We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure thermodynamics of inhomogeneous fluids. The exact map from profile to one-body direct correlation function is represented locally by deep neural network. substantiate general framework hard sphere fluid use grand canonical Monte Carlo simulation data systems in randomized external environments during training as reference. Functional calculus implemented...

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur soft matter. To give guidance navigating the theoretical practical challenges lie ahead, we discuss exemplify limitations density functional (DDFT). Instead implied adiabatic sequence equilibrium states this approach provides as makeshift true time evolution, posit pending tasks systematic understanding relationships govern...

Topological protection allows robust transport of localized phenomena such as quantum information, solitons, and dislocations. The can be either dissipative or non-dissipative. Here, we experimentally demonstrate theoretically explain the topologically protected motion colloidal particles above a periodic hexagonal magnetic pattern. By driving system with modulation loops an external spatially homogeneous field, achieve total control over diamagnetic paramagnetic colloids. We simultaneously...

Using Monte Carlo simulation, we analyse the behaviour of two-dimensional hard rods in four different types geometric confinement: (i) a slit pore where particles are confined between two parallel walls with homeotropic anchoring; (ii) hybrid formed by planar and wall; square cavities that frustrate orientational order imposing either (iii) or (iv) wall anchoring. We present results for state diagram as function packing fraction degree confinement. Under extreme confinement, unexpected...

We investigate motility-induced phase separation of active Brownian particles, which are modeled as purely repulsive spheres that move due to a constant swim force with freely diffusing orientation. develop on the basis power functional concepts an analytical theory for nonequilibrium coexistence and interfacial structure. Theoretical predictions validated against dynamics computer simulations. show internal one-body field has four contributions: (i) isotropic drag (ii) forces forward...

Topological growth control allows to produce a narrow distribution of outgrown colloidal rods with defined and adjustable length. We use an external magnetic field assemble paramagnetic spheres into chosen The reside above ametamorphic hexagonalmagnetic pattern. periodic repetition specific loops the orientation applied renders particles their assemblies active bipeds that walk on metamorphic patterns allow robust controlled polymerization single colloids desired are exposed this fixed loop...

We calculate the network fluid regime and phase diagrams of binary mixtures patchy colloids, using Wertheim's first order perturbation theory a generalization Flory-Stockmayer's polymerization. The colloids are modelled as hard spheres with same diameter surface patches type, $A$. only difference between species is number their -or functionality-, $f_A^{(1)}$ $f_A^{(2)}$ (with $f_A^{(2)}>f_A^{(1)}$). have found that in functionality key factor controlling behaviour mixture (percolated)...

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events particle occurrences at (histogram-resolved) space points. Here, we investigate an alternative method based on a histogram the local force density. Via exact sum rule, profile is obtained with simple spatial integration. The circumvents inherent ideal gas fluctuations. We have tested Monte Carlo, Brownian dynamics, and molecular dynamics simulations. results carry...

Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true is represented as a sequence of equilibrium states. Going beyond this simple approximation notoriously difficult problem. For case classical Brownian dynamics, we present simulation method that allows us isolate and precisely evaluate superadiabatic correlations resulting forces. Application system one-dimensional hard particles reveals importance for well complexity,...

We present a microscopic theory for the nonequilibrium interfacial tension ${\ensuremath{\gamma}}_{\mathrm{gl}}$ of free interface between gas and liquid phases active Brownian particles. The underlying square gradient treatment splitting force balance in flow structural contributions is general applies to inhomogeneous steady states. find ${\ensuremath{\gamma}}_{\mathrm{gl}}\ensuremath{\ge}0$, which opposes claims by Bialk\'e et al. [Phys. Rev. Lett. 115, 098301 (2015)] delivers theoretical...

Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation the underlying classical many-body Hamiltonian. At first order in field Noether theorem yields local force balance. Three distinct two-body correlation functions emerge at second order, namely standard density, localized force-force function, and gradient. An exact sum rule interrelates these correlators. Simulations Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne...

Topologically nontrivial adiabatic loops of the orientation a homogeneous external magnetic field sort walking paramagnetic colloidal bipeds above deformed quasi-periodic square pattern.

