Search

We have investigated a rock-scissors-paper model with long-range-directed interactions in two dimensions where every site has four outgoing links but a fraction qof the outgoing links to the nearest neighbour sites are rewired to other long-distance sites chosen randomly and the lattice structure is replaced again after a Monte Carlo step. It is found that, with qincreasing, the system changes from a three species coexistence self-organizing state to a global oscillation state and then to one of the homogeneous states. However when qexceeds a third threshold value, the system returns to a self-organizing state. When we restrict the maximum number of ingoing links of a site to four, the last self-organizing state disappears, the system stays in the homogeneous state forever after qexceeds the second threshold value. And when we restrict the maximum number of ingoing links of a site to five or six, the system exhibits a transition from the homogeneous state to a global oscillation state again and then to the last self-organizing state with qincreasing. The comparison of results on different networks suggests that the sites with zero ingoing links should play a significant role in the emergences of the later self-organizing state and the subsequent global oscillation. [ABSTRACT FROM AUTHOR]

In this paper, the analytical and numerical solutions of a non-steady state mathematical model are developed and analyzed. The mathematical model development of a non-steady state heat transport for a one-dimensional system is shown, and the analytical solution of the model is presented. The numerical solution of the model, using the finite element method (FEM), is compared to its analytical solution, proving its consistency. One of the advantages of using numerical tools is that more complex solutions can be obtained, even if the corresponding analytical solution does not exist or is not known, which is useful for engineering students. To demonstrate the applications and possibilities of this work, it is shown that changing the boundary conditions, geometry, or dimension in the system and the mathematical model, it can be solved through a numerical solution method. This is easier and more comprehensive for students rather than facing the complexity of the analytical solutions. The paper shows that it is possible to use the FEM in a university teaching context to complementarily explain the underlying physical phenomena of an engineering problem, here applied to a heat transfer problem in a vegetable. [ABSTRACT FROM AUTHOR]

Localized surface plasmons (LSPs) have a wide range of applications in enhancing the performance of optoelectronic devices. For those applications, LSPs are often located on the surfaces or interfaces between dielectric mediums. Hence, it is necessary to investigate interaction between LSPs and interface. In this paper, we investigate the far-field and near-field LSP behaviors of silver nanocube arrays on a dielectric substrate. Finite-difference time-domain simulation results demonstrate that, when light is incident normally from the vacuum, a much deeper dip between the two peaks corresponding to bonding and anti-bonding modes of the LSPs generated in the metal nanocubes on dielectric mediums, comparing to the case that incident light is from the substrate. The charge distribution diagram shows that these behaviors can be described as a dipole-like mode and a quadrupole-like mode. A model based on the Fano interferences using modified Fresnel equations is employed to explain the physical mechanism of these behaviors. It reveals that this phenomenon is caused by the phase difference between the superimposed dipolar modes generated on the upper and lower interfaces of nanocube. A simplified mathematical model has been built to illustrate that symmetric dips can arise from the Fano interference between two discrete states and one continuum state. [ABSTRACT FROM AUTHOR]

Objective. Measuring the respiratory signal from a video based on body motion has been proposed and recently matured in products for contactless health monitoring. The core algorithm for this application is the measurement of tiny chest/abdominal motions induced by respiration (i.e. capturing sub-pixel displacement caused by subtle motion between subsequent video frames), and the fundamental challenge is motion sensitivity. Though prior art reported on the validation with real human subjects, there is no thorough or rigorous benchmark to quantify the sensitivities and boundary conditions of motion-based core respiratory algorithms. Approach. A set-up was designed with a fully-controllable physical phantom to investigate the essence of core algorithms, together with a mathematical model incorporating two motion estimation strategies and three spatial representations, leading to six algorithmic combinations for respiratory signal extraction. Their promises and limitations are discussed and clarified through the phantom benchmark. Main results. With the variation of phantom motion intensity between 0.5 mm and 8 mm, the recommended approach obtains an average precision, recall, coverage and MAE of 88.1%, 91.8%, 95.5% and 2.1 bpm in the day-light condition, and 81.7%, 90.0%, 93.9% and 4.4 bpm in the night condition. Significance. The insights gained in this paper are intended to improve the understanding and applications of camera-based respiration measurement in health monitoring. The limitations of this study stem from the used physical phantom that does not consider human factors like body shape, sleeping posture, respiratory diseases, etc., and the investigated scenario is focused on sleep monitoring, not including scenarios with a sitting or standing patient like in clinical ward and triage. [ABSTRACT FROM AUTHOR]

A physico-mathematical model of open systems proposed in a previous paper (Delle Site and Klein 2020 J. Math. Phys. 61 083102) can represent a guiding reference in designing an accurate simulation scheme for an open molecular system embedded in a reservoir of energy and particles. The derived equations and the corresponding boundary conditions are obtained without assuming the action of an external source of heat that assures thermodynamic consistency of the open system with respect to a state of reference. However, in numerical schemes the temperature in the reservoir must be controlled by an external heat bath otherwise thermodynamic consistency cannot be achieved. In this perspective, the question to address is whether the explicit addition of an external heat bath in the theoretical model modifies the equations of the open system and its boundary conditions. In this work we consider this aspect and explicitly describe the evolution of the reservoir employing the Bergmannâ€"Lebowitz statistical model of thermostat. It is shown that the resulting equations for the open system itself are not affected by this change and an example of numerical application is reviewed where the current result shows its conceptual relevance. Finally, a list of pending mathematical and modelling problems is discussed the solution of which would strengthen the mathematical rigour of the model and offer new perspectives for the further development of a new multiscale simulation scheme. [ABSTRACT FROM AUTHOR]

