In this paper, we will study the influence of TDs on dif- ferent axisymmetric membrane shapes where orientational ordering and defects are allowed to break this symmetry. In particular, we will investigate the impacts of this TD in in-plane membrane orientational ordering on membrane budding initiated fission (vesiculation) processes. We will use a minimal model, which will allow us to study the impact of membrane curvature on the number and position of TDs (ie, frustrations in in-plane orientational ordering). The outline of the paper is as follows: in section 2, we will present the theo- retical background. Results are presented in section 3. In the last section, we will summarize our results. Some technical details are given in the Supplementary materials section.
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A molecular field theory and coarse grained computer simulations with dissipative particle dy- namics have been used to study the spontaneous orientational ordering of anisotropic nanoparticles in the lamellae and hexagonal phases of diblock copolymers and the effect of nanoparticles on the phase behaviour of these systems. Both a molecular theory and computer simulations indicate that strongly anisotropic nanoparticles are ordered orientationally mainly in the boundary region be- tween the domains, and the nematic order parameter possesses opposite signs in adjacent domains. The orientational order is induced by the boundary and by the interaction between nanoparticles and the monomer units in different domains. In simulations, sufficiently long and strongly selec- tive nanoparticles order also inside the domains. Nematic order parameter and local concentration profiles of nanoparticles have been calculated numerically using the model of a nanoparticle with two interaction centres and also determined using the results of computer simulations. A number of phase diagrams have been obtained which illustrate the effect of nanoparticle selectivity and molar fraction of the stability ranges of various phases. Different morphologies have been identified by analysing the static structure factor and a phase diagram has been constructed in coordinates nanoparticle concentration - copolymer composition. Orientational ordering of even a small frac- tion of nanoparticles may result in a significant increase of the dielectric anisotropy of a polymer nanocomposite which is important for various applications.
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Nanoparticles of various chemical structure may also significantly improve mechanical, elctrical and optical characteristics of block copolymers [24–30]. However, from the stand- point of liquid crystal science the most interesting effects are related to the orinetational ordering of anisotropic nanoparticles in block copolymers. One notes that both hexagonal and lamellae block copolymers are uniaxial, and thus , in principle, sufficiently anisotropic nanorods should possess some degree of induced orientational order in the corresponding composites. In the lamellae phase the symmetry axis is in the direction perpendicular to the flat boundaries between the blocks while in the hexagonal phase the axis is parallel to that of the cylindrical block. On the other hand, the physical anisotropy of diblock copolymers is relatively weak because the material in the bulk of each block is isotropic and the macroscopic anisotropy is only determined by the boundaries.Thus sufficiently small anisotropic nanoparticles are expected to order orientationally only in the interfacial regions between the adjacent blocks where the nanoparticles interact with the monomers of both blocks. Nanoparticles interact differently with the monomers of the two different kinds and this results in the effective anisotropic mean-field in the boundary region which aligns the nanoparticles .If the length of the nanorod is comparable with the size of the block, one expects some orientational ordering throughout the system becuase a given nanorod always interacts with at least one block boundary. The orientational ordering of nanorods in di- block copolymers has indeed been observed experimentally. Metal nanorods with various functional groups are aligned parallel to the domain walls in the lamellae  and to the cylindrical domain walls in the hexagonal phase  . In contrast, polystyrene functionalised nanorods are ordered in the hexagonal phase perpendicular to the cylinders [32, 33].
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characterizes the average orientation of the nanorod axes a(|a| = 1) with respect to the selected direction h. Here the angular brackets denote the averaging over a local subset of rods. In the lamellar microphase h is the unit vector normal to lamellar planes. Zero value of the order parameter corresponds to uncorrelated orientations of nanorods, whereas S > 0(S < 0) specifies the orientational ordering in the direction perpendicular (parallel) to the lamellar plane. In general, −0.5 < S < 1. The profiles φ(z) and S(z) are presented in Figs. 7 and 8, where the z-axis is parallel to h and the center of the layer B is chosen as the origin (z = 0).
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In this paper, we consider a different model of a NP which is composed of two equal spheres separated by the distance L. Both spheres interact with the monomers via a model isotropic potential, but the effective interaction between such a NP and a monomer appears to be anisotropic due to the geometrical anisotropy of the “dumbbell”. This anisotropy can be varied by changing the length L. The paper is arranged as follows. In Section II we summarise the results of the existing molecular theory  based on the simple model potential and present typical numerical profiles of the NP concentration and the nematic order parameter. In Section III we investigate the orientational ordering of the anisotropic NPs in the lamellae phase using the new model of the NP and compare the results with those of the previous theory. Finally, in Section IV we present our conclusions.
