Scaling arguments are presented for end-to-wall reaction and end-to-end reactions of grafted chains for non-self-avoiding and self-avoiding chains with and without hydrodynamic interaction. The most realistic minimal model for the experiments of Kim and Lee (J Phys Chem Lett 12:4576, 2021. https://doi.org/10.1021/acs.jpclett.1c00962 ) is a chain tethered to a plane, the chain having excluded volume and hydrodynamic interaction with end-to-end reactions. From our scaling argument, such a chain obeys a law of mass action where the macroscopic reaction rate is proportional to the microscopic reaction rate multiplied by the probability that the chain ends are close together. More precisely, this means for long chains there is no diffusion controlled limit. In addition, a polymer attached to a plane where the end reacts with the entire plane, end-to-wall reactions, was also investigated. For sufficiently long polymers, this system is always diffusion controlled, even with excluded volume and hydrodynamic interaction. We test the scaling arguments for the simplest case of a non-self-avoiding chains obeying Rouse dynamics. The numerical results agree with the scaling analysis for both end-to-wall and end-to-end reactions of the grafted chain. In particular, our numerical simulations support the end-to-end reaction of a tethered non-self-avoiding is the marginal case in the scaling sense.

The idea of linear Diophantine fuzzy sets (LDFs) is a novel tool for analysis, soft computing, and optimization. Recently, the concept of a linear Diophantine fuzzy graph has been proposed in 2022. The aim of this research is to extend topological numbers to LDFSs. A real value assigned to a particular graph is known as a topological graph theoretic parameter. We extend the bound of the crisp graph toward the linear Diophantine fuzzy graph (LDFG), including the edge and vertex deletion operations via LDFG theoretic parameters. We also investigate the interesting bound of the LDFGs via LDFG theoretic parameters. Finally, for decision-making problems, we developed an algorithm by exploiting the relationship between LDFG theoretic parameters and LDFSs. Based on the established approach, we discussed a numerical example of an application of a medical diagnosis using the linear Diophantine fuzzy Sombor graph parameter and the first, fifth, and sixth versions of the linear Diophantine fuzzy Sombor graph parameters.

We propose a simple numerical model for the motion of microswimmers based on the immersed boundary method. The swimmer, either pusher or puller, is represented by a distribution of point forces corresponding to the body and the flagellum. We study in particular the minimal model consisting of only three beads (two for the body and one for the flagellum) connected by rigid, inextensible links. When the beads are collinear, standard straight swimming is realized and, in the absence of propulsion, we demonstrate that the model recovers Jeffery's equation for a thin rod. Conversely, by imposing an angle between body and flagellum the swimmer moves on circular orbits. We discuss how two swimmers, in collinear or non-collinear geometry, scatter upon encounter. Finally, we explore the dynamics of a large number of swimmers reacting to one another only via hydrodynamic interactions, and exemplify their complex collective dynamics in both straight and circular swimmers.

This work examines a field theory for directed homopolymers in a good solvent. The field theory is based on a lattice model for single- and double-strand polymers with length variables, direction-dependent pairing energy and interactions. As for the less explicit O(n)-symmetric model, there is a close relation to the conventional one-component branched polymer and the associated Lee-Yang problem. We derive results in the limiting cases of nearly complete denaturation and nearly complete renaturation. The single-strand critical exponent is calculated in two-loop order. A plausible physical realization is RNA molecules with a periodic base sequence like AUAU.

Self-propelled collective motion is a highly complex phenomenon, necessitating advanced practical and theoretical tools for comprehension. The significance of studying collective motion becomes apparent in its diverse applications. For instance, addressing evacuation challenges in scenarios with multiple agents can be achieved through an examination of collective motion. Research indicates that the transition of individuals (such as birds, fish, etc.) from a state of rest to equilibrium constitutes a phase transition. Our interest of the issue is to delve into the nature of this transitional phase and elucidate the parameters that shape it. Hence, the primary aim of this paper is to grasp the kinetic phase transition by examining how initial velocity and repulsive interactions impact the dynamics of the system. To gain insight into the complex behavior of multi-agent systems, we apply an extended version of the classical Vicsek model. This extension includes an additional interaction zone, the repulsive zone, where particles repel each other at close range to avoid collisions. Our study uses numerical simulations to explore the system's behavior under various conditions. The focus of this study is the impact of initial velocity on the collective movement of particles. The importance of this research lies in comprehending how velocity affects the overall movement. The conclusion we can draw from these results is that the initial velocity affects both the noise and the density. The novelty of the work is the transition phase, yet it lacks universal characteristics because the critical noise depends on the initial velocity system and the repulsion radius zone. Notably, the repulsion radius and particle density play pivotal roles in achieving a phase transition from one equilibrium state to another aligned equilibrium state.

