@article{StraubeKowalikNetzetal., author = {Straube, Arthur and Kowalik, Bartosz G. and Netz, Roland R. and H{\"o}fling, Felix}, title = {Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures}, series = {Commun. Phys.}, volume = {3}, journal = {Commun. Phys.}, publisher = {Nature}, doi = {10.1038/s42005-020-0389-0}, pages = {126}, abstract = {Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes-Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.}, language = {en} } @article{DibakFroehnerNoeetal., author = {Dibak, Manuel and Fr{\"o}hner, Christoph and No{\´e}, Frank and H{\"o}fling, Felix}, title = {Diffusion-influenced reaction rates in the presence of pair interactions}, series = {The Journal of Chemical Physics}, volume = {151}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.5124728}, pages = {164105}, abstract = {The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi- analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions.}, language = {en} } @article{HoeflingDietrich, author = {H{\"o}fling, Felix and Dietrich, Siegfried}, title = {Finite-size corrections for the static structure factor of a liquid slab with open boundaries}, series = {The Journal of Chemical Physics}, volume = {153}, journal = {The Journal of Chemical Physics}, doi = {10.1063/5.0017923}, pages = {054119}, abstract = {The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular, at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential μ and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a μT reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures.}, language = {en} } @article{EbrahimiViandHoeflingKleinetal., author = {Ebrahimi Viand, Roya and H{\"o}fling, Felix and Klein, Rupert and Delle Site, Luigi}, title = {Theory and simulation of open systems out of equilibrium}, series = {The Journal of Chemical Physics}, volume = {153}, journal = {The Journal of Chemical Physics}, doi = {10.1063/5.0014065}, pages = {101102}, abstract = {We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.}, language = {en} } @article{DelleSiteKrekelerWhittakeretal., author = {Delle Site, Luigi and Krekeler, Christian and Whittaker, John and Agarwal, Animesh and Klein, Rupert and H{\"o}fling, Felix}, title = {Molecular Dynamics of Open Systems: Construction of a Mean-Field Particle Reservoir}, series = {Advanced Theory and Simulations}, volume = {2}, journal = {Advanced Theory and Simulations}, doi = {10.1002/adts.201900014}, pages = {1900014}, abstract = {The simulation of open molecular systems requires explicit or implicit reservoirs of energy and particles. Whereas full atomistic resolution is desired in the region of interest, there is some freedom in the implementation of the reservoirs. Here, a combined, explicit reservoir is constructed by interfacing the atomistic region with regions of point-like, non-interacting particles (tracers) embedded in a thermodynamic mean field. The tracer molecules acquire atomistic resolution upon entering the atomistic region and equilibrate with this environment, while atomistic molecules become tracers governed by an effective mean-field potential after crossing the atomistic boundary. The approach is extensively tested on thermodynamic, structural, and dynamic properties of liquid water. Conceptual and numerical advantages of the procedure as well as new perspectives are highlighted and discussed.}, language = {en} } @misc{MokhtariPattersonHoefling, author = {Mokhtari, Zahra and Patterson, Robert I. A. and H{\"o}fling, Felix}, title = {Spontaneous trail formation in populations of auto-chemotactic walkers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-84466}, abstract = {We study the formation of trails in populations of self-propelled agents that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g., ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium \add{state} diagram of the model, spanned by the strength of the agent--pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation.}, language = {en} } @article{PathaniaChakrabortyHoefling, author = {Pathania, Yogyata and Chakraborty, Dipanjan and H{\"o}fling, Felix}, title = {Continuous demixing transition of binary liquids: finite-size scaling from the analysis of sub-systems}, series = {Advances Theory and Simulation}, volume = {4}, journal = {Advances Theory and Simulation}, doi = {10.1002/adts.202000235}, pages = {2000235}, language = {en} } @article{FroembergHoefling, author = {Fr{\"o}mberg, Daniela and H{\"o}fling, Felix}, title = {Generalized master equation for first-passage problems in partitioned spaces}, series = {Journal of Physics A: Mathematical and Theoretical}, volume = {54}, journal = {Journal of Physics A: Mathematical and Theoretical}, doi = {10.1088/1751-8121/abf2ec}, pages = {215601}, language = {en} } @article{KleinEbrahimiViandHoeflingetal., author = {Klein, Rupert and Ebrahimi Viand, Roya and H{\"o}fling, Felix and Delle Site, Luigi}, title = {Nonequilibrium induced by reservoirs: Physico-mathematical model and numerical tests}, series = {Advances Theory and Simulation}, volume = {4}, journal = {Advances Theory and Simulation}, doi = {10.1002/adts.202100071}, pages = {2100071}, language = {en} } @article{GholamiHoeflingKleinetal., author = {Gholami, Abbas and H{\"o}fling, Felix and Klein, Rupert and Delle Site, Luigi}, title = {Thermodynamic relations at the coupling boundary in adaptive resolution simulations for open systems}, series = {Advances Theory and Simulation}, volume = {4}, journal = {Advances Theory and Simulation}, doi = {10.1002/adts.202000303}, pages = {2000303}, language = {en} } @article{MokhtariPattersonHoefling, author = {Mokhtari, Zahra and Patterson, Robert I. A. and H{\"o}fling, Felix}, title = {Spontaneous trail formation in populations of auto-chemotactic walkers}, series = {New Journal of Physics}, volume = {24}, journal = {New Journal of Physics}, doi = {10.1088/1367-2630/ac43ec}, pages = {013012}, language = {en} } @article{StraubeWinkelmannSchuetteetal., author = {Straube, Arthur and Winkelmann, Stefanie and Sch{\"u}tte, Christof and H{\"o}fling, Felix}, title = {Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles}, series = {J. Phys. Chem. Lett.