We investigate the thermodynamics and percolation regimes of model binary mixtures patchy colloidal particles. The particles each species have three sites two types, one which promotes bonding same while other different species. find up to four percolated structures at low temperatures densities: gels where only percolates, a mixed gel both percolate but neither percolates separately, bicontinuous separately forming interconnected networks. competition between entropy energy drives stability...

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting study of nonequilibrium dynamics overdamped Brownian many-body systems. The functional depends on local velocity gradient is systematically obtained from treating microscopic stress distribution as a conjugate field. resulting forces are beyond dynamical density theory viscous nature. Their high accuracy demonstrated by comparison to simulation results.

We present a general and formally exact method to obtain the canonical one-body density distribution free energy from direct decomposition of classical functional results in grand ensemble. test for confined one-dimensional hard-core particles which potential is explicitly known. The agree within high accuracy with those methods our Monte Carlo many-body simulations. relevant treating finite systems dynamical theory.

We present a fundamental classification of forces relevant in nonequilibrium structure formation under collective flow Brownian many-body systems. The internal one-body force field is systematically split into contributions for the spatial and coupled motion. demonstrate that both can be obtained straightforwardly computer simulations power functional theory describes all types quantitatively. Our conclusions methods are inertial systems, such as molecular liquids granular media.

Abstract We simulate the motion of paramagnetic particles between two magnetic patterns with hexagonal symmetry that are twisted at a magic angle. The resulting Morié pattern develops flat channels in potential along which colloidal can be transported via drift force magnitude larger than critical value. Colloidal transport is also possible modulation loops uniform external field time varying orientation, case topologically protected. Drift and topological compete or cooperate giving rise to...

Using density-functional theory, we have analyzed the phase behavior of a model liquid crystal confined between two parallel, planar surfaces (i.e., so-called slit pore). As result confinement, rich arises. The complete liquid-crystal diagram fluid is mapped out as function wall separation and chemical potential. Strong commensuration effects in film with respect to lead enhanced smectic ordering, which gives capillary smectization formation pore), or frustrated suppresses smectization....

We investigate the effect of distinct bonding energies on onset criticality low functionality fluid mixtures. focus mixtures particles with two and three patches as this includes mixture where “empty” fluids were originally reported. In addition to number patches, species differ in type or sites. For simplicity, we consider that each are identical: one has A other B. have found a rich phase behavior closed miscibility gaps, liquid–liquid demixing, negative azeotropes. Liquid–liquid demixing...

The phase behaviour of colloidal dispersions is interesting for fundamental reasons and technological applications such as photonic crystals electronic paper. Sedimentation, which in everyday life relevant from blood analysis to the shelf paint, a means determine boundaries by observing distinct layers samples that are sedimentation-diffusion equilibrium. However, disentangling effects due interparticle interactions, generate bulk diagram, those gravity complex task. Here we show line space...

Using Monte Carlo simulation, we study a fluid of two-dimensional hard rods inside small circular cavity bounded by wall, from the dilute regime to high-density, layering regime. Both planar and homeotropic anchoring nematic director can be induced at walls through free-energy penalty. The geometry creates frustration in phase polar-symmetry configuration with distorted field plus two +1/2 disclinations is created. At higher densities, quasi-uniform structure observed (minimal) distortion...

The observation of stacks distinct layers in a colloidal or liquid mixture sedimentation-diffusion equilibrium is striking consequence bulk phase separation. Drawing quantitative conclusions about the diagram is, however, very delicate. Here we introduce Legendre transform chemical potential representation to obtain unique stacking all possible under gravity. Simple diagrams generically lead complex diagrams. We apply theory binary hard core platelet with only two-phase coexistence, and find...

The orientational order in vertically agitated granular-rod monolayers is investigated experimentally and compared quantitatively with equilibrium Monte Carlo simulations density functional theory. At sufficiently high number density, short rods form a tetratic state long uniaxial nematic state. length-to-width ratio at which the changes from to around $7.3$ both experiments simulations. This agreement illustrates universal aspects of ordering rod-shaped particles across nonequilibrium...