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the nematic phase is the simplest lc phase (de Gennes, prost, 1993). for presentation purposes we henceforth restrict to thermotropic lcs in which the nematic phase is reached from the isotropic (ordinary liquid) phase by lowering temperature. We also set that on average LC molecules behave as rod-like objects with head-to-tail symmetry (i.e., up and down positions are equivalent). In bulk samples (relatively large sample where we neglect boundaries) in the nematic phase LC molecules are on average aligned along a single (the so called symmetry breaking) direction. the nematic local average orientational ordering at a site r is commonly described by the unit vector n (r ) , called the nematic director field (De Gennes, Prost, 1993). The degree of ordering about this direction is quantified by the scalar nematic order parameter field l ( ) r (De Gennes, Prost, 1993). For rigidly aligned LC molecules it has maximal value. on the other hand l = 0 reflects absence of orientational ordering, where all orientations are equivalent.
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In conclusion, our simulation results have shown that this simple hard-particle mixture exhibits both an orientational ordering transition and a re-entrant N+I phase-coexistence region which occupies a significant concentration range at high volume fractions. Having established the generic behaviour of rod- sphere mixtures in the hard particle approximation, our future work will ex- plore the changes brought to this base phase diagram by the introduction of attractive interactions with various symmetries.
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linearity. i.e., the mean-field theory is based on solving the exact energies of two-level atoms in the presence of a coherent field. Thus, for the mean-field approach we can directly determine the effect of saturation by con- sidering the behavior at different filling fractions M/N. This is shown in the solid lines in Fig. 3 which show the mean-field results for the orientational ordering. Each line corresponds to a different excitation fraction, and the horizontal axis is the variable a = βg √ N (M/N), which we may still tune by adjusting βg √ N. We see that the lines do not fall on top of each other, indicating that the results depend on the values M/N and βg √ N separately — there is no reduction to a single result depending only on a = βg √ N (M/N ). This indicates an effect of sat- uration, as it means we no longer can match the large deviation result, as we could in the limit M/N → 0.
If NP is located inside a particular block far enough from its boundaries, the anisotropic interaction is aver- aged out and the orientational order parameter of anisotropic NPs vanishes. At the same time, if NP is sufficiently close to a boundary between two blocks, it may interact simul- taneously with the monomers of both blocks. The corre- sponding anisotropic interaction constants are generally different, and this asymmetry induces some orientational order of NPs in the boundary region. Moreover, the sign of the nematic order parameter is different in the two blocks, that is the rod-like NPs are expected to align parallel to the interface in one block and perpendicular to the inter- face in the other. Taking into account that the density of NPs is different in different blocks in the boundary region, one concludes that there is a nonzero average nematic or- der in the block copolymer. The corresponding average orientational order parameter is small but it may be suffi- cient to align the polymer by external electric or magnetic field if the NP anisotropy is sufficiently large. These the- oretical results are qualitatively confirmed by the exper- iment. For example, functionalized gold NRs are aligned parallel or perpendicular to the surface of the cylindrical domain in the hexagonal phase [41–43]. Similar gold NRs have also been found to align parallel to the flat block boundary in the lamellae phase . One notes that the theoretical profiles describe the average distribution and orientation of NPs. In real systems, the particles are some- times rather large and their concentration is low. In this case, the distribution is essentially discrete and individ- ual NPs may be aligned parallel or perpendicular to the interface depending on their location in a particular block. At present, there are few experimental data on the orientational ordering of NPs in block copolymers [40–43], and all of these data have been obtained using rather large NPs with dimensions comparable to the size of a block. It would be interesting to decrease the size of anisotropic NPs and increase their molar fraction. In this way, it will be possible to verify the qualitative prediction of the the- ory which indicates that NPs are expected to align per- pendicular to the boundary (between the two blocks) in one block and parallel to the boundary in another block.
