3D Parameter Space Research Articles

Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping

In this communication, the two-well Duffing oscillator with non-linear damping term proportional to the power of velocity is considered. We mainly focus our attention on how the damping exponent affects the global dynamical behaviour of the oscillator. In particular, we obtain analytically the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique and compare the results with the computational results. We also identify the major route to chaos and the regions of the 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to the various types of asymptotic dynamics under linear (viscous or friction like) and nonlinear (drag like) damping. We also attempt to analyze how the basins of attraction patterns change with the introduction of nonlinear damping. We also present our analysis for the physically less-interesting cases where damping is proportional to the 3rd and 4th power of velocity for the sake of generalizing our findings and establishing firm conclusion.

A universal ultraviolet-optical colour-colour-magnitude relation of galaxies★

Although the optical colour-magnitude diagram of galaxies allows one to select red sequence objects, neither can it be used for galaxy classification without additional observational data such as spectra or high-resolution images, nor to identify blue galaxies at unknown redshifts. We show that adding the near ultraviolet colour to the optical CMD reveals a tight relation in the three-dimensional colour-colour-magnitude space smoothly continuing from the "blue cloud" to the "red sequence". We found that 98 per cent of 225,000 low-redshift (Z<0.27) galaxies follow a smooth surface g-r=F(M,NUV-r) with a standard deviation of 0.03-0.07 mag making it the tightest known galaxy photometric relation. There is a strong correlation between morphological types and integrated NUV-r colours. Rare galaxy classes such as E+A or tidally stripped systems become outliers that occupy distinct regions in the 3D parameter space. Using stellar population models for galaxies with different SFHs, we show that (a) the (NUV-r, g-r) distribution is formed by objects having constant and exponentially declining SFR with different characteristic timescales; (b) colour evolution for exponentially declining models goes along the relation suggesting its weak evolution up-to a redshift of 0.9; (c) galaxies with truncated SFHs have very short transition phase offset from the relation thus explaining the rareness of E+A galaxies. This relation can be used as a powerful galaxy classification tool when morphology remains unresolved. Its mathematical consequence is the photometric redshift estimates from 3 broad-band photometric points. This approach works better than most existing photometric redshift techniques applied to multi-colour datasets. Therefore, the relation can be used as an efficient selection technique for galaxies at intermediate redshifts (0.3<Z<0.8) using optical imaging surveys.

Kinetics of 1H→ 13C NMR cross-polarization in polymorphs and solvates of the antipsychotic drug olanzapine

The 1H→ 13C NMR cross-polarization (CP) was studied under magic-angle spinning at 7.5 kHz in various crystal forms of the antipsychotic drug olanzapine: two polymorphs (metastable I and stable II) and eight solvates containing organic solvent and water molecules. The CP kinetics followed the non-classical I–I ⁎-S model, in which CP begins in a spin cluster of proximate abundant spins I * and rare spins S, then is controlled by spin diffusion of the abundant spins I from bulk to the I * spins of the spin cluster and finally is governed by spin-lattice relaxation of the abundant spins in the rotating frame. The corresponding CP kinetics parameters were determined and analyzed. It was demonstrated that the, λ and T df values (the CP time constant, the cluster composition parameter and the 1H spin-diffusion constant, respectively) were very useful to discriminate the functional groups, especially in the 3D parameter space. In order to conveniently analyze the large amount (175) of the collected CP parameters, the number of the observed variables was reduced using the principal component (PC) analysis. The 2D plot of PC2 vs. PC1 showed adequate separation of the CH 3, CH 2, CH and C cases (C stands for carbons without adjacent hydrogens). It was demonstrated that those cases were located along the PC1 axis in the order of increasing 1H– 13C dipolar couplings: C<CH 3<CH<CH 2. Our study showed the I–I *-S model at work and established ranges of its parameters for various functional groups.

Bifurcation and dual-parameter characteristic of the coupled dynamos system

Based on the comprehensive analysis of the basic dynamic characters of the coupled dynamos system, we have calculated the Lyapunov exponent spectra, bifurcation diagrams and so on, and discussed the chaotic bifurcation and mutative characteristic thoroughly in the periodic windows of the system, and the dual-parameter characteristic is also analyzed. It is found that a boundary line is absent in period-doubling bifurcations and a complicated bifurcation structure appears in 2D parameter space, the influences of two control parameters to the dynamic behavior are different.

