Dettmann, Carl - Department of Mathematics, University of Bristol

• Optical microdisk resonator with a small scatterer C.P. Dettmann1,3
• Statistical mechanics solution sheet 8 | ^A = ^A| = | ^A
• APDE2 2011 Problems 8 The 1D wave equation. Hand in at 10am lecture on 5th May: Q. 1, 4, 6.
• Field dependence of Lyapunov exponents for nonequilibrium systems G. P. Morriss and C. P. Dettmann
• Department of Mathematics Third and Fourth Year
• General relativity solution sheet 4 1. Use ~a ~ b = g a b where g is a diagonal matrix with entries (1; 1; 1; 1).
• VOLUME 78, NUMBER 22 P HY S I CA L REV I EW L E T T ER S 2 JUNE 1997 Stability Ordering of Cycle Expansions
• Hamiltonian Formulation of the Gaussian Isokinetic Thermostat C. P. Dettmann and G. P. Morriss
• Computing the diffusion coefficient for intermittent maps: Resummation of stability ordered cycle expansions
• Statistical mechanics problem sheet 9 1. A quantum system has three single particle states with energies j, j = 1, 2, 3.
• Special Relativity Sheet 4 are both components of tensors, show that
• Recent extensions of periodic orbit theory C. P. Dettmann
• General relativity problem sheet 2 1. Which of the following are valid equations using the Einstein Sum-
• Directional emission from an optical microdisk resonator with a point scatterer
• 00224715/02/11000747/0 2002 Plenum Publishing Corporation Journal of Statistical Physics, Vol. 109, Nos. 3/4, November 2002 ( 2002)
• General Relativity 1 Introduction 1
• Note on chaos and diffusion C. P. Dettmann
• General relativity solution sheet 3 1. Kepler's second law states that the planets move such that the area per
• 0022-4715/02/1100-0747/0 2002 Plenum Publishing Corporation Journal of Statistical Physics, Vol. 109, Nos. 3/4, November 2002 ( 2002)
• VOLUME 78, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 10 MARCH 1997 Self-Similar Magnetoresistance of a Semiconductor Sinai Billiard
• General relativity solution sheet 1 1. Einstein did the hard work (until June 1915) getting an almost correct
• Sticky and Non-sticky open Mushrooms {Orestis Georgiou, Carl P. Dettmann} School of Mathematics
• Mathematical Methods 3 2006 Sheet C Characteristics/Initial conditions/Solutions
• Mathematical Methods 3 2006 Sheet F Laplace Transforms
• General relativity solution sheet 1 1. Einstein did the hard work (until June 1915) getting an almost correct
• MATHS 1EM (ETC.): EXERCISES 12 Maths 1EM (etc.): Exercises 12
• Statistical mechanics solution sheet 5 1. The curves of constant energy are
• MATHS 1EM (ETC.): SOLUTIONS 19 Maths 1EM (etc.): Solutions 19
• MATHS 1EM (ETC.): SOLUTIONS 18 Maths 1EM (etc.): Solutions 18
• Statistical mechanics problem sheet 4 1. A time-dependent frictional force called a "Gaussian thermostat" is sometimes
• General relativity problem sheet 7 1. Find the transformation law for connection coecients, which is not
• MATHS 1EM (ETC.): SOLUTIONS 14 Maths 1EM (etc.): Solutions 14
• General relativity problem sheet 2 1. Which of the following are valid equations using the Einstein Sum-
• CONTENTS 1 INTRODUCTION General Relativity
• MATHS 1EM (ETC.): EXERCISES 11 Maths 1EM (etc.): Exercises 11
• Statistical mechanics solution sheet 7 1. At low temperatures, there are two rotational modes (since a linear molecule), so
• MATHS 1EM (ETC.): SOLUTIONS 13 Maths 1EM (etc.): Solutions 13
• Mathematical Methods 3 2006 Sheet I Green's functions for ODE's
• Mathematical Methods 3 2006 Sheet B Classification of PDE's and canonical forms
• General relativity solution sheet 2 1. The rst equation reads
• Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps
• Traces and determinants of strongly stochastic operators C. P. Dettmann*
• Mathematical Methods 3 2006 Sheet H Generalised Functions
• General relativity problem sheet 6 1. Find metrics for the following surfaces embedded in IR 3
• APDE2 2011 Solutions 9 1. (a) The PDE is ut + tux = 0 with I.C. u(x, 0) = e-x2
• Statistical mechanics problem sheet 1 Unstarred problems follow quickly from definitions and equations in the lectures; single
• Mathematical Methods 3 2006 Sheet A Revision
• nonequilibrium Rockefeller