Sedimentation characteristics of a squirmer in a power-law fluid within a vertical channel are studied numerically using the two-dimensional lattice Boltzmann method. The effects of swimming type (- 5 ≤ β ≤ 5), self-propelling strength (0.5 ≤ α ≤ 1.1), power-law indexes (0.5 ≤ n ≤ 1.5), and the density ratio of the squirmer to the fluid (γ = 1.01, 1.5 and 2.3) on the sedimentation of the squirmer are analyzed. Four settlement patterns are identified: steady falling in the center, downward along the wall, oscillating with large amplitude and oscillating around the centerline. The squirmer in the channel exhibits more fluctuations in shear-thinning (n < 1) and Newtonian (n = 1) fluids compared to shear-thickening fluids (n > 1). Additionally, a puller (β > 0) settles faster than a pusher (β < 0) in shear-thinning and Newtonian fluids. Puller generates flow towards their head and away from their tail, exhibiting small amplitude oscillations. Pushers exhibit higher amplitude oscillations throughout the channel, creating flow towards their tail and away from their head. At lower γ, the fluctuation of the squirmer is less pronounced compared to higher γ.

The pointlike curvature constraint (PCC) model and the disk detachment angle (DDA) model for the deformation-mediated interaction of conical integral protein inclusions in biomembranes are compared in the small deformation regime. Given the radius of membrane proteins, which is comparable to the membrane thickness, it is not obvious which of the two models should be considered the most adequate. For two proteins in a tensionless membranes, the PCC and DDA models coincide at the leading-order in their separation but differ at the next order. Yet, for distances larger than twice the proteins diameter, the difference is less than . Like the DDA model, the PCC model includes all multibody interactions in a non-approximate way. The asymptotic many-body energy of triangular and square protein clusters is exactly the same in both models. Pentagonal clusters, however, behave differently; they have a vanishing energy in the PCC model, while they have a non-vanishing weaker asymptotic power law in the DDA model. We quantify the importance of multibody interactions in small polygonal clusters of three, four and five inclusions with identical or opposite curvatures in tensionless or tense membranes. We find that the pairwise approximation is almost always very poor. At short separation, the three-body interaction is not sufficient to account for the full many-body interaction. This is confirmed by equilibrium Monte Carlo simulations of up to ten inclusions.

Flagellar swimming hydrodynamics confers a recognized advantage for attachment on solid surfaces. Whether this motility further enables the following environmental cues was experimentally explored. Motile E. coli (OD ~ 0.1) in a 100 µm-thick channel were exposed to off-equilibrium gradients set by a chemorepellent Ni(NO)-source (250 mM). Single bacterial dynamics at the solid surface was analyzed by dark-field videomicroscopy at a fixed position. The number of bacteria indicated their congregation into a wave escaping from the repellent source. Besides the high velocity drift in the propagation direction within the wave, an unexpectedly high perpendicular component drift was also observed. Swimming hydrodynamics CW-bends the bacteria trajectories during their primo approach to the surface (< 2 µm), and a high enough tumbling frequency likely preserves a notable lateral drift. This comprehension substantiates a survival strategy tailored to toxic environments, which involves drifting along surfaces, promoting the inception of colonization at the most advantageous sites.

