http://www.lps.ens.fr/~krauth/index.php?title=Special:Recentchanges&days=14&limit=500&hideanons=1&hidemyself=1&feed=atomWerner KRAUTH - Recent changes [en]2018-05-21T17:09:20ZTrack the most recent changes to the wiki on this page.MediaWiki 1.6.12http://www.lps.ens.fr/~krauth/index.php/Main_PageMain Page2018-05-16T17:06:06Z<p></p>
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<td colspan='2' width='50%' align='center' style="background-color: white;">Revision as of 17:06, 16 May 2018</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Current revision</td>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">=Current research=</td><td> </td><td style="background: #eee; font-size: smaller;">=Current research=</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">I am deeply interested in statistical and condensed-matter physics, often in connection to computation and algorithms.</td><td> </td><td style="background: #eee; font-size: smaller;">I am deeply interested in statistical and condensed-matter physics, often in connection to computation and algorithms.</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Current interests are in hard spheres, mainly the melting transition in two-dimensional disks and in two-dimensional melting, bosons (in collaboration with the experimental groups at ENS), and the theory of convergence and of coupling in Markov chains. Recent work in my research group has led to the redefinition of the dominant Markov-chain Monte Carlo paradigm, namely the Metropolis algorithm. This has already allowed us to propose powerful algorithms for particle systems, continuous spin models and long-range systems, and to obtain important physical results. Research on the ''beyond-Metropolis'' paradigm, together with applications in classical and quantum physics and its interfaces will likely be a focus of my research activity in the next few years. </td><td> </td><td style="background: #eee; font-size: smaller;">Current interests are in hard spheres, mainly the melting transition in two-dimensional disks and in two-dimensional melting, bosons (in collaboration with the experimental groups at ENS), and the theory of convergence and of coupling in Markov chains. Recent work in my research group has led to the redefinition of the dominant Markov-chain Monte Carlo paradigm, namely the Metropolis algorithm. This has already allowed us to propose powerful algorithms for particle systems, continuous spin models and long-range systems, and to obtain important physical results. Research on the ''beyond-Metropolis'' paradigm, together with applications in classical and quantum physics and its interfaces will likely be a focus of my research activity in the next few years. </td></tr>
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<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;">==All-atom Coulomb simulations with irreversible Markov chains==</td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;">In a nutshell, classical molecular-dynamics simulations consist in computing the forces on particles, at discretized time steps, and in moving these particles in accordance with Newton's law of motion, the famous '''F'''=m'''a'''. Likewise (in a nutshell), classical Monte Carlo calculations consist in proposing a move, then in computing the change of the total system energy, and then accepting or rejecting the move with a probability given by the Metropolis filter. How to compute the forces (for molecular dynamics) or the energies (for Monte Carlo) is a science in its own right, whenever the interactions are long-ranged, as for the Coulomb potential. Much used elaborate methods go by the names of ''PP'' (for particle-particle) or ''PPPM'' (for particle-particle / particle-mesh), or else ''particle-mesh'' Ewald etc. They have in common that much ingenuity is applied to compute a quantity (force / energy) that, as [[Kapfer_Krauth_2016| we claimed a few years ago]], is not needed to drive the system forward! [[Faulkner_Qin_Maggs_Krauth_2018|In a recent work ]], I teamed up with Michael Faulkner, Liang Qin, and Anthony C. Maggs, to show how this can be done in practice. In what, internally, we call our 'Confirmation paper', we explicitly show how to set up a highly efficient algorithm to simulate a model of liquid water. We indeed confirm that it is possible to sample the Boltzmann distribution (which involves the Boltzmann weight, and therefore the system energy), without computing the energy. As often, the difference lies in the subtle difference between the concepts of 'sampling' (that is, obtaining examples of a certain distribution) and of 'computing' (for example computing the energy). Technically, we succeed in drawing independent samples with a complexity 'N' log 'N' (just like the best PPPM algorithms but, we think, much faster). Now, of course, after the first excitement of our 'confirmation paper', we are all excited by the forthcoming 'benchmark paper', where we will compare not only complexities, but actual running times.</td></tr>
