Neutron stars as laboratories for exotic physics
|
|
- Dominic Washington
- 8 years ago
- Views:
Transcription
1 Ian Jones Neutron stars as laboratories for exotic physics 1/20 Neutron stars as laboratories for exotic physics Ian Jones General Relativity Group, Southampton University
2 Context Ian Jones Neutron stars as laboratories for exotic physics 2/20 Many different physical inputs required to build a realistic neutron star model: Shear modulus and breaking strain of crust (and core?). Thermal and electrical and viscosity coefficients. Superfluidity/superconductivity. High density equation of state P = P(ρ, T). All in the context of a rapidly rotating relativistic object.
3 Overview Ian Jones Neutron stars as laboratories for exotic physics 3/20 Will concentrate on the role of superfluidity in two particular contexts: 1. Free precession & radio astronomy. 2. Steady rotation & gravitational wave astronomy.
4 Basics: Superfluid neutron stars Ian Jones Neutron stars as laboratories for exotic physics 4/20 Can model star as a mixture of 1. Superfluid neutrons 2. Charged particles (protons & electrons) The superfluid neutrons rotate by forming an array of vortices: Ω x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
5 Evidence for vorticity: glitches Ian Jones Neutron stars as laboratories for exotic physics 5/20 Some spinning neutron stars undergo occasional glitches. Leading theory relies on pinned vorticity: some of the superfluid vortices are rigidly attached to the solid phase, preventing them from undergoing smooth spindown. When a sufficiently large angular velocity lag has built up catastrophic unpinning occurs, corotation is established, spinning up the charged part of the star.
6 Part 1: Free precession & radio astronomy Ian Jones Neutron stars as laboratories for exotic physics 6/20 Free precession is the most general motion of a rigid body. Classically, determined by moment of inertia tensor I ab. Characteristic timescale of order P fp P ǫ, where ǫ is dimensionless asymmetry in I ab. P fp months years for a typical pulsar.
7 Free precession plus superfluidity Ian Jones Neutron stars as laboratories for exotic physics 7/20 A pinned superfluid component changes the picture radically. Angular momentum now given by J a = I ab Ω b + J SF a. The pinned superfluid acts like a gyroscope, sewn into the star (Shaham 1977). Find P fp minutes or less!
8 The free precession conundrum Ian Jones Neutron stars as laboratories for exotic physics 8/20 Best evidence for precession comes from PSR B , with P fp 500 days! (Stairs, Shemar & Lyne 2000). What is going on? Do we need to redraw our picture of neutron star interiors? (Link 2006)
9 Vortex dynamics Ian Jones Neutron stars as laboratories for exotic physics 9/20 Vortices are acted upon by two forces: 1. A Magnus force, sourced by v vortex a v n a difference 2. A drag force, R(va vortex va), p caused by charged/magnetic component scattering off the vortex core. This results in a mutual friction force, fa MF, coupling the neutrons and protons: dv n a dt dva p dt = a (µ n + Φ) + f MF a, = a (µ p + Φ) fa MF /x p We therefore have a two-component coupled system.
10 An instability Ian Jones Neutron stars as laboratories for exotic physics 10/20 Consider a rotating star, and allow the protons to have some velocity w along the neutron vortices. Find a short wavelength instability for sufficiently fast relative flow, e.g. in weak drag limit (Sidery, Andersson & Comer, 2008): w > 2Ωn k This corresponds to perturbation having a speed intermediate between the neutron and proton fluids; analogue of Donnelly-Glaberson instability in helium. Will this instability occur in neutron stars?
11 Free precession and the instability Ian Jones Neutron stars as laboratories for exotic physics 11/20 Free precession automatically generates a flow w along the vortices. Find that, for sufficiently strong drag, precession triggers the instability, (probably) destroying the pinning (Glampedakis, Andersson & DIJ, 2008). So, premature to conclude that conventional view of neutron star interior is wrong! To make progress, need to: 1. Obtain more realistic model of vortex dynamics. 2. Investigate instability in non-linear regime.
12 Overview Ian Jones Neutron stars as laboratories for exotic physics 12/20 Will concentrate on the role of superfluidity in two particular contexts: 1. Free precession & radio astronomy. 2. Steady rotation & gravitational wave astronomy.