Abelian Manna model on two fractal lattices

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension d(g)=ln 3/ln 2, with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2-τ)=d(w) generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where d(w)=2. Furthermore, we observe that the lattice dimension d(g), the fractal dimension of the random walk on the lattice d(w), and the critical exponent D form a plane in three-dimensional parameter space, i.e., they obey the linear relationship D=0.632(3)d(g)+0.98(1)d(w)-0.49(3).

More power to X‐rays: New developments in X‐ray spectroscopy

AbstractRecent developments in X‐ray spectroscopy in the last decade are reviewed. A specific emphasis is placed on displaying the strong natural connection between X‐ray spectroscopy and materials science. Brief explanations of several X‐ray spectroscopic methods are given. X‐ray spectroscopic instruments such as table‐top X‐ray sources are discussed in detail, whereas those employing synchrotron and other sources are briefly addressed. The spectroscopic methods and results from materials investigations are reviewed according to their positions in a 3D parameter space of time, length, and energy. New experimental measurements on atoms, molecules, nanomaterials, and bulk materials that include insulators, semiconductors, metals and magnetic materials using both static and time‐resolved methods are reviewed.

2D to 3D rectangular waveguide filter designs from linear iterated prediction space mapping optimization

AbstractIn this article, an optimization procedure is described to align electromagnetic (EM) three‐dimensional (3D) models with two‐dimensional (2D) models for the design of RF/microwave circuits. The optimization procedure is realized from a modified standard space mapping (SM) approach. The mapping function between the 2D and 3D parameter spaces is directly obtained from a linear iterated prediction method, which reduces the computational cost and also avoids inverse transformations. The linear iterated prediction 2D to 3D SM optimization of evanescent rectangular waveguide bandpass filters with inductive posts for the 2D models and non‐inductive posts for the 3D models illustrate the advantages and the challenges of this approach. The proposed method is simple to be implemented, it requires a reduced computational cost and it can be useful for CAD environment with 2D and 3D circuit structure electromagnetic (EM) analysis. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1979–1983, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24459

Scaling relations and the fundamental line of the local group dwarf galaxies

We study the scaling relations between global properties of dwarf galaxies in the local group. In addition to quantifying the correlations between pairs of variables, we explore the 'shape' of the distribution of galaxies in log parameter space using standardized principal component analysis, the analysis is performed first in the 3D structural parameter space of stellar mass M * , internal velocity V and characteristic radius R* (or surface brightness μ*). It is then extended to a 4D space that includes a stellar population parameter such as metallicity Z or star formation rate M * . We find that the local group dwarfs basically define a one-parameter 'fundamental line' (FL), primarily driven by stellar mass, M * . A more detailed inspection reveals differences between the star formation properties of dwarf irregulars (dl's) and dwarf ellipticals (dE's), beyond the tendency of the latter to be more massive. In particular, the metallicities of dl's are typically lower by a factor of 3 at a given M * and they grow faster with increasing M * , showing a tighter FL in the 4D space for the dE's. The structural scaling relations of dl's resemble those of the more massive spirals, but the dl's have lower star formation rates for a given M. which also grow faster with increasing M * . On the other hand, the FL of the dE's departs from the fundamental plane of bigger ellipticals. While the one-parameter nature of the FL and the associated slopes of the scaling relations are consistent with the general predictions of supernova feedback from Dekel & Woo, the differences between the FL's of the dE's and the dl's remain a challenge and should serve as a guide for the secondary physical processes responsible for these two types.

An Interactive 3D Graphics Modeler Based on Simulated Human Immune System

We propose an intuitive computer graphics authoring method based on interactive evolutionary computation (IEC). Our previous systems employed genetic algorithm (GA) and mainly focused on rapid exploration of a single optimum 3D graphics model. The proposed method adopts a different computation strategy called immune algorithm (IA) to ease the creation of varied 3D models even if a user doesn’t have any specific idea of final 3D products. Because artistic work like graphics design needs a process to diversify the user’s imagery, a tool that allows the user to select his/her preferred ones from a broad range of possible design solutions is particularly desired. IA enables the user to effectively explore a wealth of solutions in a huge 3D parametric space by using its essential mechanisms such as antibody formation and self-regulating function. We conducted an experiment to verify the effectiveness of the proposed method. The results show that the proposed method helps the user to easily generating wide variety of 3D graphics models.

