Smoothed dissipative particle dynamics (SDPD) is a mesoscopic method that allows one to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a function of the size of the mesoparticles, both at equilibrium and out of equilibrium. We also propose a reformulation of the SDPD equations in terms of energy variables. This increases the similarities with dissipative particle dynamics with energy conservation and opens the way for a coupling between the two methods. Finally, we present a numerical scheme for SDPD that ensures the conservation of the invariants of the dynamics. Numerical simulations illustrate this approach.

The present work proposes a simple lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media. By incorporating forces and source terms into the lattice Boltzmann equation, the incompressible Navier-Stokes equations are recovered through the Chapman-Enskog expansion. It is found that the added terms are just the extra terms in the governing equations for the axisymmetric thermal flows through porous media compared with the Navier-Stokes equations. Four numerical simulations are performed to validate this model. Good agreement is obtained between the present work and the analytic solutions and/or the results of previous studies. This proves its efficacy and simplicity regarding other methods. Also, this approach provides guidance for problems with more physical phenomena and complicated force forms.

Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering ($S$)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The $S$-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the $S$-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.

We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased random walks. We consider three vertex properties that provide, respectively, short-, medium-, and long-range information regarding the topological role of vertices in a given network. In order to reveal the relation between these quantities, we applied the multifractal cross-correlation analysis technique, which provides information about the nonlinear effects in coupling of time series. We show that the considered network models are characterized by unique multifractal properties of the cross-correlation. In particular, it is possible to distinguish between Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks on the basis of fractal cross-correlation. Moreover, the analysis of protein contact networks reveals characteristics shared with both scale-free and small-world models.

The structural organization of a protein family is investigated by devising a method based on the random matrix theory (RMT), which uses the physiochemical properties of the amino acid with multiple sequence alignment. A graphical method to represent protein sequences using physiochemical properties is devised that gives a fast, easy, and informative way of comparing the evolutionary distances between protein sequences. A correlation matrix associated with each property is calculated, where the noise reduction and information filtering is done using RMT involving an ensemble of Wishart matrices. The analysis of the eigenvalue statistics of the correlation matrix for the $\beta$-lactamase family shows the universal features as observed in the Gaussian orthogonal ensemble (GOE). The property-based approach captures the short- as well as the long-range correlation (approximately following GOE) between the eigenvalues, whereas the previous approach (treating amino acids as characters) gives the usual short-range correlations, while the long-range correlations are the same as that of an uncorrelated series. The distribution of the eigenvector components for the eigenvalues outside the bulk (RMT bound) deviates significantly from RMT observations and contains important information about the system. The information content of each eigenvector of the correlation matrix is quantified by introducing an entropic estimate, which shows that for the $\beta$-lactamase family the smallest eigenvectors (low eigenmodes) are highly localized as well as informative. These small eigenvectors when processed gives clusters involving positions that have well-defined biological and structural importance matching with experiments. The approach is crucial for the recognition of structural motifs as shown in $\beta$-lactamase (and other families) and selectively identifies the important positions for targets to deactivate (activate) the enzymatic actions.

The adsorption of DNA or other polyelectrolyte molecules on charged membranes is a recurrent motif in soft matter and bionanotechnological systems. Two typical situations encountered are the deposition of single DNA chains onto substrates for further analysis, e.g., by force microscopy, or the pulling of polyelectrolytes into membrane nanopores, as in sequencing applications. In this paper, we present a theoretical analysis of such scenarios based on the self-consistent field theory approach, which allows us to address the important effect of charge correlations. We calculate the grand potential of a stiff polyelectrolyte immersed in an electrolyte in contact with a negatively charged dielectric membrane. For the sake of conciseness, we neglect conformational polymer fluctuations and model the molecule as a rigid charged line. At strongly charged membranes, the adsorbed counterions enhance the screening ability of the interfacial region. In the presence of highly charged polymers such as double-stranded DNA molecules close to the membrane, this enhanced interfacial screening dominates the mean-field level DNA-membrane repulsion and results in the adsorption of the DNA molecule to the surface. This picture provides a simple explanation for the recently observed DNA binding onto similarly charged substrates [G. L.-Caballero et al., Soft Matter 10, 2805 (2014)] and points out charge correlations as a non-negligible ingredient of polymer-surface interactions.

