Rational social distancing policy during epidemics with limited healthcare capacity.

Epidemics of infectious diseases posing a serious risk to human health have occurred throughout history. During recent epidemics there has been much debate about policy, including how and when to impose restrictions on behaviour. Policymakers must balance a complex spectrum of objectives, suggesting a need for quantitative tools. Whether health services might be 'overwhelmed' has emerged as a key consideration. Here we show how costly interventions, such as taxes or subsidies on behaviour, can be used to exactly align individuals' decision making with government preferences even when these are not aligned. In order to achieve this, we develop a nested optimisation algorithm of both the government intervention strategy and the resulting equilibrium behaviour of individuals. We focus on a situation in which the capacity of the healthcare system to treat patients is limited and identify conditions under which the disease dynamics respect the capacity limit. We find an extremely sharp drop in peak infections at a critical maximum infection cost in the government's objective function. This is in marked contrast to the gradual reduction of infections if individuals make decisions without government intervention. We find optimal interventions vary less strongly in time when interventions are costly to the government and that the critical cost of the policy switch depends on how costly interventions are.

Direct numerical simulations of a microswimmer in a viscoelastic fluid.

This study presents the application of the smoothed profile (SP) method to perform direct numerical simulations for the motion of both passive and active "squirming" particles in Newtonian and viscoelastic fluids. We found that fluid elasticity has a significant impact on both the transient behavior and the steady-state velocity of the particles. Specifically, we observe that the swirling flow generated by the squirmer's surface velocity significantly enhances their swimming speed as the Weissenberg number increases, regardless of the swimming type. Furthermore, we find that pushers outperform pullers in Oldroyd-B fluids, suggesting that the speed of a squirmer depends on the swimmer type. To understand the physical origin of the phenomenon of swirling flow enhancing the swimming speed, we investigate the velocity field and polymer conformation around non-swirling and swirling neutral squirmers in viscoelastic fluids. Our investigation reveals that the velocity field around the neutral swirling squirmers exhibits pusher-like extensional flow characteristics, as well as an asymmetric polymer conformation distribution, which gives rise to this increased propulsion. This is confirmed by the investigation of the force on a fixed squirmer, which revealed that the polymer stress, particularly its diagonal components, plays a critical role in enhancing the swimming speed of swirling squirmers in viscoelastic fluids. Additionally, our results demonstrate that the maximum swimming speeds of swirling squirmers occur at an intermediate value of the fluid viscosity ratio for all swimmer types. These findings have important implications for understanding the behavior of particles and micro-organisms in complex fluids.

Rational social distancing in epidemics with uncertain vaccination timing.

During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

Learning to swim efficiently in a nonuniform flow field.

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyze this navigation by combining deep reinforcement learning with direct numerical simulations to resolve the hydrodynamics. We study how local and nonlocal information can be used to train a swimmer to achieve particular swimming tasks in a nonuniform flow field, in particular, a zigzag shear flow. The swimming tasks are (1) learning how to swim in the vorticity direction, (2) learning how to swim in the shear-gradient direction, and (3) learning how to swim in the shear-flow direction. We find that access to laboratory frame information on the swimmer's instantaneous orientation is all that is required in order to reach the optimal policy for tasks (1) and (2). However, information on both the translational and rotational velocities seems to be required to accomplish task (3). Inspired by biological microorganisms, we also consider the case where the swimmers sense local information, i.e., surface hydrodynamic forces, together with a signal direction. This might correspond to gravity or, for microorganisms with light sensors, a light source. In this case, we show that the swimmer can reach a comparable level of performance to that of a swimmer with access to laboratory frame variables. We also analyze the role of different swimming modes, i.e., pusher, puller, and neutral.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles.

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.

Control of cell colony growth by contact inhibition.

Contact inhibition is a cell property that limits the migration and proliferation of cells in crowded environments. Here we investigate the growth dynamics of a cell colony composed of migrating and proliferating cells on a substrate using a minimal model that incorporates the mechanisms of contact inhibition of locomotion and proliferation. We find two distinct regimes. At early times, when contact inhibition is weak, the colony grows exponentially in time, fully characterised by the proliferation rate. At long times, the colony boundary moves at a constant speed, determined only by the migration speed of a single cell and independent of the proliferation rate. Further, the model demonstrates how cell-cell alignment speeds up colony growth. Our model illuminates how simple local mechanical interactions give rise to contact inhibition, and from this, how cell colony growth is self-organised and controlled on a local level.

Spontaneous spatiotemporal ordering of shape oscillations enhances cell migration.

The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed period, mimicking the internal cycle of biological cells. We show that shape oscillations are crucial for local rearrangements that induce ordering of neighboring cells according to their internal clocks even in the absence of signaling and regularization. Our findings reveal a novel, purely physical mechanism through which the internal dynamics of cells influences their collective behavior, which is distinct from well known mechanisms like chemotaxis, cell division, and cell-cell adhesion.

Modeling the mechanosensitivity of fast-crawling cells on cyclically stretched substrates.