13 Part 2: Steady rotation & gravitational wave astronomy Ian Jones Neutron stars as laboratories for exotic physics 13/20 So much for the precessional solutions. We already know about their GW significance: If no precesion in radio data, look only at 2Ω. If precession in radio data, look at multiple frequencies. (e.g. DIJ & Andersson 2000, Van Den Broeck 2005). Let s think about the (simpler) case of non-precessional ones, from the gravitational wave point of view. Will model the star as a triaxial body containing a pinned superfluid component.
14 The steady rotation solutions Ian Jones Neutron stars as laboratories for exotic physics 14/20 Can identify non-precessional solution as one where Ω C a is parallel to J a. Can then plug this motion into mass quadrupole approximation to General Relativity to calculate GW emission (Jones 2009). Key quantities are the multipole moments: Q lm = δρ lm (r)r l+2 dr. Tedious calculation leads to Q 21 and Q 22 in terms of stellar parameters. Key point is that both Q 21 and Q 22 non-zero if pinning axis doesn t coincide with a principal axis of I ab.
15 The gravitational wave emission Ian Jones Neutron stars as laboratories for exotic physics 15/20 Find components at both f and 2f. Signal-to-noise ratio is of the form ρ = h T obs Sh (f gw ), which leads to ρ Ω (ι) = ρ 2Ω (ι) = A Sh (Ω) Q 21 sinι(1 + cos 2 ι) 1/2, A Sh (2Ω) Q 22 2[(1 + cos 2 ι) cos 2 ι] 1/2, where ( π A = 4 15 ) 1/2 T 1/2 obs Ω2.
16 The gravitational wave emission cont... Ian Jones Neutron stars as laboratories for exotic physics 16/20 Pictorially: 4 2 K2 K K2 K4 In sky-averaged sense, Q 22 is about 4 times stronger than Q 21. Conversely, for a source of known spin-down rate, a Q 21 -dominated source is about 2 times stronger than a Q 22 -dominated one.
17 What limits the wave emission? Ian Jones Neutron stars as laboratories for exotic physics 17/20 There are a number of possible limiting factors: Finite breaking strain of crust. Finite strength of pinning. Superfluid vortex instabilities. None of these seem to be killers (Jones 2009).
18 Significance for GW searches Ian Jones Neutron stars as laboratories for exotic physics 18/20 Crucial point is multiple frequency GW emission possible, even if rotation appears to be completely steady. Of interest for both targeted and all-sky blind searches. Ω component intrinsically not as strong as 2Ω one. Exist addition failure mechanisms as compared to 2Ω case. Signal more complex than conventional 2Ω one. Will presumably need large SNR for confident detection. Computational burden of search very low.
19 Open issue Ian Jones Neutron stars as laboratories for exotic physics 19/20 Open issue: will necessary asymmetry exist in Nature? Where or not multiple frequency search ultimately worthwhile depends upon what sources Nature chooses to provide. I would argue certainly worth looking for: existence of Q 21 multipole doesn t seem any less plausible than Q 22 one! Need to break axisymmetry in either case. Magentic field might be the symmetry breaking agent.
20 Summary Ian Jones Neutron stars as laboratories for exotic physics 20/20 1. Precession: Existing radio observations of precession have provoked lively debate. They seem to imply that either our existing model of neutron star interiors is seriously flawed or vortex instabilities are operative. 2. Steady rotation: Multiple frequency GW emission possible, even if rotation appears to be completely steady. An observation of multiple frequency GW emission from a steadily rotating star would provide evidence in favour of pinned superfluidity.