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<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;">==Thermodynamic phases in two-dimensional active matter==</td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;">Active matter (for example the collective dynamics of flocks of birds, of schools of fish, etc) is a very ''active'' field of research in statistical physics. However, active matter cannot really be described by equilibrium statistical theory where the state of what is called ''the system'' is fully characterized by two numbers (for example the volume and the pressure), and where the statistical weight of each configuration can be attributed an energy E, and a statistical Boltzmann weight exp(-beta E) which depends on the energy alone. Many active materials are two-dimensional (ranging from sheep on a meadow to bacterial colonies to artificial ''Janus particles'' on a glass place. As we are so much interested in ''regular'' two-dimensional particle systems (that are described by equilibrium statistical physics), we posed the question of whether there was some kind of continuous passage between the two types of models. Teaming up with Juliane U. Klamser and Sebastian C. Kapfer, we studied this question in detail. Our conclusions are written up [[Klamser Kapfer Krauth 2018| in this paper]]. More about all this shortly.</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">==Irreversible local Markov chains with rapid convergence towards equilibrium==</td><td> </td><td style="background: #eee; font-size: smaller;">==Irreversible local Markov chains with rapid convergence towards equilibrium==</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">==Cell-veto Monte Carlo algorithm for long-range systems==</td><td> </td><td style="background: #eee; font-size: smaller;">==Cell-veto Monte Carlo algorithm for long-range systems==</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">[[Image:Kapfer Krauth Cell Schema.png|left|600px|border|Particle-based simulation (on the left) and cell-based simulation (on the right).]] [[Kapfer_Krauth_2016|In a recent paper]], together with Sebastian Kapfer, we have presented what we think might be a new start idea for the notoriously difficult simulation of long-ranged systems (such as the Coulomb 1/r interaction). Usually it poses problems, because the evaluation of the energy is so difficult: In a long-ranged system of N particles, the interactions are basically ''of everybody with everybody else''. This makes that the evaluation of the energy becomes complicated, and the energy is needed in 99.99% of all simulation algorithms (Monte Carlo or Molecular dynamics). In our new algorithm (an application of the event-chain method), one does not compute the system energy in order to decide on a change of the physical system, but rather looks at all the interactions separately. So, if a particle '''a''' (the active particle) wants to move, it has to ask all its partners '''t_1''', '''t_2''', .... (the target particles). If there is only a single veto, the move is rejected. In the cell-veto algorithm (see the right side of the figure), the identification of the rejecting particle is preceeded by that of a veto cell. The advantage of this is that cell vetos can be identified immediately (in a constant number of operations, that is, in O(1)), and then instantly confirmed or infirmed on the particle level.</td><td> </td><td style="background: #eee; font-size: smaller;">[[Image:Kapfer Krauth Cell Schema.png|left|600px|border|Particle-based simulation (on the left) and cell-based simulation (on the right).]] [[Kapfer_Krauth_2016|In a recent paper]], together with Sebastian Kapfer, we have presented what we think might be a new start idea for the notoriously difficult simulation of long-ranged systems (such as the Coulomb 1/r interaction). Usually it poses problems, because the evaluation of the energy is so difficult: In a long-ranged system of N particles, the interactions are basically ''of everybody with everybody else''. This makes that the evaluation of the energy becomes complicated, and the energy is needed in 99.99% of all simulation algorithms (Monte Carlo or Molecular dynamics). In our new algorithm (an application of the event-chain method), one does not compute the system energy in order to decide on a change of the physical system, but rather looks at all the interactions separately. So, if a particle '''a''' (the active particle) wants to move, it has to ask all its partners '''t_1''', '''t_2''', .... (the target particles). If there is only a single veto, the move is rejected. In the cell-veto algorithm (see the right side of the figure), the identification of the rejecting particle is preceeded by that of a veto cell. The advantage of this is that cell vetos can be identified immediately (in a constant number of operations, that is, in O(1)), and then instantly confirmed or infirmed on the particle level.