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Articles 1 - 30 of 87
Full-Text Articles in Applied Mathematics
Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor
Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor
Articles
In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …
Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov
Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov
Conference papers
The article surveys the recent results on integrable systems arising from quadratic pencil of Lax operator L, with values in a Hermitian symmetric space. The counterpart operator M in the Lax pair defines positive, negative and rational flows. The results are illustrated with examples from the A.III symmetric space. The modeling aspect of the arising higher order nonlinear Schrödinger equations is briefly discussed.
The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov
The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov
Articles
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some …
A Mode-Sum Prescription For The Renormalized Stress Energy Tensor On Black Hole Spacetimes, Peter Taylor, Cormac Breen, Adrian Ottewill
A Mode-Sum Prescription For The Renormalized Stress Energy Tensor On Black Hole Spacetimes, Peter Taylor, Cormac Breen, Adrian Ottewill
Articles
In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semiclassical backreaction.
Data Driven Bayesian Network To Predict Critical Alarm, Joseph Mietkiewicz, Anders Madsen
Data Driven Bayesian Network To Predict Critical Alarm, Joseph Mietkiewicz, Anders Madsen
Articles
Modern industrial plants rely on alarm systems to ensure their safe and effective functioning. Alarms give the operator knowledge about the current state of the industrial plants. Trip alarms indicating a trip event indicate the shutdown of systems. Trip events in power plants can be costly and critical for the running of the operation.This paper demonstrates how trips events based on an alarm log from an offshore gas production can be reliably predicted using a Bayesian network. If a trip event is reliably predicted and the main cause of it is identified, it will allow the operator to prevent it. …
Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen
Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen
Articles
We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct …
Multicomponent Fokas-Lenells Equations On Hermitian Symmetric Spaces, Vladimir Gerdjikov, Rossen Ivanov
Multicomponent Fokas-Lenells Equations On Hermitian Symmetric Spaces, Vladimir Gerdjikov, Rossen Ivanov
Articles
Multi-component integrable generalizations of the Fokas-Lenells equation, associated with each irreducible Hermitian symmetric space are formulated. Description of the underlying structures associated to the integrability, such as the Lax representation and the bi-Hamiltonian formulation of the equations is provided. Two reductions are considered as well, one of which leads to a nonlocal integrable model. Examples with Hermitian symmetric spaces of all classical series of types A.III, BD.I, C.I and D.III are presented in details, as well as possibilities for further reductions in a general form.
Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante
Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante
Articles
In this work we consider the problem of finding the simplest arrangement of resonant deep water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wave vectors K1 + K2 = K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wave packets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction …
Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong
Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong
Articles
We introduce two new notions of transitivity for Abelian 𝑝-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian 𝑝-group theory. Unlike the classical theory where “most” groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.
On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith
On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith
Articles
We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ! these two group classes coincide but that in the case of groups of length ! + 1 they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by the second and third named authors in Arch. Math. Basel (2009) …
Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze
Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze
Articles
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and …
On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov
On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov
Articles
A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …
Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr
Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr
Articles
A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa–Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.
Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov
Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov
Articles
Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups GR ≃ Dh. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the GR-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with Dh symmetries are presented.
Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov
Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov
Articles
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …
Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann
Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann
Articles
The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Articles
We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …
Direct Immunoassays And Their Performance: Theoretical Modelling Of The Effects Of Antibody Orientation And Associated Kinetics, Dana Mackey, Eilis Kelly, Robert Nooney, Richard O'Kennedy
Direct Immunoassays And Their Performance: Theoretical Modelling Of The Effects Of Antibody Orientation And Associated Kinetics, Dana Mackey, Eilis Kelly, Robert Nooney, Richard O'Kennedy
Articles
The orientation and activity of antibodies immobilized on solid surfaces are of direct relevance to many immunosensing applications. We therefore investigate a mathematical model which estimates the fraction of antibodies which are available for reaction in a randomly adsorbed sample. Numerical simulations are presented which highlight the separate effects of antibody orientation, accessibility and loss of binding ability on the amount of captured antigen. The assay response can then be expressed as a function of total antibody density and used for optimizing the surface coverage strategy under various conditions.
Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov
Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov
Articles
We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion …
The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm
The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm
Articles
Young children are often hyperreactive to somatosensory inputs hardly noticed by adults, as exemplified by irritation to seams or labels in clothing. The neurodevelopmental mechanisms underlying changes in sensory reactivity are not well understood. Based on the idea that neurodevelopmental changes in somatosensory processing and/or changes in sensory adaptation might underlie developmental differences in somatosensory reactivity, high-density electroencephalography was used to examine how the nervous system responds and adapts to repeated vibrotactile stimulation over childhood. Participants aged 6–18 yr old were presented with 50-ms vibrotactile stimuli to the right wrist over the median nerve at 5 blocked interstimulus intervals (ranging …
On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
Articles
We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov
Articles
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised …
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Articles
We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.
Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor
Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor
Articles
Congruent audiovisual speech enhances our ability to comprehend a speaker, even in noise-free conditions. When incongruent auditory and visual information is presented concurrently, it can hinder a listener’s perception and even cause him or her to perceive information that was not presented in either modality. Efforts to investigate the neural basis of these effects have often focused on the special case of discrete audiovisual syllables that are spatially and temporally congruent, with less work done on the case of natural, continuous speech. Recent electrophysiological studies have demonstrated that cortical response measures to continuous auditory speech can be easily obtained using …
On Mikhailov's Reduction Group, Tihomir Valchev
On Mikhailov's Reduction Group, Tihomir Valchev
Articles
We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.
Will Oscillating Wave Surge Converters Survive Tsunamis?, Laura Cooke, P. Christodoulides, E. Renzi, T. Stefanakis, F. Dias
Will Oscillating Wave Surge Converters Survive Tsunamis?, Laura Cooke, P. Christodoulides, E. Renzi, T. Stefanakis, F. Dias
Articles
With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter (OWSC) could withstand the force of an incoming tsunami. Several tools are used to provide an answer: an analytical 3D model developed within the framework of linear theory, …
A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, Adrian Constantin, Rossen Ivanov
A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, Adrian Constantin, Rossen Ivanov
Articles
We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a two-layered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an in-depth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.
On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, Alan Compelli, Rossen Ivanov
On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, Alan Compelli, Rossen Ivanov
Articles
The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring in other layers of the current does not affect the wave motion. The equations of motion are formulated as a Hamiltonian system.
Dressing Method And Quadratic Bundles Related To Symmetric Spaces: Vanishing Boundary Conditions, Tihomir Valchev
Dressing Method And Quadratic Bundles Related To Symmetric Spaces: Vanishing Boundary Conditions, Tihomir Valchev
Articles
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m) x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.
One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov
One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov
Articles
In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.