A looping pendulum is a setup that consists of two loads connected by a light string, which in turn is put over a fixed rod, with the lighter load being held by a person, and the heavier close to the rod. When the lighter load is released, experience shows there is an instant when the heavier load stops falling, and the lighter winds around the rod, bringing the system to rest. This setup is used in science demonstrations to prevent a fragile object, such as a ceramic mug, from falling to the ground, using washers as the lighter load. In this paper we propose a mathematical model for this demonstration, which we use to analyze the main parameters that influence the effectiveness of the setup. We find its equations of motion analytically, and use numerical methods to relate relevant parameters (such as falling distance and trajectory) to the initial configuration, determine the conditions that allow the phenomenon to happen, and display results as plots and parameter spaces. Lastly, through careful experimentation we found strong evidence for the validity of our theoretical predictions. We found the looping pendulum to be an extremely useful problem for introductory college physics courses interested in strengthening analytical and computational physics skills, as its construction is easy, inexpensive, and its analysis encompasses various mechanics concepts, solving differential equations numerically, and data collection through video software. [ABSTRACT FROM AUTHOR]

We consider the Sasa–Satsuma (SS) and nonlinear Schrödinger (NLS) equations posed along the line, in 1 + 1 dimensions. Both equations are canonical integrable U(1) models, with solitons, multi-solitons and breather solutions Yang (2010 SIAM Mathematical Modeling and Computation). For these two equations, we recognize four distinct localized breather modes: the Sasa–Satsuma for SS, and for NLS the Satsuma–Yajima, Kuznetsov–Ma and Peregrine breathers. Very little is known about the stability of these solutions, mainly because of their complex structure, which does not fit into the classical soliton behavior Grillakis et al (1987 J. Funct. Anal. 74 160–97). In this paper we find the natural H2 variational characterization for each of them. This seems to be the first known variational characterization for these solutions; in particular, the first one obtained for the famous Peregrine breather. We also prove that Sasa–Satsuma breathers are H2 nonlinearly stable, improving the linear stability property previously proved by Pelinovsky and Yang (2005 Chaos 15 037115). Moreover, in the SS case, we provide an alternative understanding of the SS solution as a breather, and not only as an embedded soliton. The method of proof is based in the use of a H2 based Lyapunov functional, in the spirit of Alejo and Muńoz (2013 Commun. Math. Phys. 324 233–62), extended this time to the vector-valued case. We also provide another rigorous justification of the instability of the remaining three nonlinear modes (Satsuma–Yajima, Peregrine and Kuznetsov–Ma), based in the study of their corresponding linear variational structure (as critical points of a suitable Lyapunov functional), and complementing the instability results recently proved e.g. in Muńoz (2017 Proyecciones (Antofagasta) 36 653–83). [ABSTRACT FROM AUTHOR]

In this paper we introduce a mathematical model of the image saturation phenomenon occurring in a charged coupled device (CCD), and we propose a novel computational method for restoring saturated images acquired by the atmospheric imaging assembly (AIA) telescope. The mathematical model takes into account both primary saturation, when the photon-induced charge reaches the CCD full well capacity, and the blooming effect, when the excess charge flows into adjacent pixels. The restoration of AIA saturated images is then formulated as an inverse problem with a forward operator encoding the standard diffraction of light rays by a convolution, the primary saturation by an upper limit to the number of photons and the blooming effect by the conservation of the photon-induced charge spilled over adjacent pixels. As a result of this theoretical formulation we propose an adaptive ℓ1 regularized inversion method improving the desaturation capabilities of the existing SE-DESAT method [Guastavino S et al 2019 Astrophys. J. 882 109]. We prove that this method has the consistency estimation property also in the case that a fixed unknown background is considered. We test the adaptive method both in the case of synthetic and real data, comparing the performance with the one of the SE-DESAT method, showing that the proposed method avoids edge effects and artifacts in reconstructions even when the background solar activity is particularly intense. [ABSTRACT FROM AUTHOR]

A mathematical model of an ultrahigh sensitivity piezoresistive chip of a pressure sensor with a range from −0.5 to 0.5 kPa has been developed. The optimum geometrical dimensions of a specific silicon membrane with a combination of rigid islands to ensure a trade-off relationship between sensitivity (Ssamples = 34.5 mV kPa−1 V−1) and nonlinearity (2KNL samples = 0.81%FS) have been determined. The paper also studies the range of the membrane deflection and makes recommendations on position of stops limiting diaphragm deflection in both directions; the stops allow for increasing burst pressure Pburst up to 450 kPa. The simulated data has been related to that of experimental samples and their comparative analysis showed the relevance of the mathematical model (estimated sensitivity and nonlinearity errors calculated on the basis of average values are 1.5% and 19%, respectively). [ABSTRACT FROM AUTHOR]

