By Baruch Barzel and Prof. Ofer Biham Efficient Simulations of Gas-Grain Chemistry Using Moment Equations.

Slides:

Advertisements

Similar presentations

Formation and Evolution of Molecules Behind Shocks GEORGE HASSEL Dept. of Physics, The Ohio State University Eric Herbst (Ohio.

Advertisements

School of Chemistry, University of Nottingham,UK 1 Why Does Star Formation Need Surface Science? Using Laboratory Surface Science to Understand the Astronomical.

Current Problems in Dust Formation Theory Takaya Nozawa Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo 2011/11/28.

LEARNING INFLUENCE PROBABILITIES IN SOCIAL NETWORKS Amit Goyal Francesco Bonchi Laks V. S. Lakshmanan University of British Columbia Yahoo! Research University.

NOE Transferring magnetization through scalar coupling is a “coherent” process. This means that all of the spins are doing the same thing at the same time.

An Experimental Study and Fatigue Damage Model for Fretting Fatigue

Interfacing Molecules to Electronic Materials.

Stochastic Analysis of Bi-stability in Mixed Feedback Loops Yishai Shimoni, Hebrew University CCS Open Day Sep 18 th 2008.

Heating and Cooling 10 March 2003 Astronomy G Spring 2003 Prof. Mordecai-Mark Mac Low.

Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field Gaurav Chopra 07 February 2005 CS 379 A Alan GrossfeildPengyu Ren Jay W. Ponder.

The next step in kinetics. * Molecules must collide to react. * Concentration affects rates because collisions are more likely. * Must collide hard enough.

Max P. Katz, Wayne G. Roberge, & Glenn E. Ciolek Rensselaer Polytechnic Institute Department of Physics, Applied Physics and Astronomy.

PROVIDING DISTRIBUTED FORECASTS OF PRECIPITATION USING A STATISTICAL NOWCAST SCHEME Neil I. Fox and Chris K. Wikle University of Missouri- Columbia.

Linear vs. exponential growth Linear vs. exponential growth: t = 0 A = 1x(1+1) 0 = 1 A = 1x0 + 1 = 1.

Algorithms Analysis Section 3.3 of Rosen Fall 2008 CSCE 235 Introduction to Discrete Structures Course web-page: cse.unl.edu/~cse235 Questions:

Chess Review May 10, 2004 Berkeley, CA Modeling Subtilin Production in Bacillus subtilis Using Stochastic Hybrid Systems Jianghai Hu, Wei-Chung Wu Denise.

Chemistry and line emission of outer protoplanetary disks Inga Kamp Introduction to protoplanetary disks and their modeling Introduction to protoplanetary.

Adiel Loinger Ofer Biham Nathalie Q. Balaban Azi Lipshtat

Identifiability of biological systems Afonso Guerra Assunção Senra Paula Freire Susana Barbosa.

Efficient Simulations of Gas-Grain Chemistry Using Moment Equations M.Sc. Thesis by Baruch Barzel preformed under the supervision of Prof. Ofer Biham.

The abundances of gaseous H 2 O and O 2 in dense cloud cores Eric Herbst & Helen Roberts The Ohio State University.

Intro to Chemical Reactions.  What is the difference between physical change and chemical change?  How can you be relatively sure that a chemical change.

Chemical and Physical Structures of Massive Star Forming Regions Hideko Nomura, Tom Millar (UMIST) ABSTRUCT We have made self-consistent models of the.

Chapter 19 Gas Stoichiometry.

Chemistry Chemical Reactions – Rearranging Atoms.

Planning and Verification for Stochastic Processes with Asynchronous Events Håkan L. S. Younes Carnegie Mellon University.

Optimal Nonlinear Neural Network Controllers for Aircraft Joint University Program Meeting October 10, 2001 Nilesh V. Kulkarni Advisors Prof. Minh Q. Phan.

ERIC HERBST DEPARTMENTS OF PHYSICS, CHEMISTRY AND ASTRONOMY THE OHIO STATE UNIVERSITY Gas and Dust (Interstellar) Astrochemistry.

Collaborators : Valentine Wakelam (supervisor)

Chemical Models of High Mass Young Stellar Objects Great Barriers in High Mass Star Formation H. Nomura 1 and T.J. Millar 2 1.Kyoto Univ. Japan, 2. Queen’s.

ChE 553 Lecture 12 Theory Of Sticking 1. Objective Develop a qualitative understanding of sticking Go over some models for the process 2.

ISM & Astrochemistry Lecture 2. Protoplanetary Nebula The evolutionary stage between evolved stars and planetary nebula CRL 618 – many organic molecules.

