The European Physical Journal E最新文献

We analyze the macroscopic dynamics of antiferroelectric smectic (Z_textrm{A}) and antiferromagnetic smectic (Z_textrm{M}) liquid crystals. The smectic (Z_textrm{A}) phase is characterized by antiferroelectric order in one direction in the planes of the smectic layers giving rise to an orthogonal biaxial overall symmetry without polar direction. Thus in sufficiently thick (bulk) samples without externally applied electric fields, globally (D_{2h}) symmetry results. Therefore, the macroscopic dynamics of the smectic (Z_textrm{A}) is isomorphic to that of the McMillan phase and one can take over the corresponding results in the field-free limit. This also applies to the defect structure in the sense that one can expect the appearance of half-integer defects as they have also been observed for the McMillan phase. Based on the fact that ferromagnetic nematic liquid crystals are known for about a decade, it seems natural to investigate the antiferromagnetic analog of the smectic (Z_textrm{A}) phase, which we denote as (Z_textrm{M}) in the present paper. In this phase, one also has an in-plane preferred direction, which is, however, not like a director in an ordinary nematic, but odd under time reversal. It can be characterized by a staggered magnetization, ({varvec{N}}), just as in a solid antiferromagnet like MnO. As additional macroscopic variables when compared to a usual non-polar smectic A phase, we have the in-plane staggered magnetization and the magnetization ({varvec{M}}). As a consequence, we find that spin waves (frequently called anti-magnons in solids) become possible. Therefore, we have for the antiferromagnetic smectic phase, (Z_textrm{M}), three pairs of propagating modes: first and ‘second’ sound as in usual smectic A phases and one pair of spin waves. The coupling between ‘second’ sound and spin waves is also analyzed leading to the possibility to excite spin waves by dynamic layer compressions and, vice versa, to generate ‘second’ sound by temporally varying magnetic fields. We note, however, that without additional mechanical or magnetic deformations, the coupling between spin waves on the one hand and first and second sound on the other is a higher order effect in the wave vector (textbf{q} ). We also analyze the question of antiferroelectricity and antiferromagnetism for nematic liquid crystals.

The inverse sum indeg index of a given graph G is symbolized with ISI and defined by sum of the weights (frac{d_u d_v}{d_u + d_v}) entire links (uvin G). We denote (d_u) (resp. (d_v)) the degree of a vertex u (resp. v) of G. In this paper, we obtained the sharp lower bound of tricyclic graphs with respect to the ISI index of order (ngeqslant 6) with size (n + 2). By using atoms as vertices and chemical bonds as edges, graph theory permits the representation of molecular structures as mathematical entities called graphs. Based on the above concept, we formulated the ISI index of octane isomers (OI) and benzenoid hydrocarbons (BH) and compared the values of ISI index with various degree-based TI’s via their correlations and chemical properties. The structural analysis of octane isomers is an important application of this research, as the ISI index delivers insights into stability designs across various isomeric forms.

Architectural metamaterials that span different length scales and are either self-similar or dissimilar to one another make up hierarchical lattices. Comparing hierarchical lattices to traditional ones reveals that they offer superior and customizable properties, which allows for a wide variety of material property manipulation and optimization. Each computer network can be represented as a graph, where nodes alternate as vertices and links are edges. The recent advanced topic of resolvability parameters of a graph involves shaping the entire structure to obtain each nodes’ specific position. In this article, we computed the metric, fault metric, and partition dimension of the hierarchal lattic tube. The application of the metric dimension is also covered in this paper.

Generalized hierarchal lattice tube

We study experimentally at the macroscopic and microstructure scale a dense suspension of non-Brownian neutrally buoyant spherical particles experiencing periodic reversals of flow at constant rate between parallel plates and tracked individually. We first characterize the quasi-steady state reached at the end of half periods. The volume fraction of particles increases from the walls to the center as a result of migration induced by the nonuniform strain rate. Except very close to the walls and the center, the particle pair distribution is fore-aft asymmetric with depletions of pairs in the extensional quadrants, similar to that reported for shear flows of same volume fraction as the local one. The dynamics of the periodic rearrangements occurring after each flow reversal are characterized by a microstructure tensor component. The relaxation time characterizing the reorganization increases from the walls to the center due to the inhomogeneous strain rate. On the other hand, the local accumulated strain required for this reorganization decreases with the volume fraction, like for viscosity measurements in uniform strain rate conditions. However, the variation of the microstructure with the accumulated strain is faster than that of the viscosity, showing the complementarity of the two measurements.