Rapid drying of soil leads to its fracture. The cracks left behind by these fractures are best seen in soils such as clays that are fine in the texture and shrink on drying, but this can be seen in other soils too. Hence, different soils from the same region show different characteristic desiccation cracks and can thus be used to identify the soil type. In this paper, three types soils namely clay, silt, and sandy-clay-loam from the Brahmaputra river basin in India are studied for their crack patterns using both conventional studies of hierarchical crack patterns using Euler numbers and fractal dimensions, as well as by applying deep-learning techniques to the images. Fractal dimension analysis is found to be an useful pre-processing tool for deep learning image analysis. Feed forward neural networks with and without data augmentation and with the use of filters and noise suggest that data augmentation increases the robustness and improves the accuracy of the model. Even on the introduction of noise, to mimic a real-life situation, 92.09% accuracy in identification of soil was achieved, proving the combination of conventional studies of desiccation crack images with deep learning algorithms to be an effective tool for identification of real soil types.

The response of a homogeneous material to the presence of an external low-frequency oscillating electric field can be described by means of an effective complex conductivity. Low frequencies are characterized by negligible magnetic and radiative effects. The properties of heterogeneous systems, composed of multiple homogeneous regions, can be determined from those of the individual components and their geometric arrangement. Examples of such heterogeneous systems include soft materials such as colloidal suspensions, electrolyte systems, and biological tissues. The difference in the intrinsic conductivities between the homogeneous regions leads to the creation of an oscillating charge density localized at the interfaces between these regions. We show how to express key properties of these systems using this dynamic charge as a fundamental variable. We derive a boundary integral equation for the charges and reconstruct potentials and fields from its solution. We present a variational principle that recovers the fundamental equations for the system in terms of the oscillating charge and show that, in some formulations, the associated functional can be interpreted in terms of the power dissipated in the system. The boundary integral equations are numerically solved using a finite element method for a few illustrative cases.

Motile biological cells can respond to local environmental cues and exhibit various navigation strategies to search for specific targets. These navigation strategies usually involve tuning of key biophysical parameters of the cells, such that the cells can modulate their trajectories to move in response to the detected signals. Here we introduce a reinforcement learning approach to modulate key biophysical parameters and realize navigation strategies reminiscent to those developed by biological cells. We present this approach using sperm chemotaxis toward an egg as a paradigm. By modulating the trajectory curvature of a sperm cell model, the navigation strategies informed by reinforcement learning are capable to resemble sperm chemotaxis observed in experiments. This approach provides an alternative method to capture biologically relevant navigation strategies, which may inform the necessary parameter modulations required for obtaining specific navigation strategies and guide the design of biomimetic micro-robotics.

The molecular nature of the phases that conform the two-liquid scenario is elucidated in this work in the light of a molecular principle governing water structuring, which unveils the relevance of the contraction and reorientation of the second molecular shell to allow for the existence of coordination defects in water's hydrogen bond network. In turn, such principle is shown to also determine the behavior of hydration and nanoconfined water while enabling to define conditions for wettability (quantifying hydrophobicity and predicting drying transitions), thus opening the possibility to unravel the active role of water in central fields of research.

We describe the different mixed colloidal solutions that can be obtained when mixing equivalent quantities of a synthetic anionic clay to surfactants forming lamellar phases in the absence of added salt. The important quantity driving toward insertion or depletion is the osmotic pressure, of the lamellar phase and of the clay alone. Competition for water is the main driving force toward dispersion, inclusion or exclusion (phase separation). In the case of a nonionic surfactant ( ) mixed with Laponite, undulations quenched by the surfactant-decorated clay lead to swelling; inclusion is not observed due to differences in rigidity. Long-range order is weakened leading eventually to the exclusion of surfactant in excess. In the case of a double anionic system (AOT-Laponite), electrostatic is dominant and the three regimes are encountered. In the catanionic case, admixing the double chain cationic lipid DDAB to the clay (in large charge excess), the platelets are coated by a positively charged bilayer. Long-range order is very efficiently dampened. From a low threshold (2% by weight), there is exclusion of a clay-poor collapsed lamellar phase, detected by the swelling of the main phase. The cationized clay does not interfere with the molecular force balance: the location of the critical point is unchanged. At high Laponite concentration, a very puzzling microstructure is observed. Some phase diagrams as well as representative SANS and SAXS data are extracted from the complete results concerning the lyotropic lamellar phase mixing problem available with all measures and evaluations of osmotic pressures in the PhD of the late Isabelle Grillo.

