation in the crystalline phase of ultra‐high–molecular weight polyethylene films prepared by the gelation–crystallization method is presented. WAXD scans of the undrawn films show that the lamellae are oriented in the plane of the films. Upon drawing at 130°C, the orientation of the molecular chains changes from the direction normal to the film surface (ND) to the elongation direction. The decrease of the 200/020 intensity ratio at low draw ration (λ <10) indicates that double orientation develops during the transformation from the lamellar to the fibrillar morphology, with the a‐axis oriented parallel to ND. The orientation distributions of the 110, 200, 020, and 002 planes of the orthorhombic unit cell of polyethylene were studied and characterized by the coefficients of a Legendre polynomial series. At a draw ratio of 4.5, the second‐order coefficient, 〈P2(cos χ〉, already gets close to its limiting value, but it is shown that higher order coefficients of the polynomial series can be used to describe the evolution of the orentation, even up to λ = 50. The coefficients relative to the molecular chain orientation, 〈Pn(cos χ)〉c, can be calculated from different crystalline reflections. Curve‐fitting calculations were made in order to improve the correlation between the results obtained from the orientation distribution of the 110, 020, and 002 planes. A Person VII function was found to give a better fit of the experimental curves than Gaussian or Lorentzian equations. © 1993 John Wiley & Sons, Inc.

Restructuring of the atomic condensed state under conditions of an intense external field

This paper examines the restructuring of the collective behavior of atoms in a condensed medium during intense external loads. To describe the atomic states, the ensemble of potential contours is used, the distribution law of which is given by the synergetic potential. The parameter of restructuring of the atomic system is determined by the correlation of the variation in the potential contour at macroscopic distances. The collective excitations, possessing critical behavior, reduce to the transverse acoustic branch of phonons. Using quantum field theory the equations of motion are determined for the parameter of coherent restructuring of the potential contour and the gauge field. Superconductivity and helium 4 superfluidity are studied in an analysis of the mutually dependent behavior of the atomic subsystem and the collective mode, carried out in the framework of the synergetic approach by determining the system of Lorentzian equations for the time evolution for the share of lattice sites falling into the restructured potential contour, the shear deformation of the medium as a result of atomic restructuring, and the stress field coupled to it.

Membrane current noise in toad retinal rods exposed to low external calcium.

Outer segment membrane current of single rod photoreceptors from toad retina was recorded with a suction electrode, and extracellular calcium concentration was manipulated by transferring the recorded cell from one pool of saline to another or by locally perfusing the outer segment. The large increase in dark current that resulted from exposure to low-calcium saline was accompanied by an increase in dark noise in the band 1-800 Hz. This noise was suppressed by bright light, and its power spectrum could be described by a single Lorentzian equation with average corner frequency of 40.1 +/- 9.5 Hz (mean +/- S.D., n = 11). In low-calcium saline, saturating flash responses were often followed by a transient increase in the dark current lasting 30-100 s. During this rebound period of increased dark current, increased dark noise similar to that described in 2 was observed. The power spectrum of this noise was also fitted by a single Lorentzian equation, with corner frequency averaging 29.7 +/- 6.6 Hz (mean +/- S.D., n = 27). To examine the possible role of intracellular voltage fluctuations in generating the noise, suction electrodes were filled with calcium-free saline and recordings were made from outer segments of rods attached to pieces of retina. In this recording configuration, the electrical coupling among the rods in the piece should attenuate voltage fluctuations associated with the post-light rebound period of increased dark current. In this situation, the rebound increase in dark current was still observed, but the noise was reduced or absent. Using the same recording configuration, isolated rods showed pronounced noise during the rebound. The result in 4 suggests that the noise resulted from fluctuations in intracellular voltage, not directly from fluctuations in the light-sensitive channels. In this view, the corner frequency of the noise power spectrum probably reflects the membrane time constant of the isolated rod.

Calcium-activated and voltage-dependent potassium conductances in clonal pituitary cells

Voltage clamp recordings of GH3/B6 pituitary cells reveal the presence of non linear steady state membrane properties at the level of the resting potential (about −41 mV). Clamping the cells to potentials more depolarized than −60 mV is associated with a potential dependent increase in membrane conductance and membrane current variance. Tetra-ethylammonium (TEA), Cobalt (Co 2+) and methoxy-verapamil (D-600) each attenuate these potential-dependent changes. Spectral analysis of membrane current fluctuations shows that power spectral densities calculated for fluctuations occuring over the − 70 to − 40 mV range declin≐ monotonically as a function of frequency, while spectra derived from fluctuations obtained over the − 20 mV to 0 mV range decline as the square of frequency and are usually well fitted by a single Lorentzian equation. The half-power frequency of these spectra varies from 45 to 65 Hz. If we assume that the activities of two-state (open-closed) ion channels underlie the electrical behaviour of the membrane at the resting potential and at more depolarized levels, then the results suggests the presence of K + ion channels whose activation depends both on potential and Ca 2+ ions. These K + ion channels have estimated electrical properties (conductance : 15 ps ; duration : 3 msec) similar to those present in other excitable membranes.

On transformational properties of dynamical characteristics of vector fields

It is shown that Lorentzian equations of motion of test particles in a vector field are invariant under the special transformations of dynamical characteristics of this field.