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Thermosensitive star-shaped eight-arm poly-2-alkyl-2-oxazolines (M = 21,000 g mol−1) was synthesized. The arms were gradient copolymers of 2-ethyl-2-oxazoline (EtOx) and 2-isopropyl-2-oxazoline (iPrOx). The more hydrophilic EtOx units prevailed near the calix[8]arene core. For comparison, model linear gradient copolymer (M = 3800 g mol−1) was investigated. For both polymers, comonomer molar ratio was 1/1. The aqueous solutions of copolymers were studied by light scattering and turbidimetry. Self-organization of linear and star-shaped molecules in solution was different, but the phase separation temperatures for these copolymers coincided. In order to find out the influence of the distribution of EtOx and iPrOx units along the arms on the behavior of star-shaped polyalkyloxazolines, the behavior of investigated stars was compared with that for stars, whose arms was block copolymers poly-2-isopropyl-2-oxazoline and poly-2-ethyl-2-oxazoline. It was shown that the phase separation temperature for gradient copolymer solutions was higher than one for block copolymers.

A new polycondensation aromatic rigid-chain polyester macroinitiator was synthesized and used to graft linear poly-2-ethyl-2-oxazoline as well as poly-2-isopropyl-2-oxazoline by cationic polymerization. The prepared copolymers and the macroinitiator were characterized by NMR, GPC, AFM, turbidimetry, static, and dynamic light scattering. The molar masses of the polyester main chain and the grafted copolymers with poly-2-ethyl-2-oxazoline and poly-2-isopropyl-2-oxazoline side chains were 26,500, 208,000, and 67,900, respectively. The molar masses of the side chains of poly-2-ethyl-2-oxazoline and poly-2-isopropyl-2-oxazoline and their grafting densities were 7400 and 3400 and 0.53 and 0.27, respectively. In chloroform, the copolymers conformation can be considered as a cylinder wormlike chain, the diameter of which depends on the side chain length. In water at low temperatures, the macromolecules of the poly-2-ethyl-2-oxazoline copolymer assume a wormlike conformation because their backbones are well shielded by side chains, whereas the copolymer with short side chains and low grafting density strongly aggregates, which was visualized by AFM. The phase separation temperatures of the copolymers were lower than those of linear analogs of the side chains and decreased with the concentration for both samples. The LCST were estimated to be around 45 °C for the poly-2-ethyl-2-oxazoline graft copolymer, and below 20 °C for the poly-2-isopropyl-2-oxazoline graft copolymer.

Self-organization of diphilic star-shaped poly(2-isopropyl-2-oxazoline) with carbosilane dendrimer core was investigated in aqueous solutions on heating by light scattering and turbidimetry methods. The temperature dependences of light scattering intensity, optical transmittance, hydrodynamic radii of each type of particles and their contribution to integral light scattering intensity were obtained. The phase separation temperatures were determined at concentration ranging from 0.00023 to 0.0135 g cm−3. It is shown that these temperatures are higher than for the eight-arm analog because of the different degree of hydrophobic core shielding by hydrophilic arms.

Statistical copolymers of N-isopropylacrylamide containing 2.2 – 2.7 mol % D,L-allylglycine were synthesized. The sample with 2.2 mol % allylglycine and molar mass 320000 g/mol was studied ...

Behavior of grafted copolymers composed of aromatic polyester (PAPE) backbone and poly-2-ethyl-2-oxazoline (PEOZ) side chains differing in grafting density in aqueous solutions was studied when heated at various concentrations and pH using static and dynamic light scattering and turbidimetry. Aggregates and individual macromolecules were registered in solutions at all times. It was shown that the aggregates of the brush with higher PEOZ side chains’ grafting density undergo compaction on heating below phase separation, whereas the size of the loose polymer brush aggregates continuously increases with the increase of temperature. Phase separation temperatures of both copolymers decreased with dilution. Strong influence of pH on the thermosensitivity of both samples was shown, the copolymer solubility being decreased with the acidity decrease. The nature of the pH effect is under discussion.

The paper analyzes the redistribution of atomic displacements in an initially defect-free copper crystallite after shear deformation with emphasis on the evolution of dynamic structures formed by self-consistent collective atomic rotations. The analysis is based on an original technique which allows one to identify vortex motion in a vector variable space with a discrete step. The results of research show that the direction of consistent atomic motion in vortex structures varies with time and from vortex to vortex. Such spatial alternation of rotations in the material provides its continuity along the boundaries of vortex structures, and their time-variant direction ensures stress and strain transfer from the bulk of the loaded crystal to its peripheral free boundaries. When the strain goes above its critical value, such redistribution can lead to the formation of structural defects. Thus, the vortex structures formed by elastic atomic displacements can be considered as dynamic defects because they provide a way for internal relaxation in the loaded material.