Predoc’ school, Les Houches,september 2004

From the Arrhenius equation we have: 301. From the Arrhenius equation we have: 302.

Statistical / empirical models Model ‘validation’ –should obtain biomass/NDVI measurements over wide range of conditions –R 2 quoted relates only to conditions.

A Gas Grain Model of ISM Cores with Moment Equations to Treat Surface Chemistry Yezhe Pei & Eric Herbst The Ohio State University June 25 th, th.

Qiang Chang, Eric Herbst Chemistry department, University of Virginia

Some RMG Basics William H. Green MIT Dept. of Chemical Engineering RMG Study Group Sept. 27, 2013.

Summary  We have implemented numerically stable, continuous method of treating condensation on to grains in Titan’s atmosphere.  Our model can establish.

Synergism in magnetosphere- exosphere-ice interactions enhances gas trapping and radiation chemistry Raúl A. Baragiola University of Virginia, Charlottesville,

A Stochastic Model of Platoon Formation in Traffic Flow USC/Information Sciences Institute K. Lerman and A. Galstyan USC M. Mataric and D. Goldberg TASK.

ERIC HERBST DEPARTMENTS OF PHYSICS, CHEMISTRY AND ASTRONOMY THE OHIO STATE UNIVERSITY Interstellar Chemistry: Triumphs & Shortcomings.

Astrochemistry Les Houches Lectures September 2005 Lecture 1

The Interstellar Medium and Star Formation Material between the stars – gas and dust.

ISM & Astrochemistry Lecture 3. Models - History – Grain surface chemistry – H 2, CH, CH – Ion-neutral chemistry – HD, DCO

Jacqueline Keane NASA Astrobiology Pavel Senin University of Hawaii at

Planetary Nebulae as a Testground of Interstellar Molecular Chemistry Tatsuhiko Hasegawa.

School of Physics and Astronomy FACULTY OF MATHEMATICS & PHYSICAL SCIENCES The IR-mm spectrum of a starburst galaxy Paola Caselli Astrochemistry of the.

Testing grain-surface chemistry in massive hot-core regions and the laboratory (A&A, 465, 913 and A&A submitted) Suzanne Bisschop Jes Jørgensen, Ewine.

Moles and gas volumes At the end of this section you should be able to calculate the amount of substance in moles, using gas volume.

Interstellar Chemical Models with Molecular Anions Eric Herbst, OSU T. Millar, M. Cordiner, C. Walsh Queen’s Univ. Belfast R. Ni Chiumin, U. Manchester.

Quantum Mechanics/ Molecular Mechanics (QM/MM) Todd J. Martinez.

The ideal gas equation. Room temperature and pressure, RTP Limitations At RTP, 1 mol of gas molecules occupies 24.0 dm 3 Conditions are not always room.

Astrochemistry University of Helsinki, December 2006 Lecture 3 T J Millar, School of Mathematics and Physics Queen’s University Belfast,Belfast BT7 1NN,

Astrochemistry Les Houches Lectures September 2005 Lecture 2 T J Millar School of Physics and Astronomy University of Manchester PO Box88, Manchester M60.

R. T. Garrod & E. Herbst The Ohio State University R. T. Garrod & E. Herbst Grain Surface Formation of Methyl Formate Grain Surface Formation of Methyl.

Network Science K. Borner A.Vespignani S. Wasserman.

EE 460 Advanced Control and Sys Integration Feedback Summary Mon, Oct 26 EE 460 Advanced Control and System Integration Slide 1 of 4.

8 H : 8 O Imagine that paperclips are atoms and that we’re starting with an equal number of hydrogen atoms and oxygen atoms. For example: Let’s assemble.

Mellinger Lesson 6 molecular line & clouds Toshihiro Handa Dept. of Phys. & Astron., Kagoshima University Kagoshima Univ./ Ehime Univ. Galactic radio astronomy.

Interstellar N 2 toward 20 Aql. Observations of the Interstellar Medium.

IC-1/38 Lecture Kinetics IC-2/38 Lecture What is Kinetics ? Analysis of reaction mechanisms on the molecular scale Derivation.

Complex Organic Molecules formation on Interstellar Grains Qiang Chang Xinjiang Astronomical Observatory Chinese Academy of Sciences April 22, 2014.

ChE 553 Lecture 30 Catalysis By Metals 1. Objective Examine the trends in bonding over the periodic table 2.