We investigated a mathematical model for Korteweg-type fluids, formulated in the form of the General equation for the non-equilibrium reversible–irreversible coupling (GENERIC) as proposed by Grmela and Öttinger, in comparison with the classical work of Dunn and Serrin. Interstitial working introduced by Dunn and Serrin reappeared in the formulation and proved to be necessary if we claim that the work done by the Korteweg stress is 'isentropic'. Indeed, the GENERIC formalism provides a fairly simple derivation of the governing equations with the interstitial working for Korteweg-type fluids. In the accompanying paper, and within this formalism, we derived a higher-order model including the second-order gradient of the density. We also discussed the relation of the interstitial working to the microforces introduced by Gurtin. [ABSTRACT FROM AUTHOR]

The authors comments on the paper "An analytic functional form for characterization and generation of axisymmetric plasma boundaries." They mention that the proposed alternative form describe boundaries in the axisymmetric plasma between an X-point and D-shaped ones and can be used to study fusion plasmas.

We consider the free-boundary problem for the plasma–vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the pre-Maxwell dynamics for the magnetic field. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma–vacuum system is not isolated from the outside world, because of a given surface current on the fixed boundary that forces oscillations.Under a suitable stability condition satisfied at each point of the initial interface, stating that the magnetic fields on either side of the interface are not collinear, we show the existence and uniqueness of the solution to the nonlinear plasma–vacuum interface problem in suitable anisotropic Sobolev spaces. The proof is based on the results proved in the companion paper (Secchi and Trakhinin 2013 Interfaces Free Boundaries15 323–57), about the well-posedness of the homogeneous linearized problem and the proof of a basic a priori energy estimate. The proof of the resolution of the nonlinear problem given in the present paper follows from the analysis of the elliptic system for the vacuum magnetic field, a suitable tame estimate in Sobolev spaces for the full linearized equations, and a Nash–Moser iteration. [ABSTRACT FROM AUTHOR]

This paper presents a 90 min tutorial intervention which permits the use of the Tutorials in Introductory Physics curriculum in a conventional physics course. In addition, the paper describes the impact of the intervention on students' understanding of the ray model of light in the context of geometrical images. In 2011 and 2012 a total of 79 introductory students participated in the intervention, where they worked with the Light and Shadow tutorial after having received lecture-based instruction in a conventional physics course. The impact of the intervention on the students' learning was assessed by means of paper-and-pencil test questions at the beginning and end of the intervention. The results showed that the proportion of correct or nearly correct answers increased by 17 percentage points during the intervention. Thus, it can be claimed that the intervention was a useful supplement to a conventional physics course by helping students to improve their understanding of the ray model of light. In addition, the intervention may serve as an intermediate step towards adopting the tutorials, since it permits the curriculum of a conventional physics course to be tested without large changes being made to the course. This type of information is needed in support of institutional changes towards more research-based instructional practices. [ABSTRACT FROM AUTHOR]

I approach the problem of time and other foundations of quantum (QM) cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle mechanics (RPMs). If there is also commutation with Lin--the Kuchař observables condition--the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchař observables is explicitly resolved for 1D and 2D RPMs. Then as a first route to Halliwell's approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kucha?r observables are formally known, giving the relational triangle as an example. As a second route, I apply an indirect method that generalizes both group averaging and Barbour's best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 sharp-edged window function. I leave the elsewiseimproved softened case of Halliwell 2009 for a subsequent paper II. Finally, I provide comments on Halliwell's approach and how well it fares as regards the various facets of the problem of time and as an implementation of QM propositions. [ABSTRACT FROM AUTHOR]

In this paper we continue our earlier studies (Diao et al 2011 J. Phys. A: Math. Theor. 44 405202, Diao et al J. Phys. A: Math. Theor. 45 275203) on the generation methods of random equilateral polygons confined in a sphere. The first half of this paper is concerned with the generation of confined equilateral random walks.We show that if the selection of a vertex is uniform subject to the position of its previous vertex and the confining condition, then the distributions of the vertices are not uniform, although there exists a distribution such that if the initial vertex is selected following this distribution, then all vertices of the random walk follow this same distribution. Thus in order to generate a confined equilateral random walk, the selection of a vertex cannot be uniform subject to the position of its previous vertex and the confining condition. We provide a simple algorithm capable of generating confined equilateral random walks whose vertex distribution is almost uniform in the confinement sphere. In the second half of this paper we show that any process generating confined equilateral random walks can be turned into a process generating confined equilateral random polygons with the property that the vertex distribution of the polygons approaches the vertex distribution of the walks as the polygons get longer and longer. In our earlier studies, the starting point of the confined polygon is fixed at the center of the sphere. The new approach here allows us to move the starting point of the confined polygon off the center of the sphere. [ABSTRACT FROM AUTHOR]