• Microscopic chaos from Brownian motion? In a recent Letter in Nature, Gaspard et al. [1] claimed to present empirical
• Open Circular Billiards and the Riemann Hypothesis Southeast Applied Analysis Center, Georgia Institute Technology, Atlanta, Georgia 303321060, USA
• APDE2 2011 Solutions 7 1. (a) With the choice of f (x), the solution reduces to u(x, t) =
• Microdisk Resonators with Two Point Scatterers C. P. Dettmann1
• Escape from a circle and Riemann hypotheses Leonid A Bunimovich 1 and Carl P Dettmann 2
• Special Relativity Sheet 3 is the matrix that generates the Lorentz transformation from S to
• Open Mushrooms: Stickiness revisited Carl P. Dettmann 1
• Statistical mechanics problem sheet 5 1. Calculate the Boltzmann entropy and hence temperature of a 1D harmonic oscil-
• Special Relativity Sheet 5 1. Prove that the 4-velocity and 4-momentum are 4-vectors. Explain why
• Mathematical Methods 3 2006 Sheet I Green's functions for ODE's
• General relativity problem sheet 9 This counts as ve questions for credit purposes. The marking scheme is as
• General relativity solution sheet 9 Here is a sample essay, with relevant points marked by stars* -please don't put these in
• 1 INTRODUCTION 1 Introduction
• The work reported in this paper was supported by the EPSRC grant EP/C515137/1. TM and TE Directional Modes of an Optical Microdisk Resonator
• Special relativity problem sheet 1 In the following questions, S and S0 will denote inertial frames in stan-
• Statistical mechanics problem sheet 7 1. The main component of Venus's atmosphere, carbon dioxide, is a linear molecule
• Statistical mechanics solution sheet 3 1. No, the entropy diverges in the limit T 0 (see problem 2.6). The third law is
• Mathematical Methods 3 2006 Sheet C Characteristics/Initial conditions/Solutions
• Fractal asymptotics C. P. Dettmann
• Mathematical Methods 3 2006 Sheet E Fourier Transforms for PDEs
• General relativity problem sheet 1 Unstarred problems follow quickly from de nitions and equations in the lec-
• Stable synchronised states of coupled Tchebysche maps
• THERMOSTATS: Application
• Statistical mechanics problem sheet 2 1. Sketch a Carnot cycle in (S, T) space.
• Hamiltonian for a restricted isoenergetic thermostat C. P. Dettmann
• Hamiltonian reformulation and pairing of Lyapunov exponents for Nose Hoover dynamics C. P. Dettmann and G. P. Morriss
• General relativity problem sheet 8 1. For the linearised theory, show that
• Mathematical Methods 3 2006 Sheet E Fourier Transforms for PDEs
• Asymmetric transport in the bouncer model: mixed, time dependent, noncompact dynamics.
• APDE2 2011 Solutions 10 1. (a) Here there are zero boundary conditions for x = 0 and x = 1.
• Escape of particles in a time dependent potential well Diogo Ricardo Costa1
• VIEW FROM THE PENNINES: A COSMIC INDIAN ROPE TRICK
• Mathematical Methods 3 2006 Sheet D Fourier Transforms
• Internal and External Resonances of Dielectric Disks C. P. Dettmann1
• Microscopic chaos and diffusion C. P. Dettmann and E. G. D. Cohen
• Hamiltonian for a restricted isoenergetic thermostat C. P. Dettmann
• Analogy of PDE classification with classification of conic This sheet provides the motivation behind the terminology used for classifying PDE's and par
• Unidirectional Emission from Circular Dielectric Microresonators with a Point C. P. Dettmann1
• Statistical mechanics solution sheet 4 by a straightforward substitution.
• MATHS 1EM (ETC.): EXERCISES 19 Maths 1EM (etc.): Exercises 19
• MATHS 1EM (ETC.): EXERCISES 16 Maths 1EM (etc.): Exercises 16
• General relativity solution sheet 3 1. Kepler's second law states that the planets move such that the area per
• General relativity solution sheet 2 1. The first equation reads
• General relativity problem sheet 5 1. (a) If A = B C , A transforms under change of basis in SR as a
• perturbation Cvitanovi' c,
• The existence of Burnett coefficients in the periodic Lorentz gas
• General relativity solution sheet 5 1. (a) We have A =
• Statistical mechanics solution sheet 9 1. The grand partition function is the sum over states of zN
• PDEs in Three Dimensions 7.1 Equilibrium Solutions: Laplace's Equation.