</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">==Event-chain algorithm for continuous spin systems: XY & Heisenberg models, spin glasses==</td><td> </td><td style="background: #eee; font-size: smaller;">==Event-chain algorithm for continuous spin systems: XY & Heisenberg models, spin glasses==</td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">[[Image:Michel Mayer Krauth fig3.png|left|600px|border|Event-chain algorithm for spin systems]] In past years, several of our key results, for example about [[Bernard_Krauth_2011|two-dimensional melting for hard disks]] but also the [[Kapfer_Krauth_2014|melting scenario for soft-disk systems]], have relied on the new ''event-chain'' algorithm, that applies to both systems, [[Bernard_Krauth_Wilson_2009|hard-core]] and [[Michel_Kapfer_Krauth_2013|soft-core]]. More recently, we realized that the event-chain algorithm could also be made to work for continuum spin systems. Earlier in 2015, work started with Manon Michel and Johannes Maier, PhD candidate and [http://www.phys.ens.fr/spip.php?rubrique284&lang=en ENS-ICFP master] student, respectively. The first simulations were followed by a period of hectic activity: We had discovered that the event-chain algorithm was about 100 times faster that the local Monte Carlo algorithm. Our findings were written up, during the month of August 2015, in a manuscript entitled [[Michel_Mayer_Krauth_2015|Event-chain Monte Carlo for classical continuous spin models]]. Only six weeks later (!), Manon Michel and I submitted another manuscript, together with our colleagues Yoshihiko Nishikawa and Koji Hukushima, from the University of Tokyo, entitled [[Nishikawa_Michel_Krauth_Hukushima_2015|Event-chain algorithm for the Heisenberg model: Evidence for z ≃ 1 dynamic scaling]]. This new finding (that still awaits confirmation for larger systems than the ones we could simulate quickly), has had an electrifying effect on us: For the first time, we see the kind of maximum speed-up that can be realized by irreversible Markov chains using the lifting paradigm, if we suppose that the recent mathematical theories apply to the algorithms we have been developing. Of course, we now hope to find the z=1 scaling in Heisenberg spin glasses and related systems and, why not, in the original hard-sphere models, in two dimensions as well as in three.</td><td> </td><td style="background: #eee; font-size: smaller;">[[Image:Michel Mayer Krauth fig3.png|left|600px|border|Event-chain algorithm for spin systems]] In past years, several of our key results, for example about [[Bernard_Krauth_2011|two-dimensional melting for hard disks]] but also the [[Kapfer_Krauth_2014|melting scenario for soft-disk systems]], have relied on the new ''event-chain'' algorithm, that applies to both systems, [[Bernard_Krauth_Wilson_2009|hard-core]] and [[Michel_Kapfer_Krauth_2013|soft-core]]. More recently, we realized that the event-chain algorithm could also be made to work for continuum spin systems. Earlier in 2015, work started with Manon Michel and Johannes Maier, PhD candidate and [http://www.phys.ens.fr/spip.php?rubrique284&lang=en ENS-ICFP master] student, respectively. The first simulations were followed by a period of hectic activity: We had discovered that the event-chain algorithm was about 100 times faster that the local Monte Carlo algorithm. Our findings were written up, during the month of August 2015, in a manuscript entitled [[Michel_Mayer_Krauth_2015|Event-chain Monte Carlo for classical continuous spin models]]. Only six weeks later (!), Manon Michel and I submitted another manuscript, together with our colleagues Yoshihiko Nishikawa and Koji Hukushima, from the University of Tokyo, entitled [[Nishikawa_Michel_Krauth_Hukushima_2015|Event-chain algorithm for the Heisenberg model: Evidence for z ≃ 1 dynamic scaling]]. This new finding (that still awaits confirmation for larger systems than the ones we could simulate quickly), has had an electrifying effect on us: For the first time, we see the kind of maximum speed-up that can be realized by irreversible Markov chains using the lifting paradigm, if we suppose that the recent mathematical theories apply to the algorithms we have been developing. Of course, we now hope to find the z=1 scaling in Heisenberg spin glasses and related systems and, why not, in the original hard-sphere models, in two dimensions as well as in three.</td></tr>
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Werner