A data-based reduced-order model for dynamic simulation and control of district-heating networks

This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called “reduced-order model” (ROM) is obtained from reduction of the conservation law for energy for each pipe segment to a semi-analytical input–output relation between the pipe outlet temperature and the pipe inlet and ground temperatures that can be identified from training data. The ROM basically is valid for generic pipe configurations involving 3D unsteady heat transfer and 3D steady flow as long as heat-transfer mechanisms are linearly dependent on the temperature field. Moreover, the training data can be generated by physics-based computational “full-order” models (FOMs) yet also by (calibration) experiments or field measurements. Performance tests using computational training data for a single-pipe configuration demonstrate that the ROM (i) can be successfully identified and (ii) can accurately describe the response of the outlet temperature to arbitrary input profiles for inlet and ground temperatures. Application of the ROM to two case studies, i.e. fast simulation of a small DH network and design of a controller for user-defined temperature regulation of a DH system, demonstrate its predictive ability and efficiency also for realistic systems. Dedicated cost analyses further reveal that the ROM may significantly reduce the computational costs compared to FOMs by (up to) orders of magnitude for higher-dimensional pipe configurations. These findings advance the proposed ROM as a robust and efficient simulation tool for practical DH systems with a far greater predictive ability than existing compact models

Localized Random Lasing Modes and a New Path for Observing Localization

We demonstrate that a knowledge of the density-of-states and the eigenstates of a random system without gain, in conjunction with the frequency profile of the gain, can accurately predict the mode that will lase first. Its critical pumping rate can be also obtained. It is found that the shape of the wavefunction of the random system remains unchanged as gain is introduced. These results were obtained by the time-independent transfer matrix method and finite-difference-time-domain (FDTD) methods. They can be also analytically understood by generalizing the semi-classical Lamb theory of lasing in random systems. These findings provide a new path for observing the localization of light, such as looking for mobility edge and studying the localized states. %inside the random systems..Comment: Sent to PRL. 3 figure

Modelling the Mechanical Behaviour of a Pharmaceutical Tablet Using PDEs.

yesDetailed design of pharmaceutical tablets is essential nowadays in order to produce robust tablets with tailor-made properties. Compressibility and compactibility are the main compaction properties involved in the design and development of solid dosage forms. The data obtained from measured forces and displacements of the punch are normally analysed using the Heckel model to assess the mechanical behaviour of pharmaceutical powders. In this paper, we present a technique for shape modelling of pharmaceutical tablets based on the PDE method. We extended the formulation of the PDE method to a higher dimensional space in order to generate a solid tablet and a cuboid mesh is created to represent the tablet¿s components. We also modelled the displacement components of a compressed PDE- based representation of a tablet by utilising the solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load. The experimental data and the results obtained from the developed model are shown in Heckel plots and a good agreement is found between both.Available in full text since 5th Feb 2013 following the publisher's embargo period

Mode Repulsion and Mode Coupling in Random Lasers

We studied experimentally and theoretically the interaction of lasing modes in random media. In a homogeneously broadened gain medium, cross gain saturation leads to spatial repulsion of lasing modes. In an inhomogeneously broadened gain medium, mode repulsion occurs in the spectral domain. Some lasing modes are coupled through photon hopping or electron absorption and reemission. Under pulsed pumping, weak coupling of two modes leads to synchronization of their lasing action. Strong coupling of two lasing modes results in anti-phased oscillations of their intensities.Comment: 13 pages, 4 figure

Information-sharing outage-probability analysis of vehicular networks

In vehicular networks, information dissemination/sharing among vehicles is of salient importance. Although diverse mechanisms have been proposed in the existing literature, the related information credibility issues have not been investigated. Against this background, in this paper, we propose a credible information-sharing mechanism capable of ensuring that the vehicles do share genuine road traffic information (RTI). We commence with the outage-probability analysis of information sharing in vehicular networks under both a general scenario and a specific highway scenario. Closed-form expressions are derived for both scenarios, given the specific channel settings. Based on the outage-probability expressions, we formulate the utility of RTI sharing and design an algorithm for promoting the sharing of genuine RTI. To verify our theoretical analysis and the proposed mechanism, we invoke a real-world dataset containing the locations of Beijing taxis to conduct our simulations. Explicitly, our simulation results show that the spatial distribution of the vehicles obeys a Poisson point process (PPP), and our proposed credible RTI sharing mechanism is capable of ensuring that all vehicles indeed do share genuine RTI with each other

Dynamical aspects of mean field plane rotators and the Kuramoto model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur

η\eta-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians

A class of spherically symmetric non-Hermitian Hamiltonians and their \eta-weak-pseudo-Hermiticity generators are presented. An operators-based procedure is introduced so that the results for the 1D Schrodinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include \eta-weak-pseudo-Hermiticity generators for the non-Hermitian weakly perturbed 1D and radial oscillators, the non-Hermitian perturbed radial Coulomb, and the non-Hermitian radial Morse models.Comment: 14 pages, content revised/regularized to cover 1D and 3D case

First-order intertwining operators with position dependent mass and η\eta- weak-psuedo-Hermiticity generators

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target $\eta$-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some $\eta$-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding $\eta$-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are given as products of the reference-target map.Comment: 11 pages, no figures, Revised/Expanded, more references added. To appear in the Int.J. Theor. Phy

PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation

PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.Comment: 13 page

(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib) (an inversely linear plus linear, leading to a PT-symmetric oscillator model), and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an $\eta$-weak-pseudo-Hermiticity generator are presented and a complexified PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise