The dispersion of airborne pollutants in the urban atmosphere is a complex, canopy-driven process. The intricate structure of the city, the high number of potential sources, and the large spatial domain make it difficult to predict dispersion patterns, to simulate a great number of scenarios, and to identify the high-impact emission areas. Here we show that these complex transport dynamics can be efficiently characterized by adopting a complex network approach. The urban canopy layer is represented as a complex network. Street canyons and their intersections shape the spatial structure of the network. The direction and the transport capacity of the flow in the streets define the direction and the weight of the links. Within this perspective, pollutant contamination from a source is modeled as a spreading process on a network, and the most dangerous areas in a city are identified as the best spreading nodes. To this aim, we derive a centrality metric tailored to mass transport in flow networks. By means of the proposed approach, vulnerability maps of cities are rapidly depicted, revealing the nontrivial relation between urban topology, transport capacity of the street canyons, and forcing of the external wind. The network formalism provides promising insight in the comprehensive analysis of the fragility of cities to air pollution.

In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation (CME). In this work, we construct an original path-integral description of the CME and show how applying Gillespie's two conditions to it directly leads to a path-integral equivalent to the CLE. We compare this approach to the path-integral equivalent of a large system size derivation and show that they are qualitatively different. In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems and are readily generalizable.

Nanostructured materials made through flow-assisted assembly of proteinaceous or polymeric nanosized fibrillar building blocks are promising contenders for a family of high-performance biocompatible materials in a wide variety of applications. Optimization of these processes relies on improving our knowledge of the physical mechanisms from nano- to macroscale and especially understanding the alignment of elongated nanoparticles in flows. Here, we study the full projected orientation distributions of cellulose nanocrystals (CNCs) and nanofibrils (CNFs) in confined flow using scanning microbeam SAXS. For CNCs, we further compare with a simulated system of dilute Brownian ellipsoids, which agrees well at dilute concentrations. However, increasing CNC concentration to a semidilute regime results in locally arranged domains called tactoids, which aid in aligning the CNC at low shear rates, but limit alignment at higher rates. Similarly, shear alignment of CNF at semidilute conditions is also limited owing to probable bundle or flock formation of the highly entangled nanofibrils. This work provides a quantitative comparison of full projected orientation distributions of elongated nanoparticles in confined flow and provides an important stepping stone towards predicting and controlling processes to create nanostructured materials on an industrial scale.

Using Monte Carlo simulations, we investigate how geometric percolation and electrical conductivity in suspensions of hard conducting platelets are affected by the addition of platelets and their degree of spontaneous alignment. In our simulation results for aspect ratios 10, 25, and 50, we consistently observe a monotonically decreasing percolation threshold as a function of volume fraction, i.e., the addition of particles always aids percolation. In the nematic phase, the distribution of particles inside the percolating clusters becomes less spherically symmetric and the aspect ratio of the clusters increases. However, the clusters are also anisotropically shaped in the isotropic phase, although their aspect ratio remains constant as a function of volume fraction and is only weakly dependent on the particle aspect ratio. Mapping the percolating clusters of platelets to linear resistor networks, and assigning unit conductance to all connections, we find a constant conductivity both across the isotropic-nematic transition and in the respective stable phases. This behavior is consistent with the other observed topological properties of the networks, namely, the average path length, average number of contacts per particle, and the Kirchhoff index, which all remain constant and unaffected by both the addition of particles and the degree of alignment of their suspension. In contrast, using an anisotropic conductance model that explicitly accounts for the relative orientation of the particles, the network conductivity decreases with increasing volume fraction in the isotropic, and further diminishes at the onset of the nematic while preserving the same trend deep in the nematic. Hence, our observations consistently suggest that, unlike for rodlike fillers, the network structures that arise from platelet suspensions are not very sensitive to the particle aspect ratio or to alignment. Hence platelets are not as versatile as fillers for dispersion in conductive composite materials as rods.

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations—often called “soft spots”—that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes—coined here nonlinear quasilocalized excitations (NQEs)—that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

Elastic waves propagating at the interface of soft solids can be altered by the presence of external forces such as capillarity and gravity. We measure the dispersion relation of waves at the free surface of agarose gels with great accuracy, revealing the existence of multiple modes as well as an apparent dispersion. We disentangle the role of capillarity and elasticity by considering the three-dimensional nature of mechanical waves, achieving quantitative agreement between theoretical predictions and experiments. Notably, our results show that capillarity plays an important role for wave numbers smaller than expected from balancing elastic and capillary forces. We further confirm the efficiency of our approach by including the effect of gravity in our predictions and quantitatively comparing it to experiments.

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the nonlinear plate theory as well as the membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence, caused by long-range interaction of relevant thermal fluctuations (flexural phonons), is responsible for the nonlinear Hooke law observed recently in graphene. It is shown that this anomalous elasticity affects the dependence of the maximal height of the bubble as a function of its radius and temperature. We determine the characteristic temperature above which the anomalous elasticity is important. It is suggested that, for graphene-based van der Waals heterostructures, the predicted anomalous regime is experimentally accessible at room temperature.

We perform equilibrium molecular dynamics simulations for nanoscale fluids confined between two parallel walls and investigate how the autocorrelation function of force acting on one wall is related to the slip length. We demonstrate that for atomically smooth surfaces, the autocorrelation function is accurately described by linearized fluctuating hydrodynamics (LFH). Excellent agreement between the simulation and the LFH solution is found over a wide range of scales, specifically, from the timescale of fluid relaxation even to that of molecular motion. Fitting the simulation data yields a reasonable estimation of the slip length. We show that LFH provides a starting point for examining the relationship between the slip length and the force fluctuations.

Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state of the one-dimensional Kuramoto-Sivashinsky (KS) deterministic PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile $h(x,t)$ for different initial conditions. We establish, therefore, that the statistical properties of the one-dimensional (1D) KS PDE in this state are in the 1D KPZ universality class.

“Can one hear the shape of a drum?” Kac raised this famous question in 1966, referring to the possibility of the existence of nonisometric planar domains with identical Dirichlet eigenvalue spectra of the Laplacian. Pairs of nonisometric isospectral billiards were eventually found by employing the transplantation method which was deduced from Sunada's theorem. Our main focus is the question to what extent isospectrality of nonrelativistic quantum billiards is present in the corresponding relativistic case, i.e., for massless spin-1/2 particles governed by the Dirac equation and confined to a domain of corresponding shape by imposing boundary conditions on the wave function components. We consider those for neutrino billiards [Berry and Mondragon, Proc. R. Soc. London A 412, 53 (1987)] and demonstrate that the transplantation method fails and thus isospectrality is lost when changing from the nonrelativistic to the relativistic case. To confirm this we compute the eigenvalues of pairs of neutrino billiards with the shapes of various billiards which are known to be isospectral in the nonrelativistic limit. Furthermore, we investigate their spectral properties, in particular, to find out whether not only their eigenvalues but also the fluctuations in their spectra and their length spectra differ.

Temperature-controlled polarization modulation near-field scanning optical microscopy measurements of a single supported $L_{{\beta }^{\prime }}$ 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayer are presented. The effective retardance ($S=\frac{2\pi (n_e-n_o)t}{\lambda }$, where $t$ is the thickness of the bilayer and $\lambda$ is the wavelength of light used) and the direction of the projection of the acyl chains ($\theta$) were measured simultaneously. We demonstrate how one is able to align the system over the sample and measure a relative retardance $\mathrm{\Delta }S$, a crucial step in performing temperature-controlled experiments. Maps of $\mathrm{\Delta }S$ and $\theta$, with a lateral resolution on the order of $\sim 100$ nm are presented, highlighting variations deriving from changes in the average molecular orientation across a lipid membrane at room temperature. A discussion of how this information can be used to map the average three-dimensional orientation of the molecules is presented. From $\mathrm{\Delta }S$ and the known thickness of the membrane $t$ the birefringence ($n_e-n_o$) of the bilayer was determined. Temperature-controlled measurements yielded a change of $\mathrm{\Delta }S\sim (3.8\pm 0.3)$ mrad at the main transition temperature ($T_m\sim {41}^{\circ }\mathrm{C}$) of a single planar bilayer of DPPC, where the membrane transitioned between the gel $L_{{\beta }^{\prime }}$ to liquid disorder $L_{\alpha }$ state. The result agrees well with previous values of ($n_e-n_o$) in the $L_{{\beta }^{\prime }}$ phase and translates to an assumed average acyl chain orientation relative to the membrane normal ($\langle \varphi \rangle \sim {32}^{\circ }$) when $T<T_m$ and $0^{\circ }$ when $T>T_m$. Evidence of super heating and cooling are presented. A discussion on how the observed behavior as $T_m$ is approached, could relate to the existence of varying microconfigurations within the lipid bilyer are presented. This conversation includes ideas from a Landau-Ginzburg picture of first-order phase transitions in nematic-to-isotropic systems.

On the basis of phase-field theory, we develop a lattice Boltzmann model for ternary fluids containing solid. We develop a modified bounce-back method to describe the interactions between the solid and N-phase $(N\ge 2)$ fluids. We derive a wetting boundary condition for three-phase flows from the point of mass conservation and propose a scheme for implementing the wetting condition on curved boundaries. We develop a diffuse interface method to compute the capillary force acting on the moving solid objects at the ternary fluids-sold contact lines. In addition, this model can deal with problems involving high density and viscosity contrasts. The proposed method is examined through several test cases. We test the modified bounce-back scheme, wetting boundary condition, and capillary force model in three different cases, and the numerical results agree well with the analytical solutions. Finally, we apply the model to two three-dimensional problems to assess its numerical accuracy and stability.

We report a mechanism for nucleation in a monolayer of hexagonally packed monodisperse droplet arrays. Upon cooling, we observe solidified droplets to nucleate their supercooled neighbors giving rise to an autocatalyticlike mechanism for accelerated crystallization. This collective mode of nucleation depends on the strength and nature of droplet contacts. Intriguingly, the statistical distribution of the solidified droplet clusters is found to be independent of emulsion characteristics except surfactant. In contrast to classical nucleation theory, our work highlights the need to consider collective effects of nucleation in supercooled concentrated emulsions where droplet crowding is inevitable.

We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counterrotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counterrotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Last, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.

We present a study comparing atomic motional amplitudes in calcium rich and depleted alpha-lactalbumin. The investigations were performed by elastic incoherent neutron scattering (EINS) and molecular dynamics (MD) simulations. As the variations were expected to be very small, three different hydration levels and timescales (instrumental resolutions) were measured. In addition, we used two models to extract the mean square displacements (MSDs) from the EINS data, one taking into account the motional heterogeneity of the MSD. At a timescale of several nanoseconds, small differences in the amplitudes between the calcium enriched and depleted alpha-lactalbumin are visible, whereas at lower timescales no changes can be concluded within the statistics. The results are compared to MD simulations at 280 and 300 K by extracting the MSDs of the trajectories in two separate ways: first by direct calculation, and second by a virtual neutron experiment using the same models as for the experimental data. We show that the simulated data give qualitatively similar results as the experimental data but quantitatively there are differences. Furthermore, the distribution of the MSDs in the simulations suggests that the inclusion of heterogeneity is reasonable for alpha-lactalbumin, but a bi-or trimodal approach may be sufficient.

In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the nonconserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Chatterjee et al., Phys. Rev. E 98, 032109 (2018)]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transition temperatures decrease with bond randomness strength $\epsilon$. Effect of $\epsilon$ on the nonequilibrium coarsening dynamics is investigated following independent rapid quenches in the quasi-long-range ordered (QLRO, $T_c^2<T<T_c^1$) regime and long-range ordered (LRO, $T<T_c^2$) regime at temperature $T$. We report that the dynamical scaling of the correlation function and structure factor is independent of $\epsilon$ and the presence of quenched disorder slows down domain coarsening. Coarsening dynamics in both LRO and QLRO regimes are further characterized by power-law growth with disorder-dependent exponents within our simulation timescales. The growth exponents in the LRO regime decrease from 0.5 in the pure case to 0.22 in the maximum disordered case, whereas the corresponding change in the QLRO regime happens from 0.45 to 0.38. We further explored the coarsening dynamics in the bond-diluted clock model and, in both the models, the effect of the disorder is more significant for the quench in the LRO regime compared to the QLRO regime.

Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant at both the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression or decompression situation.

The flow of a colloidal suspension in a narrow channel of periodically varying width is described by the one-dimensional generalized asymmetric exclusion process. Each site admits multiple particle occupancy. We consider particles of two different sizes. The sites available to particles form a comblike geometry: entropic traps due to variation of channel width are modeled by dead ends, or pockets, attached individually to each site of a one-dimensional chain. This geometry, combined with periodically alternating external driving, leads to a ratchet effect which is very sensitive to particle size, thus enabling particle sorting. A typical behavior is reversal of the current orientation when we change the density of small and big particles. In an optimal situation, the two types of particles move in opposite directions, and particle separation is in principle perfect. We show that in the simplest situation with one type of particles only, this model is exactly soluble. In the general case we use enhanced mean-field approximation as well as direct numerical simulations.