Pore water fluxes and mass balance

On the Formation of Molecules on Interstellar Grains

Algorithms Analysis Section 3.3 of Rosen Spring 2017

From Inter-stellar Chemistry to Intra-cellular Biology

Algorithms Analysis Section 3.3 of Rosen Spring 2013

Algorithms Analysis Section 3.3 of Rosen Spring 2018

Presentation transcript:

by Baruch Barzel and Prof. Ofer Biham Efficient Simulations of Gas-Grain Chemistry Using Moment Equations

2 Molecular Formation in the ISM

3 Horse-Head Nebula Molecular Formation in the ISM

4 H 2 Production in the gas phase: H + H → H 2 Gas-Phase Reactions Cannot Account for the Observed Production Rates Observed Production Rates in ISC: R H ~ (mol cm -3 s -1 ) 2 The H 2 Puzzle

5 The Solution

6 kBTkBT -E0-E0 A H = (1/S) e = F H - W H ‹ N H › - 2A H ‹ N H › 2 d ‹ N H › dt Incoming flux Desorption Recombination W H = e kBTkBT -E1-E1 The Production Rate of H 2 Molecules: R H = A H ‹ N H › 2 (mol s -1 ) 2 The Rate Equation

7 Mean-field approximation = F H - W H ‹ N H › - 2A H ‹ N H › 2 d ‹ N H › dt When the Rate Equation Fails Neglects fluctuations Ignores discretization Not valid for small grains and low flux

8 P(0) P(1) P(N H -1) P(N H ) P(N H +1) P(N H +2) P(N max ) Flux term: F H [P H (N H -1) - P H (N H )] Desorption term: W H [(N H +1)P H (N H +1) - N H P H (N H )] Reaction term: A H [(N H +2)(N H +1)P H (N H +2) - N H (N H -1)P H (N H )] FHFH WHWH AHAH Probabilistic Approach

9 = F H [P H (N H -1) - P H (N H )] + W H [(N H +1)P H (N H +1) - N H P(N H )] + A H [(N H +2)(N H +1)P H (N H +2) - N H (N H -1)P H (N H )] dP H (N H ) dt ‹ N H › =  N H P H (N H ) N H = 0 S R H = A H ( ‹ N H 2 › - ‹ N H › ) 2 The Master Equation

10

11 OHO2O2 H2H2 O H H2OH2O The parameters: F i ; W i ; A i (i=1,2,3) 13 2 Complex Reactions

12 OHO2O2 H2H2 O H H2OH2O 13 2 The Master Disaster: P(N 1,N 2,N 3 ) Exponential Growth Complex Reactions

13 ‹ N H k › =  N H k P H (N H ) NH=0NH=0 8 After applying the summation: ‹ N H › = F H + (2A H - W H ) ‹ N H › - 2A H ‹ N H 2 › ‹ N H 2 › = F H + (2F H + W H - 4A H ) ‹ N H › + (8A H - W H ) ‹ N H 2 › - 4A H ‹ N H 3 › The Moment Equations

14 We need more knowledge… Imposing a cutoff on P(N) The Daring Imposition: P(N>2) = 0 Truncating the Equations

15 ‹ N H › = F H + (2A H - W H ) ‹ N H › - 2A H ‹ N H 2 › ‹ N H 2 › = F H + (2F H + W H - 4A H ) ‹ N H › + (8A H - W H ) ‹ N H 2 › - 4A H ‹ N H 3 › And after imposing the cutoff… Moment Equations for H 2 Production

16 ‹ N H › = F H + (2A H - W H ) ‹ N H › - 2A H ‹ N H 2 › ‹ N H 2 › = F H + (2F H + W H - 4A H ) ‹ N H › + (8A H - W H ) ‹ N H 2 › - 4A H ‹ N H 3 › ‹ N H › = F H + (2A H - W H ) ‹ N H › - 2A H ‹ N H 2 › ‹ N H 2 › = F H + (2F H + W H + 4A H ) ‹ N H › - (4A H + 2W H ) ‹ N H 2 › Moment Equations for H 2 Production

17 R H vs. Grain Size 2

18 ‹N1›,‹N1›, ‹N3›‹N3›‹N2›,‹N2›, OHO2O2 H2H2 O H H2OH2O ‹N1N2›‹N1N2› ‹N1N3›‹N1N3› ‹N22›‹N22› ‹N12›‹N12› 3 vertices + 2 edges + 2 loops = 7 equations A View to Complex Networks

19 Production Rates vs. Grain Size

20 15 vertices 30 edges + 3 loops 48 equations Multi-Specie Network

21 Summary The advantages of the moment equations: Reliable even for low coverage EfficientLinear Easy to incorporate into rate equation models Directly generate the required moments Further applications should be tested.