Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the systemreservoir interaction. The formulae necessary for the higher order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the n-th order approximation are given. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.Comment: 34pages, no figur

Multivariate Topology Simplification

Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph

Effective mass overshoot in single degree of freedom mechanical systems with a particle damper

We study the response of a single degree of freedom mechanical system composed of a primary mass, M, a linear spring, a viscous damper and a particle damper. The particle damper consists in a prismatic enclosure of variable height that contains spherical grains (total mass m_p). Contrary to what it has been discussed in previous experimental and simulation studies, we show that, for small containers, the system does not approach the fully detuned mass limit in a monotonous way. Rather, the system increases its effective mass up and above M+m_p before reaching this expected limiting value (which is associated with the immobilization of the particles due to a very restrictive container). Moreover, we show that a similar effect appears in the tall container limit where the system reaches effective masses below the expected asymptotic value M. We present a discussion on the origin of these overshoot responses and the consequences for industrial applications.Comment: 16 pages, 6 figure

Indication of antiferromagnetic interaction between paramagnetic Co ions in the diluted magnetic semiconductor Zn1−x_{1-x}Cox_{x}O

The magnetic properties of Zn$_{1-x}$Co$_x$O ($x=0.07$ and 0.10) thin films, which were homo-epitaxially grown on a ZnO(0001) substrates with varying relatively high oxygen pressure, have been investigated using x-ray magnetic circular dichroism (XMCD) at Co $2p$ core-level absorption edge. The line shapes of the absorption spectra are the same in all the films and indicate that the Co$^{2+}$ ions substitute for the Zn sites. The magnetic-field and temperature dependences of the XMCD intensity are consistent with the magnetization measurements, indicating that except for Co there are no additional sources for the magnetic moment, and demonstrate the coexistence of paramagnetic and ferromagnetic components in the homo-epitaxial Zn$_{1-x}$Co$_{x}$O thin films, in contrast to the ferromagnetism in the hetero-epitaxial Zn$_{1-x}$Co$_{x}$O films studied previously. The analysis of the XMCD intensities using the Curie-Weiss law reveals the presence of antiferromagnetic interaction between the paramagnetic Co ions. Missing XMCD intensities and magnetization signals indicate that most of Co ions are non-magnetic probably because they are strongly coupled antiferromagnetically with each other. Annealing in a high vacuum reduces both the paramagnetic and ferromagnetic signals. We attribute the reductions to thermal diffusion and aggregation of Co ions with antiferromagnetic nanoclusters in Zn$_{1-x}$Co$_{x}$O.Comment: 21 pages, 7 figures, accepted for Physical Review

The role of spatial heterogeneity in the evolution of local and global infections of viruses

Viruses have two modes spread in a host body, one is to release infectious particles from infected cells (global infection) and the other is to infect directly from an infected cell to an adjacent cell (local infection). Since the mode of spread affects the evolution of life history traits, such as virulence, it is important to reveal what level of global and local infection is selected. Previous studies of the evolution of global and local infection have paid little attention to its dependency on the measures of spatial configuration. Here we show the evolutionarily stable proportion of global and local infection, and how it depends on the distribution of target cells. Using an epidemic model on a regular lattice, we consider the infection dynamics by pair approximation and check the evolutionarily stable strategy. We also conduct the Monte-Carlo simulation to observe evolutionary dynamics. We show that a higher local infection is selected as target cells become clustered. Surprisingly, the selected strategy depends not only on the degree of clustering but also the abundance of target cells per se

Cell-to-cell transmission promotes the emergence of double-drug resistance

The use of multiple antivirals in a single patient increases the risk of emergence of multidrug-resistant viruses, posing a public health challenge and limiting management options. Cell-to-cell viral transmission allows a pair of viruses that are each resistant to a single drug to persist for a prolonged period of passages although neither can survive alone under double-drug treatment. This pair should then persist until they accumulate a second mutation to generate resistance to both drugs. Accordingly, we here propose a hypothesis that viruses have a much higher probability of developing double-drug resistance when they are transmitted via a cell-to-cell mode than when they are transmitted via a cell-free mode through released virions. By using a stochastic model describing the changes in the frequencies of viral genotypes over successive infections, we analytically demonstrate that the emergence probability of double resistance is approximately the square of the number of viral genomes that establish infection times greater in cell-to-cell transmission than in cell-free transmission. Our study suggests the importance of inhibiting cell-to-cell transmission during multidrug treatment