The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear $k$-mers (particles occupying $k$ adjacent adsorption sites) onto a square lattice was studied by means of computer simulation. Overlapping with predeposited $k$-mers and detachment from the surface were forbidden. The RSA process continued until the saturation jamming limit, $p_j$. The isotropic (equiprobable orientations of $k$-mers along $x$ and $y$ axes) and anisotropic (all $k$-mers aligned along the $y$ axis) depositions for two different models—of an insulating substrate and conducting $k$-mers (C model) and of a conducting substrate and insulating $k$-mers (I model)—were examined. The Frank-Lobb algorithm was applied to calculate the electrical conductivity in both the $x$ and $y$ directions for different lengths ($k=1$ – 128) and concentrations ($p=0$ – $p_j$) of the $k$-mers. The “intrinsic electrical conductivity” and concentration dependence of the relative electrical conductivity $\mathrm{\Sigma }\left(p\right)$ ($\mathrm{\Sigma }=\sigma /{\sigma }_m$ for the C model and $\mathrm{\Sigma }={\sigma }_m/\sigma$ for the I model, where ${\sigma }_m$ is the electrical conductivity of substrate) in different directions were analyzed. At large values of $k$ the $\mathrm{\Sigma }\left(p\right)$ curves became very similar and they almost coincided at $k=128$. Moreover, for both models the greater the length of the $k$-mers the smoother the functions ${\mathrm{\Sigma }}_{xy}\left(p\right),{\mathrm{\Sigma }}_x\left(p\right)$ and ${\mathrm{\Sigma }}_y\left(p\right)$. For the more practically important C model, the other interesting findings are (i) for large values of $k$ ($k=64,128$), the values of ${\mathrm{\Sigma }}_{xy}$ and ${\mathrm{\Sigma }}_y$ increase rapidly with the initial increase of $p$ from 0 to 0.1; (ii) for $k\ge 16$, all the ${\mathrm{\Sigma }}_{xy}\left(p\right)$ and ${\mathrm{\Sigma }}_x\left(p\right)$ curves intersect with each other at the same isoconductivity points; (iii) for anisotropic deposition, the percolation concentrations are the same in the $x$ and $y$ directions, whereas, at the percolation point the greater the length of the $k$-mers the larger the anisotropy of the electrical conductivity, i.e., the ratio ${\sigma }_y/{\sigma }_x$ ($>1$).

The flame or flow behavior of a turbulent reacting wake is known to be fundamentally different at high and low values of flame density ratio $\left({\rho }_u/{\rho }_b\right)$, as the flow transitions from globally stable to unstable. This paper analyzes the nonlinear dynamics present in a bluff-body stabilized flame, and identifies the transition characteristics in the wake as ${\rho }_u/{\rho }_b$ is varied over a Reynolds number (based on the bluff-body lip velocity) range of 1000–3300. Recurrence quantification analysis (RQA) of the experimentally obtained time series of the flame edge fluctuations reveals that the time series is highly aperiodic at high values of ${\rho }_u/{\rho }_b$ and transitions to increasingly correlated or nearly periodic behavior at low values. From the RQA of the transverse velocity time series, we observe that periodicity in the flame oscillations are related to periodicity in the flow. Therefore, we hypothesize that this transition from aperiodic to nearly periodic behavior in the flame edge time series is a manifestation of the transition in the flow from globally stable, convective instability to global instability as ${\rho }_u/{\rho }_b$ decreases. The recurrence analysis further reveals that the transition in periodicity is not a sudden shift; rather it occurs through an intermittent regime present at low and intermediate ${\rho }_u/{\rho }_b$. During intermittency, the flow behavior switches between aperiodic oscillations, reminiscent of a globally stable, convective instability, and periodic oscillations, reminiscent of a global instability. Analysis of the distribution of the lengths of the periodic regions in the intermittent time series and the first return map indicate the presence of type-II intermittency.

Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016)]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.

The current gold standard for detecting or quantifying target analytes from blood samples is the ELISA (enzyme-linked immunosorbent assay). The detection limit of ELISA is about 250 pg/ml. However, to quantify analytes that are related to various stages of tumors including early detection requires detecting well below the current limit of the ELISA test. For example, Interleukin 6 (IL-6) levels of early oral cancer patients are <100 pg/ml and the prostate specific antigen level of the early stage of prostate cancer is about 1 ng/ml. Further, it has been reported that there are significantly less than $1\mathrm{pg}/\mathrm{mL}$ of analytes in the early stage of tumors. Therefore, depending on the tumor type and the stage of the tumors, it is required to quantify various levels of analytes ranging from ng/ml to pg/ml. To accommodate these critical needs in the current diagnosis, there is a need for a technique that has a large dynamic range with an ability to detect extremely low levels of target analytes ($\sim \mathrm{zmoles}$).