Polymethacrylic molecular brushes with oligo(ethylene glycol)-block-oligo(propylene glycol) side chains were investigated by static and dynamic light scattering and viscometry. The solvents used were acetonitrile, tetrahydrofuran, chloroform, and water. The grafted copolymers were molecularly dispersed and dissolved in tetrahydrofuran and acetonitrile. In these solvents, the molar masses of copolymers were determined. In thermodynamically good solvents, namely tetrahydrofuran and acetonitrile, investigated copolymers have a high intramolecular density and the shape of their molecules resembles a star-shaped macromolecule. In chloroform and water, the micelle-like aggregates were formed. Critical micelle concentrations decreased with the lengthening of the hydrophobic block. Molecular brushes demonstrated thermosensitive behavior in aqueous solutions. The phase separation temperatures reduced with an increase in the content of the oligo(propylene glycol) block.

N-acryloyl-L-valine (AV) was synthesized as a pH-sensitive monomer possessing both acrylamide and isopropyl sequences similar to the chemical architecture of N-isopropylacrylamide (NIPAAm). Poly(NIPAAm-co-AV) copolymer contained 5.03 mol % randomly introduced AV units was prepared and analyzed. The sample with molar mass Mw = 24,000 g/mol was studied in aqueous solutions using static and dynamic light scattering and optical transmittance methods. Temperature dependences of scattered light intensity and turbidity as well as hydrodynamic radii of dissolved species and their relative contributions to the light scattering were obtained to determine the temperatures of phase separation in aqueous media of various acidities. The dependence of the phase separation onset temperatures on pH corresponded to that obtained for anionic pH-responsive polymers. Aggregated structures were observed in solutions; moreover, in a strongly acidic medium, with an increase in temperature, the compaction of aggregates predominated, and with an increase in pH, the formation of new aggregates dominated over their compaction.

The water–salt solutions of star-shaped six-arm poly-2-alkyl-2-oxazines and poly-2-alkyl-2-oxazolines were studied by light scattering and turbidimetry. The core was hexaaza[26]orthoparacyclophane and the arms were poly-2-ethyl-2-oxazine, poly-2-isopropyl-2-oxazine, poly-2-ethyl-2-oxazoline, and poly-2-isopropyl-2-oxazoline. NaCl and N-methylpyridinium p-toluenesulfonate were used as salts. Their concentration varied from 0–0.154 M. On heating, a phase transition was observed in all studied solutions. It was found that the effect of salt on the thermosensitivity of the investigated stars depends on the structure of the salt and polymer and on the salt content in the solution. The phase separation temperature decreased with an increase in the hydrophobicity of the polymers, which is caused by both a growth of the side radical size and an elongation of the monomer unit. For NaCl solutions, the phase separation temperature monotonically decreased with growth of salt concentration. In solutions with methylpyridinium p-toluenesulfonate, the dependence of the phase separation temperature on the salt concentration was non-monotonic with minimum at salt concentration corresponding to one salt molecule per one arm of a polymer star. Poly-2-alkyl-2-oxazine and poly-2-alkyl-2-oxazoline stars with a hexaaza[26]orthoparacyclophane core are more sensitive to the presence of salt in solution than the similar stars with a calix[n]arene branching center.

The term ‘solid-state turbulence’ may sound like an oxymoron, but in fact it is not. In this article we demonstrate that solid-state turbulence may emerge owing to a defining property of the solid state: the ability of a solid to retain its shape. We consider shear flow of layers of solids with different stiffness and show that the stiffer ones may spontaneously decompose into a set of blocks. This breakdown of isometry is a key to plasticity of solids and is fundamental for the occurrence of solid-state turbulence. To visualise the piecewise isometric transformations of the blocky structure in a turbulent flow regime, we use a heuristic model based on discretisation of a continuum into interacting ‘particles’. The outcomes of the numerical experiments conducted support the occurrence of pulsations of velocity and pressure in plastically deforming solids and the emergence of vortices characteristic of classical turbulence. This phenomenon may have important practical implications for solid-state mixing as an ecologically beneficial alternative to conventional metallurgical processing routes.