X-ray observations and nuclear physics of GW-driven r-modes
X-ray observations and nuclear physics of GW-driven r-modes Wynn Ho University of Southampton, UK Nils Andersson Ian Jones University of Southampton, UK Nathalie Degenaar University of Michigan, USA Bryn
More informationPrecession of spin and Precession of a top
6. Classical Precession of the Angular Momentum Vector A classical bar magnet (Figure 11) may lie motionless at a certain orientation in a magnetic field. However, if the bar magnet possesses angular momentum,
More informationGravitomagnetism and complex orbit dynamics of spinning compact objects around a massive black hole
Gravitomagnetism and complex orbit dynamics of spinning compact objects around a massive black hole Kinwah Wu Mullard Space Science Laboratory University College London United Kingdom kw@mssl.ucl.ac.uk
More informationLet s first see how precession works in quantitative detail. The system is illustrated below: ...
lecture 20 Topics: Precession of tops Nutation Vectors in the body frame The free symmetric top in the body frame Euler s equations The free symmetric top ala Euler s The tennis racket theorem As you know,
More informationLecture L22-2D Rigid Body Dynamics: Work and Energy
J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for
More informationBasic Equations, Boundary Conditions and Dimensionless Parameters
Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were
More informationHeating & Cooling in Molecular Clouds
Lecture 8: Cloud Stability Heating & Cooling in Molecular Clouds Balance of heating and cooling processes helps to set the temperature in the gas. This then sets the minimum internal pressure in a core
More informationDimensional Analysis
Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationPhysics of the Atmosphere I
Physics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uni-heidelberg.de heidelberg.de Last week The conservation of mass implies the continuity equation:
More information11 Navier-Stokes equations and turbulence
11 Navier-Stokes equations and turbulence So far, we have considered ideal gas dynamics governed by the Euler equations, where internal friction in the gas is assumed to be absent. Real fluids have internal
More informationDynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 5_31_2012 Goals for Chapter
More informationBasic Principles in Microfluidics
Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces
More informationLecture L29-3D Rigid Body Dynamics
J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 2.0 Lecture L29-3D Rigid Body Dynamics 3D Rigid Body Dynamics: Euler Angles The difficulty of describing the positions of the body-fixed axis of
More information1 The basic equations of fluid dynamics
1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which
More informationElliptical Galaxies. Houjun Mo. April 19, 2004. Basic properties of elliptical galaxies. Formation of elliptical galaxies
Elliptical Galaxies Houjun Mo April 19, 2004 Basic properties of elliptical galaxies Formation of elliptical galaxies Photometric Properties Isophotes of elliptical galaxies are usually fitted by ellipses:
More informationLecture L30-3D Rigid Body Dynamics: Tops and Gyroscopes
J. Peraire, S. Widnall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L30-3D Rigid Body Dynamics: Tops and Gyroscopes 3D Rigid Body Dynamics: Euler Equations in Euler Angles In lecture 29, we introduced
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables τ
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationDimensional Analysis, hydraulic similitude and model investigation. Dr. Sanghamitra Kundu
Dimensional Analysis, hydraulic similitude and model investigation Dr. Sanghamitra Kundu Introduction Although many practical engineering problems involving fluid mechanics can be solved by using the equations
More informationContents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationIndiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.
.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations
More informationNotes on Polymer Rheology Outline
1 Why is rheology important? Examples of its importance Summary of important variables Description of the flow equations Flow regimes - laminar vs. turbulent - Reynolds number - definition of viscosity
More informationChapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations
Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.
More informationWhite Dwarf Properties and the Degenerate Electron Gas
White Dwarf Properties and the Degenerate Electron Gas Nicholas Rowell April 10, 2008 Contents 1 Introduction 2 1.1 Discovery....................................... 2 1.2 Survey Techniques..................................
More informationLecture 8 - Turbulence. Applied Computational Fluid Dynamics
Lecture 8 - Turbulence Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Turbulence What is turbulence? Effect of turbulence
More informationGravity Field and Dynamics of the Earth
Milan Bursa Karel Pec Gravity Field and Dynamics of the Earth With 89 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo HongKong Barcelona Budapest Preface v Introduction 1 1 Fundamentals
More information= = GM. v 1 = Ωa 1 sin i.
1 Binary Stars Consider a binary composed of two stars of masses M 1 and We define M = M 1 + and µ = M 1 /M If a 1 and a 2 are the mean distances of the stars from the center of mass, then M 1 a 1 = a
More informationFluids and Solids: Fundamentals
Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.
More informationState of Stress at Point
State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,
More information3 Vorticity, Circulation and Potential Vorticity.