Left: Experimental image showing the particle suspension inside a slice of the channel. Middle: Representation of a pair of particles and its relative position vector. Right: Pair distribution function by the end of an oscillation

A liquid drop resting on a soft substrate is numerically simulated as an energy minimization problem. The elastic substrate is modeled as a cubic lattice of mass-springs, to which an energy term controlling the change of volume is associated. The interfacial energy between three phases of solid, liquid, and vapor is also introduced. Under the constant volume constraint of the liquid drop, the total energy of the system is subjected to a numerical minimization process by which profiles of both substrate and drop are obtained. The numerical simulation enables the modeling of the wetting setup with various parameters associated with solid and liquid phases, including the Young’s modulus and Poisson’s ratio of the solid, the surface tension of the three phases, and geometrical parameters such as the contact radius or thickness of the solid. The direct outputs of the minimization process are the displacements of the solid lattice and boundary points of the liquid, by which the behavior of all relevant quantities, such as contact angles in the three phases, as well as the effective surface tension of the solid, can be quantitatively studied. The resulting displacements of the solid are compared with the exact solution of the elasticity equation under the assumption of no tangential traction, and a quite satisfactory agreement is observed. However, at larger Young’s modulus or lower Poisson’s ratios the agreement between the numerical results and the analytical solutions is lost in the vicinity of the contact points. Interestingly, a non-zero tangential traction in the vicinity of contact points is calculated by the numerical outputs, indicating that the assumption of zero tangential traction is not valid generally around the contact points. The effective surface tension at the contact points is calculated for an incompressible solid substrate, showing a linear increase with respect to the Young’s modulus of the solid, as (delta gamma =c,E).

We employ graph neural networks (GNN) to analyse and classify physical gel networks obtained from Brownian dynamics simulations of particles with competing attractive and repulsive interactions. Conventionally such gels are characterized by their position in a state diagram spanned by the packing fraction and the strength of the attraction. Gel networks at different regions of such a state diagram are qualitatively different although structural differences are subtile while dynamical properties are more pronounced. However, using graph classification the GNN is capable of positioning complete or partial snapshots of such gel networks at the correct position in the state diagram based on purely structural input. Furthermore, we demonstrate that not only supervised learning but also unsupervised learning can be used successfully. Therefore, the small structural differences are sufficient to classify the gel networks. Even the trend of data from experiments with different salt concentrations is classified correctly if the GNN was only trained with simulation data. Finally, GNNs are used to compute backbones of gel networks. As the node features used in the GNN are computed in linear time (mathcal {O}(N)), the use of GNN significantly accelerates the computation of reduced networks on a particle level.

We present a simple and inexpensive method for measuring weak cohesive interactions. This technique is applied to the specific case of oil droplets with a depletion interaction, dispersed in an aqueous solution. The experimental setup involves creating a short string of droplets while immobilizing a single droplet. The droplets are held together via depletion interactions, and a single cohesive bond holds together nearest neighbours. Initially, the buoyant droplets are held in a flat horizontal chamber. The droplets float to the top of the chamber and are in contact with a flat glass interface. In the horizontal configuration, there is no component of the effective buoyant force acting in the plane of the chamber. The angle of the chamber is gradually increased, and the effective buoyant force acting on the string of droplets slowly increases. At a critical point, when the combination of gravity and buoyancy is equal to the cohesive force, the droplet string will detach from the immobile droplet. Our method allows for a simple direct measurement of cohesive forces on the tens of pico-Newton scale. To illustrate the validity of this technique, the droplet radii and concentration of depletant are varied, and their impact on the cohesive force is measured. This method offers a simple, accessible, and reproducible means of exploring cohesive interactions beyond the specific case of oil droplets and a depletion interaction.

(Top) Side and top-down view schematic of the experimental chamber. (Bottom) Stable and unstable dangling chain of droplets. The chain detaches from the stationary droplet once the effective buoyant force is greater than the cohesive force

The creep behavior of an amorphous poly(etherimide) polymer is investigated in the vicinity of its glass transition in a weakly non linear regime where the acceleration of the creep response is driven by local configurational rearrangements. From the time shifts of the creep compliance curves under stresses from 1 to 15 MPa and in the temperature range between (T_g -10K) and (T_g), where (T_g) is the glass transition temperature, we determine a macroscopic acceleration factor. The macroscopic acceleration is shown to vary as (e^{-(Sigma /Y)}) temperature with (n=2 pm 0.2), where (Sigma ) is the macroscopic stress and Y is a decreasing function of compliance. Because at the beginning of creep, the stress is homogeneous, the macroscopic acceleration is thus similar to the local one, in agreement with the recent theory of Long et al. (Phys Rev Mat 2:105601, 2018) which predicts (n=2). For larger compliances, the decrease of Y is interpreted as a signature of the development of stress disorder during creep.

Left: The acceleration of creep kinetics in a weakly non-linear regime in the vicinity of the glass transition is described through an acceleration function F which depends on both the applied stress and the compliance J(t) as a result of the stress induced shift of the relaxation time of nanometric domains (from top to bottom: increasing applied creep stresses). Right : Description of an amorphous polymer glass as a disordered medium made up of nanometric domains with widely distributed relaxation times.

Understanding the values and origin of fundamental physical constants, one of the grandest challenges in modern science, has been discussed in particle physics, astronomy and cosmology. More recently, it was realized that fundamental constants have a biofriendly window set by life processes involving motion and flow. This window is related to intrinsic fluid properties such as energy and length scales in condensed matter set by fundamental constants. Here, we discuss important extrinsic factors governing the viscosity of complex fluids operating in life processes due to collective effects. We show that both extrinsic and intrinsic factors affecting viscosity need to be taken into account when estimating the biofriendly range of fundamental constants from life processes, and our discussion provides a straightforward recipe for doing this. Remarkably, the viscosity of a complex fluid such as blood with significant extrinsic effects is not far from the intrinsic viscosity calculated using the fundamental constants only, and we discuss the reason for this in terms of dynamics of contact points between cells.