}, volume = {12}, journal = {J. Phys. Chem. Lett.}, doi = {10.1021/acs.jpclett.1c03016}, pages = {9888 -- 9893}, abstract = {The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.}, language = {en} } @article{delRazoFroembergStraubeetal., author = {del Razo, Mauricio and Fr{\"o}mberg, Daniela and Straube, Arthur and Sch{\"u}tte, Christof and H{\"o}fling, Felix and Winkelmann, Stefanie}, title = {A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations}, series = {Letters in Mathematical Physics}, volume = {112}, journal = {Letters in Mathematical Physics}, number = {49}, doi = {10.1007/s11005-022-01539-w}, language = {en} } @article{delRazoWinkelmannKleinetal., author = {del Razo, Mauricio and Winkelmann, Stefanie and Klein, Rupert and H{\"o}fling, Felix}, title = {Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level}, series = {Journal of Mathematical Physics}, volume = {64}, journal = {Journal of Mathematical Physics}, number = {1}, doi = {10.1063/5.0129620}, abstract = {The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects.}, language = {en} } @article{StraubeWinkelmannHoefling, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, series = {The Journal of Physical Chemistry B}, volume = {127}, journal = {The Journal of Physical Chemistry B}, number = {13}, doi = {10.1021/acs.jpcb.2c09092}, pages = {2955 -- 2967}, abstract = {This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.}, language = {en} } @article{StraubeHoefling, author = {Straube, Arthur and H{\"o}fling, Felix}, title = {Depinning transition of self-propelled particles}, abstract = {A depinning transition is observed in a variety of contexts when a certain threshold force must be applied to drive a system out of an immobile state. A well-studied example is the depinning of colloidal particles from a corrugated landscape, whereas its active-matter analogue has remained unexplored. We discuss how active noise due to self-propulsion impacts the nature of the transition: it causes a change of the critical exponent from 1/2 for quickly reorienting particles to 3/2 for slowly reorienting ones. In between these analytically tractable limits, the drift velocity exhibits a superexponential behavior as is corroborated by high-precision data. Giant diffusion phenomena occur in the two different regimes. Our predictions appear amenable to experimental tests, lay foundations for insight into the depinning of collective variables in active matter, and are relevant for any system with a saddle-node bifurcation in the presence of a bounded noise.}, language = {en} } @misc{StraubeWinkelmannHoefling, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, issn = {1438-0064}, doi = {10.12752/8817}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88179}, abstract = {Our theoretical study concerns an urea-urease-based pH oscillator confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.}, language = {en} } @article{HoeflingDietrich, author = {H{\"o}fling, Felix and Dietrich, Siegfried}, title = {Structure of liquid-vapor interfaces: perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence X-ray diffraction}, series = {J Chem Phys.}, volume = {160}, journal = {J Chem Phys.}, doi = {10.1063/5.0186955}, pages = {104107}, abstract = {Grazing-incidence X-ray diffraction (GIXRD) is a scattering technique which allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of the surface tension and of the interface roughness. However, the corresponding standard data analysis at non-zero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here we overcome this ambiguity by proposing a physically consistent model of the bulk contribution which is based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the X-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid--vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid--vapor coexistence line. A sensitivity analysis demonstrates the robustness of our findings concerning the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.}, language = {en} } @inproceedings{SkoblinHoeflingChristgau, author = {Skoblin, Viktor and H{\"o}fling, Felix and Christgau, Steffen}, title = {Gaining Cross-Platform Parallelism for HAL's Molecular Dynamics Package using SYCL}, series = {29. PARS-Workshop 2023}, volume = {36}, booktitle = {29. PARS-Workshop 2023}, issn = {0177-0454}, abstract = {Molecular dynamics simulations are one of the methods in scientific computing that benefit from GPU acceleration. For those devices, SYCL is a promising API for writing portable codes. In this paper, we present the case study of HAL's MD package that has been successfully migrated from CUDA to SYCL. We describe the different strategies that we followed in the process of porting the code. Following these strategies, we achieved code portability across major GPU vendors. Depending on the actual kernels, both significant performance improvements and regressions are observed. As a side effect of the migration process, we obtained impressing speedups also for execution on CPUs.}, language = {en} }