• MATHS 1EM (ETC.): SOLUTIONS 17 Maths 1EM (etc.): Solutions 17
• APDE2 2011 Problems 6 Fourier Transforms Hand in at 3pm lecture on Monday 21st March: Q. 1, 6, 7, 9.
• General relativity problem sheet 4 1. Show that the dot product of 4-vectors satisfies
• Carl Dettmann 4 lectures in October 2003
• The Burnett expansion of the periodic Lorentz gas C. P. Dettmann \Lambda
• General relativity solution sheet 6 1. (a) We have
• Special Relativity Sheet Two 1. Two clocks, A and B, move with constant velocities. They meet momentarily, when
• Mathematical Methods 3 2006 Sheet D Fourier Transforms
• MATHS 1EM (ETC.): SOLUTIONS 16 Maths 1EM (etc.): Solutions 16
• Product of n independent Uniform Random Variables Carl P. Dettmann 1
• First Order PDEs 6.1 Characteristics
• General relativity solution sheet 7 1. Given the fact that the covariant derivative of a vector
• Statistical mechanics problem sheet 6 1. Derive the canonical ensemble (in a discrete form) from a variational principle
• Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport
• VOLUME 78, NUMBER 10 P HY S I CA L REV I EW L E T T ER S 10 MARCH 1997 SelfSimilar Magnetoresistance of a Semiconductor Sinai Billiard
• Mathematical Methods 3 2006 Sheet B Classification of PDE's and canonical forms
• General relativity solution sheet 5 1. (a) We have A 0 =
• The Lorentz gas: A paradigm for nonequilibrium stationary states
• Statistical mechanics problem sheet 3 1. Does an ideal gas satisfy the third law of thermodynamics? Explain.
• Traces and determinants of strongly stochastic operators C. P. Dettmann*
• General relativity solution sheet 8 1. (a) The upper components of the metric correspond to the matrix inverse.
• Applied Mathematics 2 1 Introduction
• General relativity solution sheet 7 1. Given the fact that the covariant derivative of a vector
• General relativity problem sheet 4 1. Show that the dot product of 4-vectors satis es
• Mathematical Methods 3 2006 Sheet J Green's functions for PDE's
• Statistical mechanics solution sheet 2 1. The isothermal transformations are at constant T and the adiabatic transforma-
• Mathematical Methods 3 2006 Sheet A Revision
• MATHS 1EM (ETC.): EXERCISES 18 Maths 1EM (etc.): Exercises 18
• Stochastic dynamics of relativistic turbulence C. P. Dettmann and N. E. Frankel
• Proof of Lyapunov exponent pairing for systems at constant kinetic energy C. P. Dettmann and G. P. Morriss
• Hamiltonian formulation of the Gaussian isokinetic thermostat C. P. Dettmann and G. P. Morriss
• Crisis in the periodic Lorentz gas C. P. Dettmann* and G. P. Morriss
• Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics C. P. Dettmann and G. P. Morriss
• VOLUME 78, NUMBER 22 P H Y S I C A L R E V I E W L E T T E R S 2 JUNE 1997 Stability Ordering of Cycle Expansions
• January 29, 2004 12:0 WSPC/INSTRUCTION FILE SPRADO International Journal of Modern Physics D
• Open Circular Billiards and the Riemann Hypothesis L. A. Bunimovich
• Open circular billiards and the Riemann Hypothesis
• J Stat Phys (2007) 128: 13211336 DOI 10.1007/s10955-007-9365-2
• Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time
• OPTICAL MICRODISK RESONATOR WITH A SMALL BUT FINITE SIZE C. P. Dettmann 1
• Survival Probability for the Stadium Billiard Carl P. Dettmann 1
• Asymptotic expansions for the escape rate of stochastically perturbed dynamical systems
• The work reported in this paper was supported by the EPSRC grant EP/C515137/1. Systematization of All Resonance Modes in
• Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport.