Abstract: Membranous nanostructures, such as nanovesicles and nanotubules, are an important pool of biological membranes. Recent results indicate that they constitute cell-cell communica- tion systems and that cancer development is influenced by these systems. Nanovesicles that are pinched off from cancer cells can move within the circulation and interact with distant cells. It has been suggested and indicated by experimental evidence that nanovesicles can induce metastases from the primary tumor in this way. Therefore, it is of importance to understand better the mechanisms of membrane budding and vesiculation. Here, a theoretical description is presented concerning consistently related lateral membrane composition, orientational ordering of membrane constituents, and a stable shape of nanovesicles and nanotubules. It is shown that the character of stable nanostructures reflects the composition of the membrane and the intrinsic shape of its constituents. An extension of the fluid mosaic model of biological membranes is suggested by taking into account curvature-mediated orientational ordering of the membrane constituents on strongly anisotropically curved regions. Based on experimental data for artificial membranes, a possible antimetastatic effect of plasma constituents via mediation of attractive interaction between membranous structures is suggested. This mediated attractive interaction hypothetically suppresses nanovesiculation by causing adhesion of buds to the mother membrane and preventing them from being pinched off from the membrane.
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When a disperse system is sufficiently dilute—which is definitely so if the objective is to investigate the properties of the matrix itself—the main contribution to the spectra comes from the behavior of individual particles. Unlike the situation in more coarse suspensions, in nanosystems the orientational dynamics is always a result of joint action of the determin- istic 共 applied field, elasticity, and viscosity of the matrix 兲 and fluctuational 共 Brownian diffusion 兲 factors. This circumstance is of vital importance 关 6,7 兴 for the understanding of the dy- namical spectra of complex magnetic fluids.
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Abstract: Liquid-crystalline polyacrylamides with mesogenic side-chains were synthesized by the radical polymerization of a mesogenic acrylamide derivative. Their thermal properties and orientational behavior were examined by polarizing microscopy, differential scanning calorimetry, temperature-variable IR, and X-ray diffraction measurements. The liquid-crystalline polyacrylamides containing secondary amide groups formed smectic A and smectic B phases during heating and cooling processes. The glass-smectic B, smectic B-A, and smectic A-isotropic phase transition temperatures increased with increasing molecular weight. The liquid-crystalline polyacrylamide showed higher phase transition temperatures than a liquid-crystalline polyacrylate, in which the secondary amide group was replaced with an ester group. The X-ray diffraction pattern of a smectic B-oriented sample of the liquid-crystalline polyacrylamide consisted of sharp inner and very sharp outer reflections. The very sharp reflection in the wide-angle region of the X-ray diffraction pattern indicated the formation of hexatic packing within the layer. The relationship between the layer distance and the extended mesogenic side-chain length suggested that the liquid-crystalline polyacrylamide formed an interdigitated bilayer structure. The IR spectra of the liquid-crystalline polyacrylamide exhibited that the number of hydrogen bonds between the secondary amide groups decreased with increasing temperature. In the liquid-crystalline polyacrylamide, smectic A and smectic B phases, with enhanced thermal stability, were formed through the formation of hydrogen bonds between the secondary amide groups.
A sequence database consists of sequences of ordered elements or events, recorded with or without a concrete notion of time. Sequences are common, occurring in any metric space that facilitates either partial or total ordering. Customer transactions, codons or nucleotides in an amino acid, website traversal, computer networks, DNA sequences and characters in a text string are examples of where the existence of sequences may be significant and where the detection of frequent (totally or partially ordered) subsequences might be useful. Sequential pattern mining has arisen as a technology to discover such subsequences. A subsequence, such as buying first a PC, then a digital camera, and then a memory card, if it occurs frequently in a customer transaction database, is a (frequent) sequential pattern.
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tion of new possible eects in a moderate magnetic eld. Specically, we predict the existence of orientational hysteresis in a homeotropic ferronematic cell governed by conditions on the cell thickness and on the director anchoring energy at the ferroparticle surface and planes of the cell. A direct consequence of this eect is magnetic eld induced orientational bistability in such a system. The phenomenon under con- sideration can occur if the thickness of the cell is in the range from D
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This paper introduces a Japanese-Chinese SMT system which employs a pre-ordering approach based on dependency parsing. Since Japanese is a language with a fairly free word order, depen- dency parsing can describe the relation between two Japanese cases in a sentence better than con- stituent parsing. Therefore, we adopt dependency parsing for pre-ordering. Experimental results show that our approach can improve the BLEU score on the test set by 0.18, compared with the baseline system (without pre-ordering).
should be noted that MS theory is concerned with predicting the orientational properties of uniaxial nematic liquid crystals and so it is therefore not surprising that it fails to describe the orientational properties of the splay modulated nematic phase, however, this does highlight the need for an analytic theory of this phase of matter to be developed.