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations shows very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction.

Global health concerns persist due to the multifaceted nature of heart diseases, which include lifestyle choices, genetic predispositions, and emerging post-COVID complications like myocarditis and pericarditis. This broadens the spectrum of cardiovascular ailments to encompass conditions such as coronary artery disease, heart failure, arrhythmias, and valvular disorders. Timely interventions, including lifestyle modifications and regular medications such as antiplatelets, beta-blockers, angiotensin-converting enzyme inhibitors, antiarrhythmics, and vasodilators, are pivotal in managing these conditions. In drug development, topological indices play a critical role, offering cost-effective computational and predictive tools. This study explores modified reverse degree topological indices, highlighting their adjustable parameters that actively shape the degree sequences of molecular drugs. This feature makes the approach suitable for datasets with unique physicochemical properties, distinguishing it from traditional methods that rely on fixed degree approaches. In our investigation, we examine a dataset of 30 drug compounds, including sotagliflozin, dapagliflozin, dobutamine, etc., which are used in the treatment of cardiovascular diseases. Through the structural analysis, we utilize modified reverse degree indices to develop quantitative structure-property relationship (QSPR) models, aiming to unveil essential understandings of their characteristics for drug development. Furthermore, we compare our QSPR models against the degree-based models, clearly demonstrating the superior effectiveness inherent in our proposed method.

Shear thickening fluids are liquids that stiffen as the applied stress increases. If many of these types of fluids follow a monotonic rheological curve, some experimental and numerical studies suggest that certain fluids, like cornstarch, may exhibit a non-monotonic, S-shaped rheology. Such non-monotonic behavior has however proved very difficult to observe experimentally in classical rheometer. To explain such difficulties, the possible presence of vorticity banding in the rheometer has been considered. To prevent such instabilities, we use a capillary rheometer, which is a cylindrical tube, measuring the flow rate versus the applied pressure drop. With this setup, we indeed observe a non-monotonic behavior: the flow rate increases monotonically at low pressure drops up to a maximum, after which it abruptly decreases to an almost constant flow rate regardless of further increases in pressure drop. This maximum-jump-plateau behavior occurs over a wide range of concentrations and is reproducible without hysteresis, which is in agreement with an S-shaped rheology. However, the obtained flow versus pressure difference function does not agree with the classical Wyart-Cates rheological model, which predicts an S-shaped non-monotonic function, but with neither a jump nor a plateau. To understand this jump-plateau behavior, we remark that any rheological model would establish a relationship between the flow rate and the local pressure gradient, but not the total pressure drop. We thus discuss and analyze the implications of having an S-shaped non-monotonic flow rate-pressure gradient in Poiseuille flow. In particular, we discuss the possibility of a non-uniform pressure gradient in the direction of the flow, i.e., a kind of streamwise banding. The key issue is then the selection of the gradient pressure distribution along the tube. One solution could arise from an analogy of this problem with the spinodal decomposition. It, however, leads to an increase in flow rate with up to a plateau between two values of as determined by the Maxwell construction. To account for the bump-jump behavior, we have implemented a simple dynamical stochastic version of the Wyart-Cates model, where the thickening occurs with a characteristic time. As a result, with increasing the total pressure drop, the flow rate increases monotonically up to a maximum value. Beyond this point, the flow rate drops abruptly to a lower value, forming a slowly decreasing plateau. This behavior is likely to account for the maximum-jump-plateau observed in the experiments. We also show that in such a system, the final state is quite sensitive to the initial state of the fluid, especially its homogeneity. Our results then demonstrate that the mere presence of a non-monotonic rheological curve is sufficient to predict the occurrence of stress banding in the streamwise direction and a plateau flow rate, even if the suspension remains homogeneous.