• New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis
• Open billiards and Applications Carl P. Dettmann (Bristol)
• 8 INTEGRATION Mathematics 1EM/1ES/1FM/1FS Notes, weeks 13-17
• MATHS 1EM (ETC.): EXERCISES 13 Maths 1EM (etc.): Exercises 13
• MATHS 1EM (ETC.): SOLUTIONS 11 Maths 1EM (etc.): Solutions 11
• MATHS 1EM (ETC.): SOLUTIONS 12 Maths 1EM (etc.): Solutions 12
• 12 MATRICES Mathematics 1EM/1ES/1FM/1FS Notes, weeks 18-23
• APDE2 2011 Problems 7 Fourier Transforms Hand in at 3pm lecture on Monday 28st March: Q. 1, 2.
• APDE2 2011 Problems 9 1st order PDE's. Traffic Flow Hand in at 10am lecture on 12th May: Q. 1, 4, 6.
• APDE2 2011 Problems 10 Normal Modes, Polar Coordinates Voluntary hand in on 16th May: Q. 1, 2, 4.
• APDE2 2011 Solutions 5 1. (a) Look for a solution of the form (x, y) = X(x)Y(y). Then xx = X(x)Y(y) and
• APDE2 2011 Solutions 6 1. (a) Because f = 0 for x < 0 and x > a, we have f =
• APDE2 2011 Solutions 8 1. The solution is u = f (x -ct) + g(x + ct), and since ut(x, 0) 0, we have (as shown in
• 1D PDE's on infinite Domains: Fourier PDE's on infinite domains need a new technique.
• The Wave Equation in One Dimension We concentrate on the wave equation
• General relativity problem sheet 1 Unstarred problems follow quickly from definitions and equations in the lec-
• General relativity problem sheet 3 1. State Kepler's second law, and give its physical significance. Do you
• General relativity solution sheet 4 1. Use ab = ga
• General relativity problem sheet 5 1. (a) If A = BC
• General relativity problem sheet 7 1. Find the transformation law for connection coefficients, which is not
• General relativity problem sheet 8 1. For the linearised theory, show that
• General relativity problem sheet 9 This counts as five questions for credit purposes. The marking scheme is as
• General relativity solution sheet 9 Here is a sample essay, with relevant points marked by stars* -please don't put these in
• 1.1 Books 1 INTRODUCTION General Relativity
• 1.1 Thermodynamic systems 1 THERMODYNAMICS Statistical Mechanics
• 1 INTRODUCTION 1 Introduction
• Mathematical Methods 3 2006 Sheet F Laplace Transforms
• Mathematical Methods 3 2006 Sheet H Generalised Functions
• Statistical mechanics solution sheet 6 1. (a) Use i for /i for shorthand.
• MATHS 1EM (ETC.): EXERCISES 14 Maths 1EM (etc.): Exercises 14
• Escape from a circle and Riemann hypotheses Leonid A Bunimovich1
• January 16, 2004 9:6 WSPC/Trim Size: 9.75in x 6.5in for Proceedings cmb STOCHASTIC STABILIZATION OF THE COSMIC MICROWAVE
• General Relativity 1 Introduction 1
• INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 37 (2004) L377L383 PII: S0305-4470(04)78396-1
• Statistical mechanics solution sheet 1 1. The solar system is open, as it transfers energy and particles to the environment.
• MATHS 1EM (ETC.): EXERCISES 17 Maths 1EM (etc.): Exercises 17
• Analogy of PDE classification with classification of conic This sheet provides the motivation behind the terminology used for classifying PDE's and par-
• General relativity problem sheet 3 1. State Kepler's second law, and give its physical signi cance. Do you
• Proof of Lyapunov Exponent Pairing for Systems at Constant Kinetic Energy C. P. Dettmann and G. P. Morriss
• Averaging systems with quasiperiodic forcing C.P. Dettmann and T.B. Howard1
• Statistical mechanics problem sheet 8 1. Show that | =
• Scaling invariance for the escape of particles from a periodically corrugated waveguide
• Quantifying intermittency in the open drivebelt billiard Carl P. Dettmann1
• Recurrence of particles in static and time varying oval billiards Edson D. Leonel1
• Quantum Billiards Martin Sieber (Bristol)
• Impact of Boundaries on Fully Connected Random Geometric Networks Justin Coon,1
• Known results New "results" Skeletons of arguments Other models Phenomena Lecture II: Intermittency in planar billiards
• Where to place a hole to achieve a maximal diffusion coefficient Georgie Knight,1, a)
• Connectivity of Confined Dense Networks: Boundary Effects and Scaling Laws
• Ergodicity of a single particle confined in a nanopore Stefano Bernardi
• Open circle maps: Small hole asymptotics Carl Dettmann