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SynopsisWe discuss the symmetric solutions of the semilinear elliptic equation Δu+ λ(u+u|u|p−1) = 0,u|∂B= 0 (*), whereBis the unit ball in ℝ3. The value ofpis taken close to 5, the critical Sobolev exponent for ℝ3. An asymptotic... more
SynopsisWe discuss the symmetric solutions of the semilinear elliptic equation Δu+ λ(u+u|u|p−1) = 0,u|∂B= 0 (*), whereBis the unit ball in ℝ3. The value ofpis taken close to 5, the critical Sobolev exponent for ℝ3. An asymptotic description of the solutions of (*) with large norm is obtained. This predicts a fold bifurcation ifp> 5 and the structure of this bifurcation is studied in the limitp– 5→ 0. We find good agreement between the asymptotic description and some numerical calculations. These results are illuminated by recasting the problem (*) in the form of a dynamical system by means of a suitable change of variables. When |p– 5|≪1 and ∥u≫1, the transformed solutions of (*) are also solutions of a perturbed Hamiltonian system and we study the behaviour of these solutions by using Melnikov methods.
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A carillon is a musical instrument consisting of a (fairly large) set of bells that can be tolled by playing a keyboard, which is usually located one storey below the bells in a tower. Wires connect the keyboard to the clappers of the... more
A carillon is a musical instrument consisting of a (fairly large) set of bells that can be tolled by playing a keyboard, which is usually located one storey below the bells in a tower. Wires connect the keyboard to the clappers of the bells, forming an intricate web that is hinged to the walls. The web may vibrate, rub and tangle during play and some of the keys may require more pressure than others. The paper presents some methods to prevent these problems.
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Research Interests: Mechanical Engineering, Mathematics, Applied Mathematics, Image Processing, Reservoir Engineering, and 13 moreModeling, Data Assimilation, State Estimation, Tikhonov Regularization, Ill Posed Inverse Problems, Inverse Problem, Interdisciplinary Engineering, Dynamic System, Burgers equation, Regular Variation, Variational Calculus, Time window, and model error
In this problem the bulk of the liquid resides in the interval x ∈ [0,x∗(t)] where the moving interface x∗(t) is called the wetting front, and u ≪ 1 if x > x∗. The physical derivation of this equation is given in [6], [9], [10]. The... more
In this problem the bulk of the liquid resides in the interval x ∈ [0,x∗(t)] where the moving interface x∗(t) is called the wetting front, and u ≪ 1 if x > x∗. The physical derivation of this equation is given in [6], [9], [10]. The numerical treatment of this problem was first discussed in [12]. A comprehensive overview of numerical methods for flow in porous media is given for instance in [8]. In the present paper we do not focus on a simulation of the full model, but adopt a numerical approach to investigate the asymptotical behavior of self-similar solutions of the equation (1), which are stable ...
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The COVID-19 pandemic has caused unprecedented disruption, particularly in retail. Where essential demand cannot be fulfilled online, or where more stringent measures have been relaxed, customers must visit shop premises in person. This... more
The COVID-19 pandemic has caused unprecedented disruption, particularly in retail. Where essential demand cannot be fulfilled online, or where more stringent measures have been relaxed, customers must visit shop premises in person. This naturally gives rise to some risk of susceptible individuals (customers or staff) becoming infected. It is essential to minimize this risk as far as possible while retaining economic viability of the shop. We therefore explore and compare the spread of COVID-19 in different shopping situations involving person-to-person interactions: (i) free-flowing, unstructured shopping; (ii) structured shopping (e.g. a queue). We examine which of (i) or (ii) may be preferable for minimizing the spread of COVID-19 in a given shop, subject to constraints such as the geometry of the shop; compliance of the population to local guidelines; and additional safety measures which may be available to the organizers of the shop. We derive a series of conclusions, such as un...