The study looks into magnetically induced orientational transitions in suspensions of goethite nanorods based on a nematic liquid crystal. The study considers magnetically compensated suspension, which is a liquid-crystal analogue of an antiferromagnet. Unlike conventional magnetic particles, goethite nanorods have a remanent magnetic moment directed along the long axis of the particle and also they have negative diamagnetic anisotropy. Thus, it can be claimed that liquid-crystal composites of goethite nanorods have three mechanisms of interaction with an external magnetic field. The first two mechanisms are originally quadrupolar and are related to diamagnetic susceptibility anisotropies of liquid-crystal matrix and impurity goethite nanorods. The third mechanism is a dipolar one and is due to a remanent longitudinal magnetic moment of each dispersed particle. The magnetic-field-induced birefringence is used to show that the presence of three competing orientational mechanisms of interaction with an external magnetic field can both increase and decrease the Fréedericksz transition threshold compared to a pure liquid crystal. Diagrams of orientational phases of the suspension were constructed, and cases of various orientational mechanism predominance were analysed. Besides, a representation of the free energy of the suspension near the Fréedericksz transition in the form of the Landau expansion was obtained. This made it possible to establish that the Fréedericksz transition can occur as a phase transition of both the first and second order.

The process by which adaptive evolution preserves a population threatened with extinction due to environmental changes is known as evolutionary rescue. Several factors determine the fate of those populations, including demography and genetic factors, such as standing genetic variation, gene flow, availability of de novo mutations, and so on. Despite the extensive debate about evolutionary rescue in the current literature, a study about the role of epistasis and the topography of the fitness landscape on the fate of dwindling populations is missing. In the current work, we aim to fill this gap and study the influence of epistasis on the probability of extinction of populations. We present simulation results, and analytical approximations are derived. Counterintuitively, we show that the likelihood of extinction is smaller when the degree of epistasis is higher. The reason underneath is twofold: first, higher epistasis can promote mutations of more significant phenotypic effects, but also, the incongruence between the maps genotype-phenotype and phenotype-fitness turns the fitness landscape at low epistasis more rugged, thus curbing some of its advantages.

Topological indices quantify the connectivity and structural properties of chemical compounds. We use the topological indices for predicting and evaluating the numerous properties of molecules, such as boiling temperatures, toxicity, and biological activity. Zagreb connection indices are a useful tool for studying the structural characteristics of the DNA backbone network. These indices provide important information on the arrangement and connections between nucleotide bases inside the DNA molecule. These indices show compactness, complexity, and topological properties in order to predict DNA bending propensity, DNA-protein interaction, and DNA stability. DNA folding patterns and the impact of mutations on DNA networks are areas of further research for these topological indices. In this study, we calculate Zagreb connection indices and modified Zagreb connection indices for backbone DNA network and subdivided backbone DNA network. Furthermore, we compute the hyper-Zagreb connection index, the inverse sum connection index, and the harmonic connection index.

We explore a novel mechanism of interactions between nematic order and flow including odd and rotational viscosities, and investigate activity-induced instabilities in the framework of this model. We show how these modes of viscous dissipation can be incorporated in the Ericksen-Leslie formalism, but it does not eliminate deficiencies of the approach based on Onsager's reciprocal relations that lead to spurious instabilities. The suggested way of deriving nematodynamic equations, based on a specific mechanism applicable to rigid rods, is not universal, but it avoids referring to Onsager's relations and avoids spurious instabilities in the absence of an active inputs. The model is further applied to the analysis of instabilities in active media.

The dissipation behavior of granular balls inside quasi-two-dimensional closed containers with different levels of bottom bumpiness under vibration is examined in this article using the discrete element method. The quasi-two-dimensional closed granular system used in this paper has dimensions of , and the diameters of the 279 filled granular balls are 4 mm. First, the dynamic behavior and damping effects of granular balls within a flat-bottomed closed container are explored across the range of relevant excitation parameters, identifying four high damping granular phases. Second, this study investigated the impact of the container's bottom surface bumpiness, convex height, and number of bumps on the dissipative behavior of internal granular balls. The findings reveal that a single 2 mm bump on the container's bottom surface maximally enhances the damping effect on the granular balls. Finally, by comparing the optimal damping behavior of granular balls inside a flat-bottomed container with that of a container featuring a single 2 mm bump at the bottom, this study revealed how the protruding bottom surface enhances the damping effect on the granular balls inside the container. This provides theoretical support for optimizing the performance of granular dampers in engineering practice by controlling the morphology of the cavity bottom surface.