The behavior of star-shaped six-arm poly-2-alkyl-2-oxazines and poly-2-alkyl-2-oxazolines in aqueous solutions on heating was studied by light scattering, turbidimetry and microcalorimetry. The core of stars was hexaaza [26] orthoparacyclophane and the arms were poly-2-ethyl-2-oxazine, poly-2-isopropyl-2-oxazine, poly-2-ethyl-2-oxazoline, and poly-2-isopropyl-2-oxazoline. The arm structure affects the properties of polymers already at low temperatures. Molecules and aggregates were present in solutions of poly-2-alkyl-2-oxazines, while aggregates of two types were observed in the case of poly-2-alkyl-2-oxazolines. On heating below the phase separation temperature, the characteristics of the investigated solutions did not depend practically on temperature. An increase in the dehydration degree of poly-2-alkyl-2-oxazines and poly-2-alkyl-2-oxazolines led to the formation of intermolecular hydrogen bonds, and aggregation was the dominant process near the phase separation temperature. It was shown that the characteristics of the phase transition in solutions of the studied polymer stars are determined primarily by the arm structure, while the influence of the molar mass is not so significant. In comparison with literature data, the role of the hydrophobic core structure in the formation of the properties of star-shaped polymers was analyzed.

Three-component molecular brushes with a polyimide backbone and amphiphilic block copolymer side chains with different contents of the &ldquo, inner&rdquo, hydrophilic (poly(methacrylic acid)) and &ldquo, outer&rdquo, hydrophobic (poly(methyl methacrylate)) blocks were synthesized and characterized by molecular hydrodynamics and optics methods in solutions of chloroform, dimethylformamide, tetrahydrofuran and ethanol. The peculiarity of the studied polymers is the amphiphilic structure of the grafted chains. The molar masses of the molecular brushes were determined by static and dynamic light scattering in chloroform in which polymers form molecularly disperse solutions. Spontaneous self-assembly of macromolecules was detected in dimethylformamide, tetrahydrofuran and ethanol. The aggregates size depended on the thermodynamic quality of the solvent as well as on the macromolecular architectural parameters. In dimethylformamide and tetrahydrofuran, the distribution of hydrodynamic radii of aggregates was bimodal, while in ethanol, it was unimodal. Moreover, in ethanol, an increase in the poly(methyl methacrylate) content caused a decrease in the hydrodynamic radius of aggregates. A significant difference in the nature of the blocks included in the brushes determines the selectivity of the used solvents, since their thermodynamic quality with respect to the blocks is different. The macromolecules of the studied graft copolymers tend to self-organization in selective solvents with formation of a core&ndash, shell structure with an insoluble solvophobic core surrounded by the solvophilic shell of side chains.

One of the principal methods of preventing large earthquakes is stimulation of a large series of small events. The result is a transfer of the rapid tectonic dynamics in a creep mode. In this chapter, we discuss possibilities for such a transfer in the framework of simplified models of a subduction zone. The proposed model describes well the basic characteristic features of geo-medium behavior, in particular, statistics of earthquakes (Gutenberg Richter and Omori laws). Its analysis shows that local relatively low-energy impacts can switch block dynamics from stick–slip to creep mode. Thus, it is possible to change the statistics of seismic energy release by means of a series of local, periodic, and relatively low energy impacts. This means a principal possibility of “suppressing” strong earthquakes. Additionally, a modified version of the Burridge-Knopoff model including a simple model for state dependent friction force is derived and studied. The friction model describes a velocity weakening of friction between moving blocks and an increase of static friction during stick periods. It provides a simplified but qualitatively correct stability diagram for the transition from smooth sliding to a stick–slip behavior as observed in various tribological systems. Attractor properties of the model dynamic equations were studied under a broad range of parameters for one- and two-dimensional systems.

Inthepresent paper, we considered the phenomena of understanding and discoveries (as a sort of “social understanding”) and found that the empirical properties of these phenomena (the critical character and emerging of a new property) have much in common with first-order phase transitions. From this point of view, we discuss both the process of understanding and discoveries and the reasons impeding “seeing what lies in front of our eyes”. In our opinion, these ideas can be further studied on the same phenomenological basis, without detailed understanding of the underlying neuronal mechanisms.

In this paper, we introduce general idea of trajectories attraction in phase space, which is very common phenomenon for the processes in the Nature. We start from a rather general biological example of natural selection, where adaptation to the environmental conditions can be described as attraction of some population distribution in the phenotype space to a center of ecological niche. The niche is mathematically represented as the “survival coefficient” which in turn can be linked to a kind of energy potential. This link between biological and physical approaches may be very useful for solution of a wide range of biological problems. In particular, we discuss an evolution in complex potential with a lot of valleys in a multi-dimensional space accompanied by the so-called large river effect, which corresponds to an extremely slow evolution of some, normally close to final, stages of the adaptation. This effect is related to the practically important states of the “frozen kinetics” which accompanies extremely wide spectrum of phenomena and allows understanding different physical and biological processes. Electronic supplementary material The online version of this article (10.1007/s11538-020-00766-3) contains supplementary material, which is available to authorized users.