3 Vorticity, Circulation and Potential Vorticity. 3.1 Definitions Vorticity is a measure of the local spin of a fluid element given by ω = v (1) So, if the flow is two dimensional the vorticity will be
More informationChapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any
Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass
More informationSpecific Intensity. I ν =
Specific Intensity Initial question: A number of active galactic nuclei display jets, that is, long, nearly linear, structures that can extend for hundreds of kiloparsecs. Many have two oppositely-directed
More informationElectric Dipole moments as probes of physics beyond the Standard Model
Electric Dipole moments as probes of physics beyond the Standard Model K. V. P. Latha Non-Accelerator Particle Physics Group Indian Institute of Astrophysics Plan of the Talk Parity (P) and Time-reversal
More informationChapter 4. Dimensionless expressions. 4.1 Dimensional analysis
Chapter 4 Dimensionless expressions Dimensionless numbers occur in several contexts. Without the need for dynamical equations, one can draw a list (real or tentative) of physically relevant parameters,
More informationManufacturing Equipment Modeling
QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Elliptic Flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 2 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables.
More informationLecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is
Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of
More informationarxiv:gr-qc/9409057v1 27 Sep 1994
Gravitational Radiation from Nonaxisymmetric Instability in a Rotating Star J. L. Houser, J. M. Centrella, and S. C. Smith Department of Physics and Atmospheric Science, Drexel University, Philadelphia,
More informationLecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows
Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3.- 1 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical
More informationF en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself.
The Electron Oscillator/Lorentz Atom Consider a simple model of a classical atom, in which the electron is harmonically bound to the nucleus n x e F en = mω 0 2 x origin resonance frequency Note: We should
More informationUNIVERSITETET I OSLO
UNIVERSITETET I OSLO Det matematisk-naturvitenskapelige fakultet Exam in: FYS 310 Classical Mechanics and Electrodynamics Day of exam: Tuesday June 4, 013 Exam hours: 4 hours, beginning at 14:30 This examination
More informationContents. Goldstone Bosons in 3He-A Soft Modes Dynamics and Lie Algebra of Group G:
... Vlll Contents 3. Textures and Supercurrents in Superfluid Phases of 3He 3.1. Textures, Gradient Energy and Rigidity 3.2. Why Superfuids are Superfluid 3.3. Superfluidity and Response to a Transverse
More informationFluid Mechanics: Static s Kinematics Dynamics Fluid
Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three
More informationChapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.
Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems
More information1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids
1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
More informationCondensates in Neutron Star Interiors
Condensates in Neutron Star Interiors Vatsal Dwivedi submitted as a term essay for Phys 569 : Emergent States of Matter Dec 19, 2012 Abstract The pulsars, now identified as neutron stars, are one of the
More information1. Degenerate Pressure
. Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively
More informationStokes flow. Chapter 7
Chapter 7 Stokes flow We have seen in section 6.3 that the dimensionless form of the Navier-Stokes equations for a Newtonian viscous fluid of constant density and constant viscosity is, now dropping the
More informationLecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)
Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary
More informationLecture L3 - Vectors, Matrices and Coordinate Transformations
S. Widnall 16.07 Dynamics Fall 2009 Lecture notes based on J. Peraire Version 2.0 Lecture L3 - Vectors, Matrices and Coordinate Transformations By using vectors and defining appropriate operations between
More informationDynamics of Iain M. Banks Orbitals. Richard Kennaway. 12 October 2005
Dynamics of Iain M. Banks Orbitals Richard Kennaway 12 October 2005 Note This is a draft in progress, and as such may contain errors. Please do not cite this without permission. 1 The problem An Orbital
More informationLecture 2. Gravitational Waves from Binary Systems: Probes of the Universe. Historical importance of orbiting systems.