The curvature of the unstable part of the miscible interface between a circular blob and the ambient fluid in two-dimensional homogeneous porous media depends on the viscosity of the fluids. The influence of the interface curvature on the fingering instability and mixing of a miscible blob within a rectilinear displacement is investigated numerically. The fluid velocity in porous media is governed by Darcy's law, coupled with a convection-diffusion equation that determines the evolution of the solute concentration controlling the viscosity of the fluids. Numerical simulations are performed using a Fourier pseudospectral method to determine the dynamics of a miscible blob (circular or square). It is shown that for a less viscous circular blob, there exist three different instability regions without any finite $R$-window for viscous fingering, unlike the case of a more viscous circular blob. Critical blob radius for the onset of instability is smaller for a less viscous blob as compared to its more viscous counterpart. Fingering enhances spreading and mixing of miscible fluids. Hence a less viscous blob mixes with the ambient fluid quicker than the more viscous one. Furthermore, we show that mixing increases with the viscosity contrast for a less viscous blob, while for a more viscous one mixing depends nonmonotonically on the viscosity contrast. For a more viscous blob mixing depends nonmonotonically on the dispersion anisotropy, while it decreases monotonically with the anisotropic dispersion coefficient for a less viscous blob. We also show that the dynamics of a more viscous square blob is qualitatively similar to that of a circular one, except the existence of the lump-shaped instability region in the $R$-Pe plane. We have shown that the Rayleigh-Taylor instability in a circular blob (heavier or lighter than the ambient fluid) is independent of the interface curvature.

Critical fluctuations change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, reduced anisotropy of nonlinear susceptibility acquires at $T_c$ the universal value ${\delta }_4^{*}=\frac{2v^{*}}{3(u^{*}+v^{*})}$ where $u^{*}$ and $v^{*}$ are coordinates of the cubic fixed point on the flow diagram of renormalization group equations. In the paper, the critical value of the reduced anisotropy is estimated within the pseudo-$\epsilon$ expansion approach. The six-loop pseudo-$\epsilon$ expansions for $u^{*}$, $v^{*}$, and ${\delta }_4^{*}$ are derived for the arbitrary spin dimensionality $n$. For cubic crystals ($n=3$) higher-order coefficients of the pseudo-$\epsilon$ expansions obtained turn out to be so small that use of simple Padé approximants yields reliable numerical results. Padé resummation of the pseudo-$\epsilon$ series for $u^{*}$, $v^{*}$, and ${\delta }_4^{*}$ leads to the estimate ${\delta }_4^{*}=0.079\pm 0.006$, indicating that detection of the anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is certainly possible.

We discuss the statistics of first-passage times of a Brownian particle moving in a highly unstable nonlinear potential proportional to an odd power of position. We observe temperature-induced shortening of the mean first-passage time and its dependence on the power of nonlinearity. We propose a passage-time fraction as both a simple and experimentally detectable witness of the nonlinearity. It is advantageously independent of all other parameters of the experiment and observable for a small number of trajectories. To better characterize the stochastic passage in the unstable potential, we introduce an analogy of the signal-to-noise ratio for the statistical distribution of the first-passage times. Interestingly, the upper bound for the signal-to-noise ratio is temperature independent in the unstable potential. Finally, we describe the nonequilibrium steady state of the particle cyclically passing through unstable odd nonlinearity. The maximum of the steady-state probability distribution shifts against the directions of the current and this counterintuitive effect increases with temperature. All these thermally induced effects are very promising targets for experimental tests of highly nonlinear stochastic dynamics of particles placed into optical potential landscapes of shaped optical tweezers.