In a recent paper (Bhullar and Watchman 2012 Phys. Med. Biol. 57 273-86), the authors comment on data concerning the effective depth of cylindrical ionization chambers in water for clinical proton beams calculated in a previous paper (Palmans 2006 Phys. Med. Biol. 51 3483-501) and propose different results. They present a closed-format expression for an integral in the analytical model and claim that the series expansion I used in the older paper does not converge to the correct solution. They also claim that this is the reason for the resulting values of the shift of the effective depth with respect to the chamber centre to be different in both papers. Both claims are, however, incorrect as I show in this comment. The values they present are most likely based on a mistake in the scaling coefficients to account for the nonwater equivalence of wall, sleeve and central electrode materials. The better agreement which they observe between their values and the recommendation of IAEA TRS-398 is thus a coincidence. My conclusion is that the best available data for the effective depth of cylindrical ionization chambers inwater in clinical proton beams are at present the values I published before (Palmans 2006 Phys. Med. Biol. 51 3483-501) and which are supported by Monte Carlo simulations and experimental evidence. [ABSTRACT FROM AUTHOR]

In this paper, an analogue model of a memristor using a light-dependent resistor (LDR) is presented. This model can be simplified into two parts: a control circuit and a variable resistor. It can be used to easily verify theoretical presumptions about the switching properties of memristors. This LDR-based memristor model can also be used in both simulations and experiments for future research into memristor applications. The paper includes mathematical models, simulations, and experimental results. [ABSTRACT FROM AUTHOR]

We summarize the findings of a large number of studies concerning the totally asymmetric simple exclusion process (TASEP) with complex lattice geometries. The TASEP has been recognized as a paradigm in modeling and analyzing non-equilibrium traffic systems. The paper surveys both the observed physical phenomena and several popular meanfield approaches used to analyze the extended TASEP models. Several interesting physical phenomena, such as phase separation, spontaneous symmetry breaking, and the finite-size effect, have been identified and explained. The future investigations of the extended TASEP with complex lattice geometries are also introduced. This paper may help to obtain a better understanding of non-equilibrium systems. [ABSTRACT FROM AUTHOR]

Normally, a mechanics laboratory at the undergraduate level includes an experiment to verify compliance with Hooke's law in materials, such as a steel spring and an elastic rubber band. Stress-strain curves are found for these elements. Compression in elastic bands is practically impossible to achieve due to flaccidity. A typical experiment for the complete loading-unloading cycle is to subject a tubular object to torsion. This paper suggests simple experiments for studying properties concerning elasticity and plasticity in elements of common use, subjected to stretching or compression, and also torsion reinforcing. The experiments use plastic binders, rubber bands and metal springs under a moderate load. This paper discusses an experiment with an original device to measure torsion deformations as a function of applied torques, which permitted construction of the hysteresis cycle for a rubber hose and various tubes. Another experiment was designed to define the temporal recovery of a plastic spring with initial stretching. A simple mathematical model was developed to explain this phenomenon. [ABSTRACT FROM AUTHOR]

In a classical paper, Cahn derived expressions for the kinetics of transformations nucleated on random planes and lines. He used those as a model for nucleation on the boundaries, edges and vertices of a polycrystal consisting of equiaxed grains. In this paper it is demonstrated that Cahn's expression for random planes may be used in situations beyond the scope envisaged in Cahn's original paper. For instance, we derived an expression for the kinetics of transformations nucleated on random parallel planes that is identical to that formerly obtained by Cahn considering random planes. Computer simulation of transformations nucleated on random parallel planes is carried out. It is shown that there is excellent agreement between simulated results and analytical solutions. Such an agreement is to be expected if both the simulation and the analytical solution are correct. [ABSTRACT FROM AUTHOR]

The mathematical modelling and simulation of ion transport through biological and synthetic channels (nanopores) is a challenging problem, with direct application in biophysics, physiology and chemistry. At least two major effects have to be taken into account when creating such models: the electrostatic interaction of ions and the effects due to size exclusion in narrow regions. While mathematical models and methods for electrostatic interactions are welldeveloped and can be transferred from other flow problems with charged particles, e.g. semiconductor devices, less is known about the appropriate macroscopic modelling of size exclusion effects. Recently several papers proposed simple or sophisticated approaches for including size exclusion effects into entropies, in equilibrium as well as off equilibrium. The aim of this paper is to investigate a second potentially important modification due to size exclusion, which often seems to be ignored and is not implemented in currently used models, namely the modification of mobilities due to size exclusion effects. We discuss a simple model derived from a self-consisted random walk and investigate the stationary solutions as well as the computation of conductance. The need of incorporating nonlinear mobilities in high density situations is demonstrated in an investigation of conductance as a function of bath concentrations, which does not lead to obvious saturation effects in the case of linear mobility. [ABSTRACT FROM AUTHOR]