Gravitational Waves Notes for Lectures at the Azores School on Observational Cosmology September 2011 B F Schutz Albert Einstein Institute (AEI), Potsdam, Germany http://www.aei.mpg.de, Bernard.Schutz@aei.mpg.de
More informationOnboard electronics of UAVs
AARMS Vol. 5, No. 2 (2006) 237 243 TECHNOLOGY Onboard electronics of UAVs ANTAL TURÓCZI, IMRE MAKKAY Department of Electronic Warfare, Miklós Zrínyi National Defence University, Budapest, Hungary Recent
More informationFLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions
FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or
More informationExamples of magnetic field calculations and applications. 1 Example of a magnetic moment calculation
Examples of magnetic field calculations and applications Lecture 12 1 Example of a magnetic moment calculation We consider the vector potential and magnetic field due to the magnetic moment created by
More information4 Microscopic dynamics
4 Microscopic dynamics In this section we will look at the first model that people came up with when they started to model polymers from the microscopic level. It s called the Oldroyd B model. We will
More informationRadiation reaction for inspiralling binary systems with spin-spin
Radiation reaction for inspiralling binary systems with spin-spin coupling 1 Institute of Theoretical Physics, Friedrich-Schiller-University Jena December 3, 2007 1 H. Wang and C. M. Will, Phys. Rev. D,
More informationSo if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold.
Name: MULTIPLE CHOICE: Questions 1-11 are 5 points each. 1. A safety device brings the blade of a power mower from an angular speed of ω 1 to rest in 1.00 revolution. At the same constant angular acceleration,
More informationChapter 28 Fluid Dynamics
Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example
More informationFluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationthermal history of the universe and big bang nucleosynthesis
thermal history of the universe and big bang nucleosynthesis Kosmologie für Nichtphysiker Markus Pössel (vertreten durch Björn Malte Schäfer) Fakultät für Physik und Astronomie, Universität Heidelberg
More informationTheory of electrons and positrons
P AUL A. M. DIRAC Theory of electrons and positrons Nobel Lecture, December 12, 1933 Matter has been found by experimental physicists to be made up of small particles of various kinds, the particles of
More informationPractice final for Basic Physics spring 2005 answers on the last page Name: Date:
Practice final for Basic Physics spring 2005 answers on the last page Name: Date: 1. A 12 ohm resistor and a 24 ohm resistor are connected in series in a circuit with a 6.0 volt battery. Assuming negligible
More informationColumbia University Department of Physics QUALIFYING EXAMINATION
Columbia University Department of Physics QUALIFYING EXAMINATION Monday, January 13, 2014 1:00PM to 3:00PM Classical Physics Section 1. Classical Mechanics Two hours are permitted for the completion of
More informationBig Bang Cosmology. Big Bang vs. Steady State
Big Bang vs. Steady State Big Bang Cosmology Perfect cosmological principle: universe is unchanging in space and time => Steady-State universe - Bondi, Hoyle, Gold. True? No! Hubble s Law => expansion
More informationATM 316: Dynamic Meteorology I Final Review, December 2014
ATM 316: Dynamic Meteorology I Final Review, December 2014 Scalars and Vectors Scalar: magnitude, without reference to coordinate system Vector: magnitude + direction, with reference to coordinate system
More informationMasses in Atomic Units
Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents
More informationBroadband microwave conductance across the T=0 superconductor-resistive magnetic field tuned transition in InO x!
Broadband microwave conductance across the T=0 superconductor-resistive magnetic field tuned transition in InO x! N. Peter Armitage! Dept. of Physics and Astronomy! The Johns Hopkins University! Lidong
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More information8.1 Radio Emission from Solar System objects
8.1 Radio Emission from Solar System objects 8.1.1 Moon and Terrestrial planets At visible wavelengths all the emission seen from these objects is due to light reflected from the sun. However at radio
More informationMASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)
MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for non-physics majors, a GPA of 2.5 or better in at least 15 units in the following advanced
More informationThe rate of change of velocity with respect to time. The average rate of change of distance/displacement with respect to time.
H2 PHYSICS DEFINITIONS LIST Scalar Vector Term Displacement, s Speed Velocity, v Acceleration, a Average speed/velocity Instantaneous Velocity Newton s First Law Newton s Second Law Newton s Third Law
More informationOUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS
Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS 3 Be able to determine the behavioural characteristics and parameters of real fluid
More informationThe Viscosity of Fluids
Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et
More informationCompressible Fluids. Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004
94 c 2004 Faith A. Morrison, all rights reserved. Compressible Fluids Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004 Chemical engineering
More informationChapter 18: The Structure of the Atom
Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.