An additional evidence in favor of the model by Gorkunov et al. 关7兴 and Osipov et al. 关8兴 is provided by optical measurements. The sample birefringence 共 Fig. 6 兲 measured without an external field, shows an abrupt increase at the Sm C ⴱ -Sm A ⴱ transition 共by 36%, which compares with a 43% increase for the analog material, TSiKN65 关12兴兲. The best and simplest explanation of this behavior is a large increase of the uniaxial orientational order, i.e., S ⬘ . Let us make a brief calculation at this point. From Eq. 共3兲 we can calculate S ⬘ knowing values of S and ⌰. Optical tilt data for DSiKN65 were published by Naciri et al. 关9兴, and ⌰ satu- rates at about 32° at the temperature 15° below the Sm A ⴱ -Sm C ⴱ phase transition. We can then calculate that S ⬘ saturates at 0.8—a value, which is very typical for the Sm C ⴱ phase 关29兴. If we now assume that the birefringence depends primarily on S ⬘ , and we can neglect all other contributions, we can use a simple equation: ⌬n = B· S ⬘ , where B is a con-
The thermal characteristics of bimetallic Pt-Pd nanoparticles, both free and graphite-supported, were investigated through molecular dynamics simulations using quantum Sutton-Chen many-body potentials for the metal-metal interac- tions. The graphite substrate was represented as layers of fixed carbons sites and modeled with the Lennard-Jones po- tential model. The melting temperatures for bimetallic nanoparticles were estimated based on variations in thermody- namic properties such as potential energy and heat capacity. Melting temperatures of the nanoparticles were found to be considerably lower than those of bulk Pt and Pd. The Pt-Pd clusters exhibited a two-stage melting, where surface melt- ing of the external atoms is followed by homogeneous melting of the internal atoms. The melting transition temperature was found to increase when the particle is on the graphite support, with an increase at least 180 K higher than that of the same-sized free nanoparticle. The results of the density distributions perpendicular to the surface indicate that the Pd atoms have a tendency to remain at the surface, and the Pd atoms wet the graphite surface more than the Pt atoms, while root mean squares suggest that surface melting starts from the cluster surface, and surface melting was seen in both free and graphite-supported nanoparticles. Structural changes accompanying the thermal evolution were studied by the bond-orientational order parameter method.
Retailers ordering strategies affect retailers last remaining inventory cost and shortage cost. Influencing factors on the two aspects, retailers need to find a suitable quantity. This paper firstly analyzes the effect of order decision on retailers' profit, and then discusses the thinking strategy behavior and do not consider the consumer strategy behavior, affect the ordering decisions on income. The article concludes that in the presence of the consumer strategy behavior, retailers in order cannot ignore the strategy behavior of consumers.
Unlike solids and simple liquids, the model equations for complex fluids continue to evolve as new experimental evidences and applications become available . The com- plicated phenomena and properties exhibited by these materials reflects the coupling and competition between the microscopic interactions and the macroscopic dynamics. New mathematical theories are needed to resolve the ensemble of micro-elements, their intermolecular and distortional elastic interactions, their coupling to hydrodynamics and the applied electric or magnetic fields. The most common origin and manifesta- tion of anomalous phenomena in complex fluids are different “elastic” effects . They can be attributed to the elasticity of deformable particles; elastic repulsion between charged liquid crystals, polarized colloids or multi-component phases; elasticity due to microstructures, or bulk elasticity endowed by polymer molecules in viscoelastic complex fluids. These elastic effects can be represented in terms of certain internal variables, for example, the orientational order parameter in liquid crystals (related to their microstructures), the distribution density function in the dumbbell model for polymeric materials, the magnetic field in magnetohydrodynamic fluids, the volume fraction in mixture of different materials, etc. The different rheological and hydrody- namic properties will be attributed to the special coupling (interaction) between the transport (macroscopic fluid motions) of the internal variable and the induced (micro- scopic) elastic stress [116, 117]. This coupling gives not only the complicated rheological phenomena, but also formidable challenges in analysis and numerical simulations of the materials.
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