A comprehensive and completely parameterized model is proposed to determine the related electrical and mechanical dynamic system response of a voltage-driven capacitive coupled micromechanical switch. As an advantage over existing parameterized models, the model presented in this paper returns within few seconds all relevant system quantities necessary to design the desired switching cycle. Moreover, a sophisticated and detailed guideline is given on how to engineer a MEMS switch. An analytical approach is used throughout the modelling, providing representative coefficients in a set of two coupled time-dependent differential equations. This paper uses an equivalent mass moving along the axis of acceleration and a momentum absorption coefficient. The model describes all the energies transferred: the energy dissipated in the series resistor that models the signal attenuation of the bias line, the energy dissipated in the squeezed film, the stored energy in the series capacitor that represents a fixed separation in the bias line and stops the dc power in the event of a short circuit between the RF and dc path, the energy stored in the spring mechanism, and the energy absorbed by mechanical interaction at the switch contacts. Further, the model determines the electrical power fed back to the bias line. The calculated switching dynamics are confirmed by the electrical characterization of the developed RF switch. The fabricated RF switch performs well, in good agreement with the modelled data, showing a transition time of 7 µs followed by a sequence of bounces. Moreover, the scattering parameters exhibit an isolation in the off-state of >8 dB and an insertion loss in the on-state of <0.6 dB up to frequencies of 50 GHz. The presented model is intended to be integrated into standard circuit simulation software, allowing circuit engineers to design the switch bias line, to minimize induced currents and cross actuation, as well as to find the mechanical structure dimensions necessary for the desired switching time and actuation voltage waveform. Moreover, process related design rules can be automatically verified. [ABSTRACT FROM AUTHOR]

A brane picture in type IIA superstring for the Yang monopole is reconsidered. It makes use of D2 and D4-branes wrapped on cycles in the K3 surface. When the model was first presented, some problems concerning the charges of the monopoles arose. In this paper, they are shown to be cured by the model itself. Surprisingly, the incompatibility between the multi-charge configuration and the spherical symmetry of the Yang monopole is seen in the brane description as the emergence of the enhanc,on shell and the fuzzy geometry. This consistency is deep and surprising, and is the point that triggered this work. It nontrivially relates a purely geometrical problem in ordinary spacetime with the emergence of noncommutative geometries. Besides, this paper includes an extended model for SO(4)-monopoles and a T-dual model in type IIB superstring. [ABSTRACT FROM AUTHOR]

Large catalogs of shear-selected peaks have recently become a reality. In order to properly interpret the abundance and properties of these peaks, it is necessary to take into account the effects of the clustering of source galaxies, among themselves and with the lens. In addition, the preferred selection of magnified galaxies in a flux- and size-limited sample leads to fluctuations in the apparent source density that correlate with the lensing field. In this paper, we investigate these issues for two different choices of shear estimators that are commonly in use today: globally normalized and locally normalized estimators. While in principle equivalent, in practice these estimators respond differently to systematic effects such as magnification and cluster member dilution. Furthermore, we find that the answer to the question of which estimator is statistically superior depends on the specific shape of the filter employed for peak finding; suboptimal choices of the estimator+filter combination can result in a suppression of the number of high peaks by orders of magnitude. Magnification and size bias generally act to increase the signal-to-noise ν of shear peaks; for high peaks the boost can be as large as Δν ≈ 1-2. Due to the steepness of the peak abundance function, these boosts can result in a significant increase in the observed abundance of shear peaks. A companion paper investigates these same issues within the context of stacked weak-lensing mass estimates. [ABSTRACT FROM AUTHOR]

When extracting the weak lensing shear signal, one may employ either locally normalized or globally normalized shear estimators. The former is the standard approach when estimating cluster masses, while the latter is the more common method among peak finding efforts. While both approaches have identical signal-to-noise in the weak lensing limit, it is possible that higher order corrections or systematic considerations make one estimator preferable over the other. In this paper, we consider the efficacy of both estimators within the context of stacked weak lensing mass estimation in the Dark Energy Survey (DES). We find that the two estimators have nearly identical statistical precision, even after including higher order corrections, but that these corrections must be incorporated into the analysis to avoid observationally relevant biases in the recovered masses. We also demonstrate that finite bin-width effects may be significant if not properly accounted for, and that the two estimators exhibit different systematics, particularly with respect to contamination of the source catalog by foreground galaxies. Thus, the two estimators may be employed as a systematic cross-check of each other. Stacked weak lensing in the DES should allow for the mean mass of galaxy clusters to be calibrated to ≈2% precision (statistical only), which can improve the figure of merit of the DES cluster abundance experiment by a factor of ~3 relative to the self-calibration expectation. A companion paper investigates how the two types of estimators considered here impact weak lensing peak finding efforts. [ABSTRACT FROM AUTHOR]

Thermoacoustic instability can appear in any thermal device when the unsteady heat transfer is favourably coupled with the fluctuations of acoustic pressure. In this paper, we present a project type of physical measuring and modelling task; the aim of our project is to help our students increase their knowledge of thermoacoustics. Our paper proposes several experiments and describes some tools' setups that are easy to obtain and work with. Free software is offered to analyse the signals with a personal computer. In this paper, the basis of standing wave theory and the tie between thermodynamics and acoustical oscillations are also discussed; some devices and technical applications of thermoacoustic oscillations are presented. The objective of this paper is to present the theory of frequency shifting of thermoacoustic oscillations as well. The frequencies of the acoustic modes in the excited state are of interest for practical purposes; the differences between the calculated and the measured values of these frequencies are shown. The behaviour of the properties of the exited modes shows the complexity of the real thermoacoustic systems; the mathematical modelling intended to simulate the effect of frequency shifting is observed in tests. We think that these experiments can be implemented in physics courses on thermodynamics for graduates or specialized courses for undergraduates. [ABSTRACT FROM AUTHOR]