Spherically Symmetric Accretion onto a Black Hole at the Center of a Young Stellar Cluster

We present a self-consistent, bimodal stationary solution for spherically symmetric flows driven by young massive stellar clusters with a central supermassive black hole. We demonstrate that the hydrodynamic regime of the flow depends on the location of the cluster in the 3D (star cluster mechanical luminosity - BH mass - star cluster radius) parameter space. We show that a threshold mechanical luminosity (L_crit) separates clusters which evolve in the BH dominated regime frome those whose internal structure is strongly affected by the radiative cooling. In the first case(below the threshold energy) gravity of the BH separates the flow into two distinct zones: the inner accretion zone and the outer zone where the star cluster wind is formed. In the second case (above the critical luminosity), catastrophic cooling sets in inside the cluster. In this case the injected plasma becomes thermally unstable that inhibits a complete stationary solution. We compared the calculated accretion rates and the BH luminosities with those predicted by the classic Bondi accretion theory and found that Bondi's theory is in good agreement with our results in the case of low mass clusters. However, it substantially underestimates the accretion rates and BH luminosities if the star cluster mechanical luminosity, L_sc, approaches the threshold value (L_sc > 0.1 L_crit).

An extended advancing front technique for closed surfaces mesh generation

AbstractAn extended advancing front technique (AFT) with shift operations and Riemann metric named as shifting‐AFT is presented for finite element mesh generation on 3D surfaces, especially 3D closed surfaces. Riemann metric is used to govern the size and shape of the triangles in the parametric space. The shift operators are employed to insert a floating space between real space and parametric space during the 2D parametric space mesh generation. In the previous work of closed surface mesh generation, the virtual boundaries are adopted when mapping the closed surfaces into 2D open parametric domains. However, it may cause the mesh quality‐worsening problem. In order to overcome this problem, the AFT kernel is combined with the shift operator in this paper. The shifting‐AFT can generate high‐quality meshes and guarantee convergence in both open and closed surfaces. For the shifting‐AFT, it is not necessary to introduce virtual boundaries while meshing a closed surface; hence, the boundary discretization procedure is largely simplified, and moreover, better‐shaped triangles will be generated because there are no additional interior constraints yielded by virtual boundaries. Comparing with direct methods, the shifting‐AFT avoids costly and unstable 3D geometrical computations in the real space. Some examples presented in this paper have demonstrated the advantages of shift‐AFT in 3D surface mesh generation, especially for the closed surfaces. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Registration of cortical surfaces using sulcal landmarks for group analysis of MEG data

We present a method to register individual cortical surfaces to a surface-based brain atlas or canonical template using labeled sulcal curves as landmark constraints. To map one cortex smoothly onto another, we minimize a thin-plate spline energy defined on the surface by solving the associated partial differential equations (PDEs). By using covariant derivatives in solving these PDEs, we compute the bending energy with respect to the intrinsic geometry of the 3D surface rather than evaluating it in the flattened metric of the 2D parameter space. This covariant approach greatly reduces the confounding effects of the surface parameterization on the resulting registration.

Experimental identification of chaotic fibers

In a 2D parameter space, by using nine experimental time series of a Chua’s circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis.

Some remarks on a singular reaction-diffusion system arising in predator-prey modeling

This note is dedicated to the question of global existence for solutions to a two component singular system of reaction-diffusion equations modeling predator-prey interactions in insular environments. Depending on a 2D parameter space, positive orbits of the underlying ODE system undergo interesting dynamics, e.g., finite time existence and global existence may coexist. These results are partially extended to the reaction-diffusion system in the case of identical diffusivities. Our analysis relies on an auxiliary non singular reaction-diffusion system whose solutions may or may not blow up in finite time. Numerical simulations illustrate our analysis, including a numerical evidence of spatio-temporal oscillations.

