Covering space for monotonic homotopy of trajectories of control systems

This paper considers monotonic (or causal) homotopy between trajectories of control systems. The main result is the construction of an analogue of the simply connected covering space. The constructed covering Γ(Σ,x) has the structure of a manifold and satisfies the property that two trajectories are monotonic homotopic if and only if the end points of their liftings coincide.     

First-principles study on the electronic structures of iron phthalocyanine monolayer

The electronic band structure and magnetic properties of iron phthalocyanine (FePc) monolayer were investigated by using the first-principles all-electron full-potential linearized augmented plane wave energy band method. It is found that the ferromagnetic FePc monolayer is energetically more stable than the paramagnetic one. The exchange interaction, which splits the majority and minority bands, influences strongly on the electronic structure near the Fermi level (E_F). Magnetic moment of the central Fe atom is calculated to 1.95 μ_B. The range of the positive polarization of Fe site is larger in the out-of-plane than in the in-plane direction. The FePc ligand remains paramagnetic. The presence of states at E_F indicates the metallic character of FePc monolayer both for the paramagnetic and ferromagnetic states. However, the large density of states at E_F of the majority spins in the ferromagnetic state is expected to cause a phase transition to insulating antiferromagnetic state from the metallic ferromagnetic one.     

Glassy dynamics of polymers confined to nanoporous glasses revealed by relaxational and scattering experiments

The glassy dynamics of poly(propylene glycol) (PPG) and poly(dimethyl siloxane) (PDMS) confined to a nanoporous host system revealed by dielectric spectroscopy, temperature-modulated DSC and neutron scattering is compared. For both systems the relaxation rates estimated from dielectric spectroscopy and temperature-modulated DSC agree quantitatively indicating that both experiments sense the glass transition. For PPG the segmental dynamics is determined by a counterbalance of adsorption and confinement effect. The former results form an interaction of the confined macromolecules with the internal surfaces. A confinement effect originates from an inherent length scale on which the underlying molecular motions take place. The increment of the specific-heat capacity at the glass transition vanishes at a finite length scale of 1.8 nm. Both results support the conception that a characteristic length scale is relevant for glassy dynamics. For PDMS only a confinement effect is observed which is much stronger than that for PPG. Down to a pore size of 7.5 nm, the temperature dependence of the relaxation times follows the Vogel-Fulcher-Tammann dependence. At a pore size of 5 nm this changes to an Arrhenius-like behaviour with a low activation energy. At the same pore size vanishes for PDMS. Quasielastic neutron scattering experiments reveal that also the diffusive character of the relevant molecular motions --found to be characteristic above the glass transition-- seems to disappear at this length scale. These results gives further strong support that the glass transition has to be characterised by an inherent length scale of the relevant molecular motions.Received: 1 January 2003, Published online: 14 October 2003PACS: 64.70.Pf Glass transitions - 77.22.Gm Dielectric loss and relaxation - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Optical activity of microemulsion induced by electric field and its tunable behaviors

It has been shown that optical activity can occur in microemulsion under external electric field and rotation angle can also be tuned by the electric field. A set of microemulsions (water/Span80/transformer oil) with different water concentration were prepared and their optical activity was measured with the changes of applied electric field and θ, the angle between the electric vector of the incident linearly polarized light and the external electric field, using an automatic polarimeter. The experiments indicate that when none of the external electric field, water concentration and θ are zero, there is optical activity in microemulsions. For a given concentration, rotation angle ψ increases with electric field, and it firstly increases, passes through a maximum at C = C0,then monotonically decreases as C increases when electric field keeps constant. The relationship between the rotation angle and θ is also obtained. It is thought that the electric field-induced destroy of spatial symmetry of microemulsion is responsible for the optical activity of microemulsion.     

Evolution of three-dimensional coherent structures in compressible axisymmetric jet

A high order difference scheme is used to simulate the spatially developing compressible axisymmetric jet. The results show that the Kelvin-Helmholtz instability appears first when the jet loses its stability, and then with development of jet the increase in nonlinear effects leads to the secondary instability and the formation of the streamwise vortices. The evolution of the three-dimensional coherent structure is presented. The computed results verify that in axisymmetric jet the secondary instability and formation of the streamwise vortices are the important physical mechanism of enhancing the flow mixing and transition occurring.     

Finite time blowup of the <Emphasis Type="Italic">n</Emphasis>-harmonic flow on <Emphasis Type="Italic">n</Emphasis>-manifolds

In this paper, we generalize the no-neck result of Qing and Tian (in Commun Pure Appl Math 50:295–310, 1997) to show that there is no neck during blowing up for the n-harmonic flow as \(t\rightarrow \infty \). As an application of the no-neck result, we settle a conjecture of Hungerbühler (in Ann Scuola Norm Sup Pisa Cl Sci 4:593–631, 1997) by constructing an example to show that the n-harmonic map flow on an n-dimensional Riemannian manifold blows up in finite time for \(n\ge 3\).     

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona–Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.     

Maximization of the total population in a reaction–diffusion model with logistic growth

This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the effect of spatial heterogeneity on the total population of a biological species at a steady state, using a reaction–diffusion logistic model. Our objective is to maximize the total population when resources are distributed in the habitat to control the intrinsic growth rate, but the total amount of resources is limited. It is shown that under some conditions, any local maximizer must be of “bang–bang” type, which gives a partial answer to the conjecture addressed by Ding et al. (Nonlinear Anal Real World Appl 11(2):688–704, 2010). To this purpose, we compute the first and second variations of the total population. When the growth rate is not of bang–bang type, it is shown in some cases that the first variation becomes nonzero and hence the resource distribution is not a local maximizer. When the first variation becomes zero, we prove that the second variation is positive. These results implies that the bang–bang property is essential for the maximization of total population.     

Scalar curvature rigidity and Ricci DeTurck flow on perturbations of Euclidean space

We prove a rigidity result for non-negative scalar curvature perturbations of the Euclidean metric on \(\mathbb {R}^n\), which may be regarded as a weak version of the rigidity statement of the positive mass theorem. We prove our result by analyzing long time solutions of Ricci DeTurck flow. As a byproduct in doing so, we extend known \(L^p\) bounds and decay rates for Ricci DeTurck flow and prove regularity of the flow at the initial data.     

Fast Laplace Transforms for the Exponential Radon Transform

The Fourier slice theorem for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with algorithms for the unequally spaced fast Laplace transform to construct fast and accurate methods for computing both the forward exponential Radon transform and the corresponding back-projection operator.