This paper studies the topological properties of knotted solitons in the (3 + 1)-dimensional Aratyn-Ferreira-Zimerman (AFZ) model. Topologically, these solitons are characterized by the Hopf invariant I, which is an integral class in the homotopy group p3(S3) = Z. By making use of the decomposition of U(1) gauge potential theory and Duan's topological current theory, it is shown that the invariant is just the total sum of all the self-linking and linking numbers of the knot family while only linking numbers are considered in other papers. Furthermore, it is pointed out that this invariant is preserved in the branch processes (splitting, merging and intersection) of these knot vortex lines. [ABSTRACT FROM AUTHOR]

Repeater optimization is the key for SOC (System on Chip) interconnect delay design. This paper proposes a novel optimal model for minimizing power and area overhead of repeaters while meeting the target performance of on-chip interconnect lines. It also presents Lagrangian function to find the number of repeaters and their sizes required for minimizing area and power overhead with target delay constraint. Based on the 65 nanometre CMOS technology, the computed results of the intermediate and global lines show that the proposed model can significantly reduce area and power of interconnected lines, and the better performance will be achieved with the longer line. The results compared with the reference paper demonstrate the validity of this model. It can be integrated into repeater design methodology and CAD (computer aided design) tool for interconnect planning in nanometre SOC. [ABSTRACT FROM AUTHOR]

This paper reports the experimental results on electromagnetically induced absorption (EIA) spectra observed in the system which does not satisfy completely the conditions given by Lezama et al [1999 Phys. Rev. A 59 4732]. EIA signals on the transitions in the Cs D2 line are able to be observed, where Fg - Fe = Fg -- 1 as open systems. Theoretical model of Lezama et al is good for the case Fg - Fe = Fg + 1, considering spontaneous transfer of atomic coherences or populations this model is not able to explain our experimental results obtained in the case Fg - Fe = Fg -- 1. This paper offers a theoretical model which is able to well explain the case Fg - Fe = Fg -- 1. It also uses this theoretical model to explain the split and shift of EIA peaks, which have been obtained in experiments. [ABSTRACT FROM AUTHOR]

A class of bound-state problems which represents the coupling of a three-level atom with a two-dimensional system involving two shape-invariant potentials was introduced in a previous paper. In this paper, we considered second-order parasupersymmetric quantum-mechanical models and two possible kinds for the coupling Hamiltonian (linear and nonlinear in the potential ladder operators). In the present paper, using an algebraic formulation for shape-invariant potential systems, we study the quantum dynamics of these coupled systems and obtain the temporal behaviour of some dynamical variables related with the atom and the coupling potentials. An application is given for a couple of shape-invariant potentials (Pöschl-Teller + self-similar potentials). [ABSTRACT FROM AUTHOR]

This paper is concerned with a multi-dimensional free boundary problem modelling the growth of a tumour with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By using the Fourier expansion of functions on unit sphere via spherical harmonics, we establish some decay estimates for the solution of the linearized system of this tumour model at the radial stationary solution, so proving that the radial stationary solution is linearly asymptotically stable when neglecting translations. [ABSTRACT FROM AUTHOR]

We consider the problem of phase retrieval in the Fresnel regime. In recent years, several techniques have been used to solve this problem applying different a priori assumptions on the two-dimensional object in space, such as positivity, finite support and amplitude constraints. In this paper, we propose a new constraint, namely the assumption that the object possesses a sparse representation in a shearlet frame. We show how a shearlet soft-thresholding procedure can be used for phase reconstruction with Fresnel data. As it turns out, the shearlet sparsity constraint yields reconstruction results that are far superior to the support constraint, and comparable to the support plus positivity constraint. [ABSTRACT FROM AUTHOR]

The Carroll group was originally introduced by Lévy-Leblond (1965 Ann. Inst. Henri Poincaré3 1) by considering the contraction of the Poincaré group as c → 0. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, spacetime structure is proposed. A ‘duality’ with the Galilean limit c → ∞ is established. Our theory is illustrated by Carrollian electromagnetism. [ABSTRACT FROM AUTHOR]

We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In it maps a function to its surface integrals over circular cones, and in it maps a function to its integrals along two rays with a common vertex. Such transforms appear in various mathematical models arising in medical imaging, nuclear industry and homeland security. This paper contains new results about inversion of conical Radon transform with fixed opening angle and vertical central axis in and . New simple explicit inversion formulae are presented in these cases. Numerical simulations were performed to demonstrate the efficiency of the suggested algorithm in 2D. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the inverse problem of determining the reaction term f(x, u) in reaction-diffusion equations of the form ∂tu − D∂xxu = f(x, u), where f is assumed to be periodic with respect to Starting from a family of exponentially decaying initial conditions u0, λ, we show that the solutions uλ of this equation propagate with constant asymptotic spreading speeds wλ. Our main result shows that the linearization of f around the steady state 0, ∂uf(x, 0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds wλ. [ABSTRACT FROM AUTHOR]