The COVID-19 pandemic has caused unprecedented disruption, particularly in retail. Where essential demand cannot be fulfilled online, or where more stringent measures have been relaxed, customers must visit shop premises in person. This... more
The COVID-19 pandemic has caused unprecedented disruption, particularly in retail. Where essential demand cannot be fulfilled online, or where more stringent measures have been relaxed, customers must visit shop premises in person. This naturally gives rise to some risk of susceptible individuals (customers or staff) becoming infected. It is essential to minimize this risk as far as possible while retaining economic viability of the shop. We therefore explore and compare the spread of COVID-19 in different shopping situations involving person-to-person interactions: (i) free-flowing, unstructured shopping; (ii) structured shopping (e.g. a queue). We examine which of (i) or (ii) may be preferable for minimizing the spread of COVID-19 in a given shop, subject to constraints such as the geometry of the shop; compliance of the population to local guidelines; and additional safety measures which may be available to the organizers of the shop. We derive a series of conclusions, such as un...
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... problems aris-ing in physics and engineering, particularly those which are governed by partialdifferential equations. ... Moreover, it is κ-non-collapsed at any scale. ... Local description We can describe the local geometry of these... more
... problems aris-ing in physics and engineering, particularly those which are governed by partialdifferential equations. ... Moreover, it is κ-non-collapsed at any scale. ... Local description We can describe the local geometry of these κ-solutions with two fundamental building blocks: ε ...
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SynopsisWe study the asymptotic behaviour asx→∞ of the solutions of the ordinary differential equation problemThis equation generalises the ordinary differential equation obtained by studying the blow-up of the similarity solutions of the... more
SynopsisWe study the asymptotic behaviour asx→∞ of the solutions of the ordinary differential equation problemThis equation generalises the ordinary differential equation obtained by studying the blow-up of the similarity solutions of the semilinear parabolic partial differential equationvt=vxx=ev. We show that if λ≦1, all solutions of (*) tend to —∞ as rapidly as the function —exp (x2/4) (E- solutions). However, if λ>1, then there also exists a solution which tends to –∞, like 2λlog(x) (L-solutions). Thus, the case λ = 1, for which (*) reduces tothe Kassoy equation, is the borderline between two quite different forms of asymptotic behaviour of the functionu(x).
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... [15] Andrei Zaharescu, Edmond Boyer, Kiran Varanasi, and Radu P. Horaud. Surface featuredetection and description with applications to mesh matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,... more
... [15] Andrei Zaharescu, Edmond Boyer, Kiran Varanasi, and Radu P. Horaud. Surface featuredetection and description with applications to mesh matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Miami Beach, Florida, June 2009. ...
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... Kavousian, Simon Fraser University (skavousi@math.sfu.ca) Michael Lamoureux, University of Calgary (mikel@math.ucalgary.ca) Joshua Madden, University of ... Written by Chris Budd, University of Bath (cjb@maths.bath.ac.uk) John... more
... Kavousian, Simon Fraser University (skavousi@math.sfu.ca) Michael Lamoureux, University of Calgary (mikel@math.ucalgary.ca) Joshua Madden, University of ... Written by Chris Budd, University of Bath (cjb@maths.bath.ac.uk) John Stockie, Simon Fraser University (jms@cs.sfu ...
We consider the steady motion of space charge from an injecting electrode to an earthed electrode in both a gas and a dielectric. Three models governing the process of charge injection from the electrode into the medium are compared and... more
We consider the steady motion of space charge from an injecting electrode to an earthed electrode in both a gas and a dielectric. Three models governing the process of charge injection from the electrode into the medium are compared and the resulting voltage–current characteristics calculated. In particular we examine injection laws in which the electric field, charge or current are specified. It is shown that if the injecting electrode is small in comparison to the underlying geometry then the resulting field distribution is almost independent of the injection process. The stability of the three models is compared and it is shown that the field specified and charge specified models are always stable. The calculations are performed exactly for the case of a symmetric problem and make use of the Deutsch approximation for a needle-plane geometry.