The mechanosensitivity of cells, which determines how they are able to respond to mechanical signals, is crucial for the functioning of biological systems. Experimentally, this is investigated by studying the reorientation of cells on cyclically stretched substrates. The reorientation depends on the type of cell and on the stretching protocol, but the mechanisms responsible for the response are still not completely understood. Here, we introduce a computational model for fast crawling cells on cyclically stretched substrates that accounts for the sub-cellular elements responsible for cell shape and motility. This includes the dynamics of the cell membrane, the actin cytoskeleton, and the focal adhesions with the stretching substrate. These processes evolve over characteristic time scales that can vary by orders of magnitude and naturally give rise to the frequency dependent reorientation observed experimentally. Depending on which processes are being probed by the stretching and on the type of coupling with the substrate, our simulations predict either no reorientation, a bi-stability in the parallel and perpendicular directions, or a complete reorientation in either the parallel or perpendicular direction. In particular, we show that an asymmetry in the adhesion dynamics during the loading and unloading phases of the stretching, whether it comes from the response of the cell itself or from the precise stretching protocol, can be used to selectively align the cells. Our results provide further evidence for the importance of focal adhesion dynamics in determining the mechanosensitive response of cells, as well as a way to interpret recent experiments.

Field-induced dipolar attraction between like-charged colloids.

The field induced anisotropic interactions between like-charged colloidal particles is studied using direct numerical simulations, where the polarization of the electric double layer is explicitly computed under external AC electric fields. These interactions are found to depend on the magnitude E0 and frequency ω of the applied field, as well as the zeta potential, the Debye length, and the relative orientation of the particles. We also determined the range of E0 and ω over which a dipolar attraction is induced between a pair of like-charged colloids. Finally, we performed simulations for systems of six and twelve colloidal particles to study the stability of pear-chain-like configurations.

Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition.

Contact inhibition plays a crucial role in cell motility, wound healing, and tumour formation. By mimicking the mechanical motion of cells crawling on a substrate, we constructed a minimal model of migrating cells that naturally gives rise to contact inhibition of locomotion (CIL). The model cell consists of two disks, a front disk (a pseudopod) and a back disk (cell body), which are connected by a finite extensible spring. Despite the simplicity of the model, the collective behaviour of the cells is highly non-trivial and depends on both the shape of the cells and whether CIL is enabled. Cells with a small front disk (i.e., a narrow pseudopod) form immobile colonies. In contrast, cells with a large front disk (e.g., a lamellipodium) exhibit coherent migration without any explicit alignment mechanism in the model. This result suggests that crawling cells often exhibit broad fronts because this helps facilitate alignment. After increasing the density, the cells develop density waves that propagate against the direction of cell migration and finally stop at higher densities.

Direct numerical simulations of rigid body dispersions. I. Mobility/friction tensors of assemblies of spheres.

An improved formulation of the "Smoothed Profile" method is introduced to perform direct numerical simulations of arbitrary rigid body dispersions in a Newtonian host solvent. Previous implementations of the method were restricted to spherical particles, severely limiting the types of systems that could be studied. The validity of the method is carefully examined by computing the friction/mobility tensors for a wide variety of geometries and comparing them to reference values obtained from accurate solutions to the Stokes-Equation.

A transferable ab initio based force field for aqueous ions.

We present a new polarizable force field for aqueous ions (Li(+), Na(+), K(+), Rb(+), Cs(+), Mg(2 +), Ca(2 +), Sr(2 +), and Cl(-)) derived from condensed phase ab initio calculations. We use maximally localized Wannier functions together with a generalized force and dipole-matching procedure to determine the whole set of parameters. Experimental data are then used only for validation purposes and a good agreement is obtained for structural, dynamic, and thermodynamic properties. The same procedure applied to crystalline phases allows to parametrize the interaction between cations and the chloride anion. Finally, we illustrate the good transferability of the force field to other thermodynamic conditions by investigating concentrated solutions.

Primitive models of ions in solution from molecular descriptions: a perturbation approach.

The development of simple, primitive model descriptions for electrolyte solutions is usually carried out by fitting the system parameters to reproduce some experimental data. We propose an alternative method, that allows one to derive implicit solvent models of electrolyte solutions from all-atom descriptions. We obtain analytic expressions for the thermodynamic and structural properties of the ions, which are in good agreement with the underlying explicit solvent representation, provided that ion association is taken into account. Effective ion-ion potentials are derived from molecular dynamics simulations and are used within a first-order perturbation theory to derive the best possible description in terms of charged hard-spheres. We show that our model provides a valid description for a series of 1-1 electrolytes.

Ions in solutions: Determining their polarizabilities from first-principles.

Dipole polarizabilities of a series of ions in aqueous solutions are computed from first-principles. The procedure is based on the study of the linear response of the maximally localized Wannier functions to an applied external field, within density functional theory. For most monoatomic cations (Li(+), Na(+), K(+), Rb(+), Mg(2+), Ca(2+) and Sr(2+)) the computed polarizabilities are the same as in the gas phase. For Cs(+) and a series of anions (F(-), Cl(-), Br(-) and I(-)), environmental effects are observed, which reduce the polarizabilities in aqueous solutions with respect to their gas phase values. The polarizabilities of H((aq)) (+), OH((aq)) (-) have also been determined along an ab initio molecular dynamics simulation. We observe that the polarizability of a molecule instantaneously switches upon proton transfer events. Finally, we also computed the polarizability tensor in the case of a strongly anisotropic molecular ion, UO(2) (2+). The results of these calculations will be useful in building interaction potentials that include polarization effects.