In this paper, we further analyze our cellular automaton (CA) traffic flow model. By changing some parameters, the characteristics of our model can be significantly varied, ranging from the features of phase transitions to the number of traffic phases. We also review the other CA models based on Kerner's three-phase traffic theory. By comparisons, we find that the core concepts for modeling the synchronized flow in these models are similar. Our model can be a good candidate for modeling the synchronized flow, since there is enough flexibility in our framework. [ABSTRACT FROM AUTHOR]

In this paper, a new model is constructed for the causation analysis of railway accident based on the complex network theory. In the model, the nodes are defined as various manifest or latent accident causal factors. By employing the complex network theory, especially its statistical indicators, the railway accident as well as its key causations can be analyzed from the overall perspective. As a case, the “7.23” China—Yongwen railway accident is illustrated based on this model. The results show that the inspection of signals and the checking of line conditions before trains run played an important role in this railway accident. In conclusion, the constructed model gives a theoretical clue for railway accident prediction and, hence, greatly reduces the occurrence of railway accidents. [ABSTRACT FROM AUTHOR]

This paper is devoted to the incompressible magnetohydrodynamic equations in . We prove that if the difference between the magnetic field and the velocity is small initially then it will remain forever, thus resulting in a global strong solution without the smallness restriction on the size of initial velocity or magnetic field. In other words, magnetic field can indeed regularize Navier–Stokes equations, due to cancellation. [ABSTRACT FROM AUTHOR]

Classical and semiclassical schemes are presented that are timeless at the primary level and recover time from Mach’s ‘time is to be abstracted from change’ principle at the emergent secondary level. The semiclassical scheme is a Machian variant of the semiclassical approach to the problem of time in quantum gravity. The classical scheme is Barbour’s, cast here explicitly as the classical precursor of the semiclassical approach. Thus the two schemes have been married up, as equally-Machian and necessarily distinct, since the latter’s timestandard is abstracted in part from quantum change. I provide perturbative schemes for these in which the timefunction is to be determined rather than assumed. This paper is useful modelling as regards the Halliwell–Hawking arena for the quantum origin of the inhomogeneous cosmological fluctuations. [ABSTRACT FROM AUTHOR]

Due to their superior optical, elastic and electrical properties, chiral nanowires have many applications as sensors, probes, and building blocks of nanoelectromechanical systems. In this paper, we develop a refined Euler–Bernoulli beam model for chiral nanowires with surface effects and material chirality incorporated. This refined model is employed to investigate the bending and buckling of chiral nanowires. It is found that surface effects and material chirality significantly affect the elastic behaviour of chiral nanowires. This study is helpful not only for understanding the size-dependent behaviour of chiral nanowires, but also for characterizing their mechanical properties. [ABSTRACT FROM AUTHOR]

In cells, dynamic microtubules organize into asters or spindles to assist positioning of organelles. Two types of forces are suggested to contribute to the positioning process: (i) microtubule-growth based pushing forces; and (ii) motor protein mediated pulling forces. In this paper, we present a general theory to account for aster positioning in a confinement of arbitrary shape. The theory takes account of microtubule nucleation, growth, catastrophe, slipping, as well as interaction with cortical force generators. We calculate microtubule distributions and forces acting on microtubule organizing centers in a sphere and in an ellipsoid. Positioning mechanisms based on both pushing forces and pulling forces can be distinguished in our theory for different parameter regimes or in different geometries. In addition, we investigate positioning of microtubule asters in the case of asymmetric distribution of motors. This analysis enables us to characterize situations relevant for Caenorrhabditis elegans embryos. [ABSTRACT FROM AUTHOR]

The sharp point of a cone is known to accumulate charges, thus representing a singularity for the electric field. However, a real pointed object has a finite radius of curvature at the apex. Thus, we investigate in this paper how the ‘roundness’ affects the behaviour of fields and charges at the tip of a cone. Two cases are considered: a double cone being the asymptote of a two-sided hyperboloid of two sheets and a one-sided cone being the asymptote of a similar one-sided hyperboloid. Our analysis employs the prolate spheroidal system of coordinates and uses Legendre functions of the first kind of non-integer degree. The behaviour of the surface charge density is illustrated graphically in terms of the distance to the apex. Simple approximate formulas for the charge density valid near the apex are given. [ABSTRACT FROM AUTHOR]

The Casimir force—at first, a rather unexpected consequence of quantum electrodynamics—was discovered by Hendrik Casimir in Eindhoven in 1948. It predicts that two uncharged metal plates experience an attractive force because of the zero-point fluctuations of the electromagnetic field. The idea was tested experimentally in the 1950s and 1960s, but the results were not so accurate that one could make a definite conclusion regarding the existence of the effect. Evgeny Lifshitz expanded the theory in 1955 so as to deal with general dielectric media. Much experimental work was later done to test the theory’s predictions, especially with regards to the temperature dependence of the effect. The existence of the effect itself was verified beyond doubt by Sabisky and Anderson in 1973. Another quarter century had to pass before Lamoreaux and collaborators were able to confirm—or at least make plausible—the temperature dependence predicted by Lifshitz formula in combination with reasonable input data for the material’s dispersive properties. The situation is not yet clear-cut, however, there are recent experiments indicating results in disagreement with those of Lamoreaux. In this paper, a brief review is given of the status of this research field. [ABSTRACT FROM AUTHOR]