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SynopsisAsymptotic estimates are established for nontrivial positive radial eigenfunctions of the nonlinear eigenvalue problem −Δu= λ(up−uq) in the unit ballBin ℝN(N> 2) with Neumann boundary conditions, as the supremum norm tends to... more
SynopsisAsymptotic estimates are established for nontrivial positive radial eigenfunctions of the nonlinear eigenvalue problem −Δu= λ(up−uq) in the unit ballBin ℝN(N> 2) with Neumann boundary conditions, as the supremum norm tends to infinity. Herepis the critical Sobolev exponent (N+ 2)/(N− 2) and 0 <q<p− 1 = 4/(N− 2).
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SynopsisWe study the asymptotic behaviour asx→∞ of the solutions of the ordinary differential equation problemThis equation generalises the ordinary differential equation obtained by studying the blow-up of the similarity solutions of the... more
SynopsisWe study the asymptotic behaviour asx→∞ of the solutions of the ordinary differential equation problemThis equation generalises the ordinary differential equation obtained by studying the blow-up of the similarity solutions of the semilinear parabolic partial differential equationvt=vxx=ev. We show that if λ≦1, all solutions of (*) tend to —∞ as rapidly as the function —exp (x2/4) (E- solutions). However, if λ>1, then there also exists a solution which tends to –∞, like 2λlog(x) (L-solutions). Thus, the case λ = 1, for which (*) reduces tothe Kassoy equation, is the borderline between two quite different forms of asymptotic behaviour of the functionu(x).
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One of the most interesting properties of an impacting system is the possibility of an infinite number of impacts occurring in a finite time (such as a ball bouncing to rest on a table). Such behaviour is usually called chatter. In this... more
One of the most interesting properties of an impacting system is the possibility of an infinite number of impacts occurring in a finite time (such as a ball bouncing to rest on a table). Such behaviour is usually called chatter. In this paper we make a systematic study of chattering behaviour for a periodically forced, single-degree-of-freedom impact oscillator with a restitution law for each impact. We show that chatter can occur for such systems and we compute the sets of initial data which always lead to chatter. We then show how these sets determine the intricate form of the domains of attraction for various types of asymptotic periodic motion. Finally, we deduce the existence of periodic motion which includes repeated chattering behaviour and show how this motion is related to certain types of chaotic behaviour.
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Read the latest and join the debate! Issue 15 May 2001 Contents Features Why knot: knots, molecules and stick numbers Backgammon, doubling the stakes, and Brownian motion How big is the Milky Way? RIP Claude Shannon Career interview... more
Read the latest and join the debate! Issue 15 May 2001 Contents Features Why knot: knots, molecules and stick numbers Backgammon, doubling the stakes, and Brownian motion How big is the Milky Way? RIP Claude Shannon Career interview Career interview: Systems administrator ...
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... T he A rtis Problem Chris Budd, Mark Peletier, Geertje Hek, David Iron, Andre Leger, Edi Cahyono, Ignacio Guerra, Paul Dario Toasa, JF Williams. Abstract. ... Detailed Anal sis In this section we will examine each term in (4) and find... more
... T he A rtis Problem Chris Budd, Mark Peletier, Geertje Hek, David Iron, Andre Leger, Edi Cahyono, Ignacio Guerra, Paul Dario Toasa, JF Williams. Abstract. ... Detailed Anal sis In this section we will examine each term in (4) and find estimates of each one. .1. Energ Inputs. ...
ABSTRACT
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National Air Traffic Services (NATS) are concerned with ensuring low probabilities of errors in determining aircraft positions. In general, error probabilities depend on the tails of some probability distributions for which there has been... more
National Air Traffic Services (NATS) are concerned with ensuring low probabilities of errors in determining aircraft positions. In general, error probabilities depend on the tails of some probability distributions for which there has been no theoretical model. Analysis of radar ...
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Airbus UK are concerned with designing efficient wings for aircraft. In the design process, the aerodynamic load on the wing is calculated for various configurations including different Mach numbers and angles of attack. The aerodynamic... more
Airbus UK are concerned with designing efficient wings for aircraft. In the design process, the aerodynamic load on the wing is calculated for various configurations including different Mach numbers and angles of attack. The aerodynamic load is calculated from the ...