In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL), which is a multifractal and whose dual is a scale-free network. The characteristic property of percolation is that it exhibits threshold phenomena as we find sudden or abrupt jump in spanning probability across $p_c$ accompanied by the divergence of some other observable quantities, which is reminiscent of a continuous phase transition. Indeed, percolation is characterized by the critical behavior of percolation strength $P\left(p\right)\sim {(p_c-p)}^{\beta }$, mean cluster size $S\sim {(p_c-p)}^{-\gamma }$, and the system size $L\sim {(p_c-p)}^{-\nu }$, which are known as the equivalent counterpart of the order parameter, susceptibility, and correlation length, respectively. Moreover, the cluster size distribution function $n_s\left(p_c\right)\sim s^{-\tau }$ and the mass-length relation $M\sim L^{d_f}$ of the spanning cluster also provide useful characterization of the percolation process. We numerically obtain a value for $p_c$ and for all the exponents such as $\beta ,\nu ,\gamma ,\tau$, and $d_f$. We find that, except for $p_c$, all the exponents are exactly the same in both bond and site percolation despite the significant difference in the definition of cluster and other quantities. Our results suggest that the percolation on WPSL belongs to a new universality class, as its exponents do not share the same value as for all the existing planar lattices. Besides, like all other cases, its site and bond type belong to the same universality class.

While the origins of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of spatially correlated noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, starting from the microscopic, deterministic model, we derive the analytical formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by the Gaussian SCN and calculate the adequate fluctuation-dissipation relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g., the singular behavior for certain types of interactions. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a nonequilibrium mechanism facilitating the molecular binding of the like-charged particles.

We investigate, via Brownian dynamics simulations, the reaction dynamics of a generic, nonlinear chemical network under spatial confinement and crowding conditions. In detail, the Willamowski-Rossler chemical reaction system has been “extended” and considered as a prototype reaction-diffusion system. Our results are potentially relevant to a number of open problems in biophysics and biochemistry, such as the synthesis of primitive cellular units (protocells) and the definition of their role in the chemical origin of life and the characterization of vesicle-mediated drug delivery processes. More generally, the computational approach presented in this work makes the case for the use of spatial stochastic simulation methods for the study of biochemical networks in vivo where the “well-mixed” approximation is invalid and both thermal and intrinsic fluctuations linked to the possible presence of molecular species in low number copies cannot be averaged out.

Peptide aggregation frequently involves sequences with strong homophilic binding character, i.e., sequences that self-assemble with like species in a crowded cellular environment, in the face of a multitude of other peptides or proteins as potential heterophilic binding partners. What kinds of sequences display a strong tendency towards homophilic binding and self-assembly, and what are the origins of this behavior? Here, we consider how sequence specificity in oligomerization processes plays out in a simple two-dimensional (2D) lattice statistical-thermodynamic peptide model that permits exhaustive examination of the entire sequence and configurational landscapes. We find that sequences with strong self-specificities have either alternating hydrophobic and hydrophilic residues or short patches of hydrophobic residues, both which minimize intramolecular hydrophobic interactions in part due to the constraints of the 2D lattice. We also find that these specificities are highly sensitive to entropic and free energetic features of the unbound conformational state, such that direct binding interaction energies alone do not capture the complete behavior. These results suggest that the ability of particular peptide sequences to self-assemble and aggregate in a many-protein environment reflects a precise balance of direct binding interactions and behavior in the unbound (monomeric) state.

Flagella are hair-like projections from the surface of eukaryotic cells, and they play an important role in many cellular functions, such as cell-motility. The beating of flagella is enabled by their internal architecture, the axoneme, and is powered by a dense distribution of motor proteins, dyneins. The dyneins deliver the required mechanical work through the hydrolysis of ATP. Although the dynein-ATP cycle, the axoneme microstructure, and the flagellar-beating kinematics are well studied, their integration into a coherent picture of ATP-powered flagellar beating is still lacking. Here we show that a time-delayed negative-work-based switching mechanism is able to convert the individual sliding action of hundreds of dyneins into a regular overall beating pattern leading to propulsion. We developed a computational model based on a minimal representation of the axoneme consisting of two representative doublet microtubules connected by nexin links. The relative sliding of the microtubules is incorporated by modeling two groups of ATP-powered dyneins, each responsible for sliding in opposite directions. A time-delayed switching mechanism is postulated, which is key in converting the local individual sliding action of multiple dyneins into global beating. Our results demonstrate that an overall nonreciprocal beating pattern can emerge with time due to the spatial and temporal coordination of the individual dyneins. These findings provide insights in the fundamental working mechanism of axonemal dyneins and could possibly open new research directions in the field of flagellar motility.