This paper describes a way to measure the radii of curvature of electrons following a curved path in a magnetic field and the radii of the concentric rings resulting from the interference of the electrons inside an evacuated diffraction tube. High-resolution imaging dramatically increases the precision of measurements of physical distances, if they are along circular arcs. Digital photographs were taken and the free software ImageJ that comes with a multitude of image-processing routines and is widely used in life sciences research was employed for measurement and analysis. [ABSTRACT FROM AUTHOR]

In this paper, we study the spatial-temporal patterns of the solutions to the diffusive non-local Nicholson's blowflies equations with time delay (maturation time) subject to the no flux boundary condition. We establish the existence of both spatially homogeneous periodic solutions and various spatially inhomogeneous periodic solutions by investigating the Hopf bifurcations at the spatially homogeneous steady state. We also compute the normal form on the centre manifold, by which the bifurcation direction and stability of the bifurcated periodic solutions can be determined. The results show that the bifurcated homogeneous periodic solutions are stable, while the bifurcated inhomogeneous periodic solutions can only be stable on the corresponding centre manifold, implying that generically the model can only allow transient oscillatory patterns. Finally, we present some numerical simulations to demonstrate the theoretic results. For these transient patterns, we derive approximation formulas which are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. [ABSTRACT FROM AUTHOR]

The ‘European Transport Simulator’ (ETS) (Coster et al 2010 IEEE Trans. Plasma Sci.38 2085–92, Kalupin et al 2011 Proc. 38th EPS Conf. on Plasma Physics (Strasbourg, France, 2011) vol 35G (ECA) P. 4.111) is the new modular package for 1D discharge evolution developed within the EFDA Integrated Tokamak Modelling (ITM) Task Force. It consists of precompiled physics modules combined into a workflow through standardized input/output data structures. Ultimately, the ETS will allow for an entire discharge simulation from the start up until the current termination phase, including controllers and sub-systems. The paper presents the current status of the ETS towards this ultimate goal. It discusses the design of the workflow, the validation and verification of its components on the example of impurity solver and demonstrates a proof-of-principles coupling of a local gyrofluid model for turbulent transport to the ETS. It also presents the first results on the application of the ETS to JET tokamak discharges with the ITER like wall. It studies the correlations of the radiation from impurity to the choice of the sources and transport coefficients. [ABSTRACT FROM AUTHOR]

Bogomolny and Schmit proposed that the critical edge percolation on the square lattice is a good model for the nodal domains of a random plane wave. Based on this they made a conjecture about the number of nodal domains. Recent computer experiments showed that the mean number of clusters per vertex and the mean number of nodal domains per unit area are very close but different. Since the original argument was mostly supported by numerics, it was believed that the percolation model is wrong. In this paper we give some numerical evidence in favour of the percolation model. [ABSTRACT FROM AUTHOR]

In this paper we discuss the connections between a Vlasov–Fokker–Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (Öttinger 2005 Beyond Equilibrium Thermodynamics (New York: Wiley-Interscience)). This interpretation provides (a) a variational formulation for GENERIC systems, (b) insight into the origin of this variational formulation, and (c) an explanation of the origins of the conditions that GENERIC places on its constitutive elements, notably the so-called degeneracy or non-interaction conditions. This work shows how the general connection between large-deviation principles on one hand and gradient-flow structures on the other hand extends to non-reversible particle systems. [ABSTRACT FROM AUTHOR]

This paper presents a systematic existence and uniqueness theory of weak measure solutions for systems of non-local interaction PDEs with two species, which are the PDE counterpart of systems of deterministic interacting particles with two species. The main motivations behind those models arise in cell biology, pedestrian movements, and opinion formation. In case of symmetrizable systems (i.e. with cross-interaction potentials one multiple of the other), we provide a complete existence and uniqueness theory within (a suitable generalization of) the Wasserstein gradient flow theory in Ambrosio et al (2008 Gradient Flows in Metric Spaces and in the Space of Probability Measures (Lectures in Mathematics ETH Zürich) 2nd edn (Basel: Birkhäuser)) and Carrillo et al (2011 Duke Math. J.156 229–71), which allows the consideration of interaction potentials with a discontinuous gradient at the origin. In the general case of non-symmetrizable systems, we provide an existence result for measure solutions which uses a semi-implicit version of the Jordan–Kinderlehrer–Otto (JKO) scheme (Jordan et al 1998 SIAM J. Math. Anal.29 1–17), which holds in a reasonable non-smooth setting for the interaction potentials. Uniqueness in the non-symmetrizable case is proven for C2 potentials using a variant of the method of characteristics. [ABSTRACT FROM AUTHOR]