{"id":452,"date":"2013-12-01T14:56:12","date_gmt":"2013-12-01T14:56:12","guid":{"rendered":"http:\/\/toschi.phys.tue.nl\/wordpress\/?p=452"},"modified":"2013-12-01T14:56:12","modified_gmt":"2013-12-01T14:56:12","slug":"3cs03-caput-theoretical-physics-theory-of-liquids","status":"publish","type":"post","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/3cs03-caput-theoretical-physics-theory-of-liquids\/","title":{"rendered":"3CS03 - Caput Theoretical Physics: Theory of liquids"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"452\">\n<div class='content-wrap'><p>Liquids lack the long-range order typical for solids. Collisional processes and short-range correlations distinguish liquids from dilute gases. Therefore, no idealized models comparable with the perfect gas or the harmonic solid are available for even simple liquids. During the last half of the 20th century a rapid progress has been made in our understanding of the microscopic structure and the dynamics of simple liquids. With advances in experiments (light and neutron scattering), theoretical analysis (statistical mechanics, kinetic theory of strongly correlated systems) and numerical tools (Molecular Dynamics and Monte Carlo simulations) a rather clear and complete picture emerged on the properties of simple atomic liquids. Since the last few decades a variety of more complicated systems are being studied: ionic, molecular and polar liquids, liquid metals, liquid-vapor interfaces, liquid crystals, and colloidal suspensions. In this lecture we will address the basic theory of the liquid state based on a statistical mechanical description of liquids. Topics that will be discussed include static properties of liquids, distribution function theories, perturbation theory and inhomogeneous fluids. We will conclude with an outlook to more complex fluids.<\/p>\n<p>Introduction (week 1-2)<br \/>\nLiquid state, intermolecular forces<br \/>\nLiouville equation, BBGKY hierarchy<br \/>\nStatistical mechanics and ensemble averages<\/p>\n<p>Static properties of liquids (week 3-4)<br \/>\nParticle densities and distribution functions<br \/>\nComputer simulations (MD and MC)<br \/>\nDiagrammatic expansions, virial expansion of the equation of state<br \/>\nEquation of state of a hard sphere fluid<\/p>\n<p>Distribution function theories (week 5-6)<br \/>\nStatic structure factor<br \/>\nOrnstein-Zernike direct correlation function<br \/>\nPercus-Yevick solution for hard spheres, mean spherical approximation<\/p>\n<p>Outlook (week 7)<br \/>\nPerturbation theories<br \/>\nComplex liquids<\/p>\n<\/div><!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 452 -->","protected":false},"excerpt":{"rendered":"<p>Liquids lack the long-range order typical for solids. Collisional processes and short-range correlations distinguish liquids from dilute gases. Therefore, no idealized models comparable with the perfect gas or the harmonic solid are available for even simple liquids. During the last half of the 20th century a rapid progress has been made in our understanding of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[38],"tags":[],"class_list":["post-452","post","type-post","status-publish","format-standard","hentry","category-master"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6tiMI-7i","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":85,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/new-directions-in-turbulence-2012\/","url_meta":{"origin":452,"position":0},"title":"New Directions in Turbulence 2012","author":"toschi","date":"February 9, 2012","format":false,"excerpt":"SCIENTIFIC CONTENT This six-week program (12 March 2012 to 20 April 2012) will focus on recent development in the understanding of fluid dynamics turbulence\u00a0with the goal to identify promising breakthrough directions. From the point of view of theoretical physics, turbulence is a classical field theory, out of equilibrium and in\u2026","rel":"","context":"In &quot;conferences&quot;","block_context":{"text":"conferences","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/conferences\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":101,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/analysis-modeling-and-simulation-of-collective-dynamics-from-bacteria-to-crowds-2012\/","url_meta":{"origin":452,"position":1},"title":"Analysis, Modeling and Simulation of Collective Dynamics from Bacteria to Crowds  2012","author":"toschi","date":"February 9, 2012","format":false,"excerpt":"Analysis, Modeling and Simulation of Collective Dynamics from Bacteria to Crowds July 9, 2012 \u2014 July 13, 2012 Coordinators: Federico Toschi\u00a0(Eindhoven University of Technology, The Netherlands) Adrian Muntean\u00a0(Eindhoven University of Technology, The Netherlands) The collective motion of individuals (correlated motion of ants or migration of bacteria, flocks of birds, just\u2026","rel":"","context":"In &quot;conferences&quot;","block_context":{"text":"conferences","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/conferences\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":805,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/3mt100-chaos\/","url_meta":{"origin":452,"position":2},"title":"3MT100 - Chaos","author":"toschi","date":"February 3, 2016","format":false,"excerpt":"Chaos is the erratic behavior of simple nonlinear dynamical systems. This course covers the basic fundamentals of chaos theory, including the concept of scaling and universal route to chaos, and its connection to these non-linear, deterministic but unpredictable dynamical systems. From simple chaotic maps, to the physics of fractals and\u2026","rel":"","context":"In &quot;master&quot;","block_context":{"text":"master","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/teaching\/master\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":793,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/3mt120\/","url_meta":{"origin":452,"position":3},"title":"3MT120 - Advanced Computational Fluid and Plasma Dynamics","author":"toschi","date":"February 1, 2016","format":false,"excerpt":"The course guides students to the hand-on discovery of several classical numerical methods commonly used to study the dynamics of fluids and plasmas: from continuum computational fluid dynamics (CFD) approaches (Spectral and finite volume), to the Lattice Boltzmann (LBM), particles based methods (Molecular Dynamics, Brownian and Stokesian dynamics) and Particle-in-cell\u2026","rel":"","context":"In &quot;master&quot;","block_context":{"text":"master","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/teaching\/master\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":754,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/matteo-lulli\/","url_meta":{"origin":452,"position":4},"title":"Matteo Lulli","author":"toschi","date":"October 3, 2015","format":false,"excerpt":"Evaporation of Droplets under flow The aim of the project if to develop a stable and accurate numerical technique based on the Lattice-Boltzmann scheme to quantitatively study the diffusion behaviour of multicomponent droplets under flow. The ability of simulating correctly the diffusive dynamics of multicomponent droplets in presence of advection\u2026","rel":"","context":"In &quot;postdoc&quot;","block_context":{"text":"postdoc","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/students\/postdoc\/"},"img":{"alt_text":"MatteoLulli_profilePic","src":"https:\/\/i0.wp.com\/toschi.phys.tue.nl\/wordpress\/wp-content\/uploads\/2015\/10\/MatteoLulli_profilePic-169x300.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":495,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/sten-rijers\/","url_meta":{"origin":452,"position":5},"title":"Sten Reijers","author":"toschi","date":"February 4, 2014","format":false,"excerpt":"Compressible effects in drops impacted by a laser pulse The impact of a laser pulse onto a liquid droplet induces strong deformation and propulsion of the droplet. Here, we aim to understand the droplet dynamics by performing lattice-Boltzmann simulations and doing a theoretical analysis. In the simulations, we model the\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"Sten","src":"https:\/\/i0.wp.com\/toschi.phys.tue.nl\/wordpress\/wp-content\/uploads\/2014\/02\/Sten-200x300.jpg?resize=350%2C200","width":350,"height":200},"classes":[]}],"_links":{"self":[{"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/posts\/452","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/comments?post=452"}],"version-history":[{"count":1,"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/posts\/452\/revisions"}],"predecessor-version":[{"id":453,"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/posts\/452\/revisions\/453"}],"wp:attachment":[{"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/media?parent=452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/categories?post=452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toschi.phys.tue.nl\/wordpress\/wp-json\/wp\/v2\/tags?post=452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}