Multi-parametric bifurcations in a piecewise–linear discontinuous map

In this paper a one-dimensional piecewise linear map with discontinuous system function is investigated. This map actually represents the normal form of the discrete-time representation of many practical systems in the neighbourhood of the point of discontinuity. In the 3D parameter space of this system we detect an infinite number of co-dimension one bifurcation planes, which meet along an infinite number of co-dimension two bifurcation curves. Furthermore, these curves meet at a few co-dimension three bifurcation points. Therefore, the investigation of the complete structure of the 3D parameter space can be reduced to the investigation of these co-dimension three bifurcations, which turn out to be of a generic type. Tracking the influence of these bifurcations, we explain a broad spectrum of bifurcation scenarios (like period increment and period adding) which are observed under variation of one control parameter. Additionally, the bifurcation structures which are induced by so-called big bang bifurcations and can be observed by variation of two control parameters can be explained.

Method of trimming PDE surfaces

A method for trimming surfaces generated as solutions to partial differential equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order elliptic PDE on the parameter space. The chosen elliptic PDE is solved analytically, even in the case of a very general complex trim, allowing the design process to be carried out interactively in real time. To demonstrate the capability for this technique we discuss a series of examples where trimmed PDE surfaces may be applicable.

Analysis of subharmonic oscillations in a ferroresonant circuit

Ferroresonance is a nonlinear oscillatory phenomenon that occurs in capacitively coupled transformers or reactors under certain conditions. In this paper, an averaging method is utilized to compute the domain in 2D parameter space where subharmonic (period-3) ferroresonant oscillations could persist. The accuracy of the analytical results is verified using numerical simulations and the power spectral density. It is shown that the proposed method yields a quick means to determine (i) the proximity to initiation of subharmonic resonance and (ii) the effect of core loss on the domains of subharmonic oscillations.

On multi-parametric bifurcations in a scalar piecewise-linear map

In this work a one-dimensional piecewise-linear map is considered. The areas in the parameter space corresponding to specific periodic orbits are determined. Based on these results it is shown that the structure of the 2D and 3D parameter spaces can be simply described using the concept of multi-parametric bifurcations. It is demonstrated that an infinite number of two-parametric bifurcation lines starts at the origin of the 3D parameter space. Along each of these lines an infinite number of bifurcation planes starts, whereas the origin represents a three-parametric bifurcation.

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

We studied the dynamic response and stochastic resonance of kinetic Ising spin system (ISS), subject to the joint external field of weak sinusoidal modulation and stochastic white-noise, through solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows the occurrence of characteristic stochastic resonance as well as nonequilibrium dynamic phase transition (NDPT) when the frequency and amplitude h0 of driving field, the temperature t of the system and noise intensity D attain a specific accordance in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to zero and unit dynamic order parameter. We also figured out the NDPT boundary surface of the system which separates the dynamic paramagnetic and dynamic ferromagnetic phase in the 3D parameter space of h0~t~D. An intriguing dynamical ferromagnetic phase with an intermediate order parameter at 0.66 was revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. Our primary result indicates that the intermediate order dynamical ferromagnetic phase is dynamic metastable in nature and owns a peculiar characteristic in its stability and response to external driving field when compared with fully order dynamic ferromagnetic phase.

VIRGO detector optimization for gravitational waves by inspiralling binaries

For future configurations, we study the relation between the abatement of the noise sources and the signal-to-noise ratio (SNR) for coalescing binaries. Our aim is not the proposition of a new design, but an indication of where in the bandwidth or for which noise source a noise reduction would be most efficient. We take VIRGO as the reference for our considerations, solely applicable to the inspiralling phase of a coalescing binary. Thus, only neutron stars and small black holes of a few solar masses are encompassed by our analysis. The contributions to the SNR given by final merge and quasi-normal ringing are neglected. It is identified that (i) the reduction in the mirror thermal noise band provides the highest gain for the SNR, when the VIRGO bandwidth is divided according to the dominant noises; (ii) there exists a specific frequency at which lies the largest potential increment in the SNR, and the enlargement of the bandwidth, where the noise is reduced, produces a shift of such an optimal frequency to higher values; (iii) the abatement of the pendulum thermal noise provides the largest, but modest, gain, when noise sources are considered separately. Our recent astrophysical analysis of event rates for neutron stars leads to a detection rate of one every 148 or 125 years for VIRGO and LIGO, respectively, while a recently proposed and improved, but still conservative, VIRGO configuration would provide an increase to 1.5 events per year. Instead, a bi-monthly event rate, similar to advanced LIGO, requires a 16 times gain. We analyse the 3D (pendulum, mirror, shot noises) parameter space showing how such a gain could be achieved.