More informationGravitational waves from compact object binaries
Gravitational waves from compact object binaries Laboratoire Univers et Théories Observatoire de Paris / CNRS aligo, avirgo, KAGRA, elisa, ( DECIGO, ET,... ( Main sources of gravitational waves (GW) elisa
More information2. Spin Chemistry and the Vector Model
2. Spin Chemistry and the Vector Model The story of magnetic resonance spectroscopy and intersystem crossing is essentially a choreography of the twisting motion which causes reorientation or rephasing
More informationPresentation of problem T1 (9 points): The Maribo Meteorite
Presentation of problem T1 (9 points): The Maribo Meteorite Definitions Meteoroid. A small particle (typically smaller than 1 m) from a comet or an asteroid. Meteorite: A meteoroid that impacts the ground
More informationAPPLIED MATHEMATICS ADVANCED LEVEL
APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications
More informationA fundamental study of the flow past a circular cylinder using Abaqus/CFD
A fundamental study of the flow past a circular cylinder using Abaqus/CFD Masami Sato, and Takaya Kobayashi Mechanical Design & Analysis Corporation Abstract: The latest release of Abaqus version 6.10
More informationPerfect Fluids: From Nano to Tera
Perfect Fluids: From Nano to Tera Thomas Schaefer North Carolina State University 1 2 Perfect Fluids sqgp (T=180 MeV) Neutron Matter (T=1 MeV) Trapped Atoms (T=0.1 nev) 3 Hydrodynamics Long-wavelength,
More informationProblem #1 [Sound Waves and Jeans Length]
Roger Griffith Astro 161 hw. # 8 Proffesor Chung-Pei Ma Problem #1 [Sound Waves and Jeans Length] At typical sea-level conditions, the density of air is 1.23 1 3 gcm 3 and the speed of sound is 3.4 1 4
More informationImplementation of a flexible fiber model in a general purpose CFD code
Implementation of a flexible fiber model in a general purpose CFD code Jelena Andrić Supervisor: Håkan Nilsson Co-supervisors: Srdjan Sasic and Alf-Erik Almstedt Department of Applied Mechanics Chalmers
More informationProblem Set V Solutions
Problem Set V Solutions. Consider masses m, m 2, m 3 at x, x 2, x 3. Find X, the C coordinate by finding X 2, the C of mass of and 2, and combining it with m 3. Show this is gives the same result as 3
More informationTesting dark matter halos using rotation curves and lensing
Testing dark matter halos using rotation curves and lensing Darío Núñez Instituto de Ciencias Nucleares, UNAM Instituto Avanzado de Cosmología A. González, J. Cervantes, T. Matos Observational evidences
More informationHow Do Galeries Form?
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-1 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-2 Galaxy Formation Leading questions for today How do
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium
More informationBACHELOR OF SCIENCE DEGREE
BACHELOR OF SCIENCE DEGREE GENERAL EDUCATION CURRICULUM and Additional Degree Requirements Engineering Science Brett Coulter, Ph.D. - Director The Engineering Science degree is a wonderful way for liberal
More informationLesson 3: Isothermal Hydrostatic Spheres. B68: a self-gravitating stable cloud. Hydrostatic self-gravitating spheres. P = "kt 2.
Lesson 3: Isothermal Hydrostatic Spheres B68: a self-gravitating stable cloud Bok Globule Relatively isolated, hence not many external disturbances Though not main mode of star formation, their isolation
More informationHow To Understand The Measurement Process
April 24, 2015 Exam #3: Solution Key online now! Graded exams by Monday! Final Exam Monday, May 4 th, 10:30 a.m. Room: Perkins 107 1 A Classical Perspective A classical view will help us understand the
More informationTHE MEANING OF THE FINE STRUCTURE CONSTANT
THE MEANING OF THE FINE STRUCTURE CONSTANT Robert L. Oldershaw Amherst College Amherst, MA 01002 USA rloldershaw@amherst.edu Abstract: A possible explanation is offered for the longstanding mystery surrounding
More informationCE 204 FLUID MECHANICS
CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Fax: +90-216-677-1486 E-mail:
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationGravitational self-force in the ultra-relativistic regime Chad Galley, California Institute of Technology
Gravitational self-force in the ultra-relativistic regime Chad Galley, California Institute of Technology with Rafael Porto (IAS) arxiv: 1302.4486 v2 soon! (with details) Capra16; Dublin, Ireland; July
More information