Tree trunks and other cylindrical objects, where aggregated insects live, represent a very specific world for predator-prey interactions, which must differ from the situation on a 2D plane. In the present paper, in order to gain a better understanding of the specificity of predator-prey interaction in a cylindrical space, we applied a theoretical approach. Here we introduce a numerical model that allows us to test the effect of different interaction properties between predator and aggregated prey on the plane (2D) and on a cylinder (3D), taking into consideration different abilities of predators to visually detect the prey in these two types of space. The main aim was to test these interactions in an environment, which more realistically reproduces the conditions where aggregated insects usually live. We showed that the aggregation in conjunction with a specific environment may bring additional advantages for the prey. When one prey subgroup aggregates on the other side of the tree trunk and becomes invisible behind the horizon of events for the predator, the subgroup will survive with an extremely high probability. After all, the predator moving along one side of the tree will finally loose the major group completely.

Star-shaped six-arm poly-2-alkyl-2-oxazine and poly-2-alkyl-2-oxazoline with hexaaza [26]orthoparacyclophane derivative core were synthesized successfully using cationic ring-opening polymerization. Conformational behavior of prepared polymer stars were investigated by the methods of molecular hydrodynamics and optics in molecular dispersed solutions. It was shown that conformation characteristics of star-shaped polypeptoids depends on arm length, while the chemical structure weakly affects the behavior of the studied polymers in solutions. This behavior is caused by the close equilibrium rigidity of arms. The star-shaped polypeptoids have relatively high intramolecular density. All synthesized stars exhibit LCST behavior. Phase separation temperature depends on arm structure. It is lower for poly-2-alkyl-2-oxazines, monomer units of which contains one methylene group more than monomers of poly-2-alkyl-2-oxazoline.

The paper studies the redistribution of internal stresses and atomic displacements in a preloaded copper crystallite using the molecular dynamics method. It is shown that relaxation within the crystallite volume is accompanied by the formation of dynamic structures in which atomic displacements produce a coherent system of vortex lines. In so doing, the displacement of atoms in neighboring vortex structures has the opposite sign of the angular velocities. The evolution of the dynamic vortex structures is analyzed using an original technique for identifying the vortex motion in the space of a vector variable with a discrete step. It is shown that a system of dynamic vortices and antivortices can propagate inside the crystallite, ensuring the transfer of stresses from the bulk of the loaded material to its unloaded periphery in order to preserve continuity. The developed technique has revealed that the lifetime of such defects depends on their size and ranges from fractions to tens of picoseconds. The simulation results correlate well with the experimental electron microscopy data on the estimation of spatial parameters and lattice curvature during strain localization in the region of elastic distortions.

Novel copolyfluorenes (CPFs) containing 2.5 or 10 mol% of carbazole-2,7-diyl (2,7-Cz) or carbazole-3,6-diyl (3,6-Cz) derivatives in the backbone have been synthesized by means of palladium-catalyzed Suzuki polymerization under microwave irradiation. The structure of the CPF polymers was also modified by insertion of additional 2-ethylhexyl or carbazole, diaryloxadiazole, or triphenylamine units via 3,6-Cz or 2,7-Cz comonomer units in the side chains of polymers. The self-organization of molecules in chloroform solutions was investigated using light scattering and within a wide concentration interval. Analysis of the behavior of the CPFs showed that the synthesized copolymers have an increased equilibrium rigidity of molecules with a Kuhn segment length A = (10–15) nm. The A value decreases with the introduction of Cz-units into the macromolecule in the meta-position. It is shown that chemical structure of the CPFs and thermal treatment in the temperature range 60–150 °C have a dominant effect on the optoelectronic properties as well as on microstructures of their films.

Linear statistic N-isopropylacrylamide copolymer containing 11.6 mol% of 4-vinylpyridine was synthesized by free radical polymerization. The copolymer was investigated in 0.015 g cm−3 aqueous solutions using methods of static and dynamic light scattering and turbidimetry in the temperature region from 10 to 50 °C. Phase separation was registered in solutions in pH interval from 1.9 to 11.5 while heating. Temperatures of the onset and the termination of the phase separation decreased with pH increase in acid and neutral conditions. Intensive aggregation of macromolecules was registered starting from the temperatures of the onset of the phase separation. The aggregate size and their fraction in solution increased rapidly within the phase separation temperature interval; the composition of the dissolved species was strongly dependent on temperature as well as on pH.

The high importance of resilin in invertebrate biomechanics is widely known. It is generally assumed to be an almost perfect elastomer in different tissues. Whereas mechanical properties of resilin were previously determined mainly in tension, here we aimed at studying its mechanical properties in compression. Microindentation of resilin from the wing hinge of Locusta migratoria revealed the clear viscoelastic response of resilin: about a quarter of the mechanical response was assigned to a viscous component in our experiments. Mechanical properties were characterized using a generalized Maxwell model with two characteristic time constants, poroelasticity theory, and alternatively using a 1D model with just one characteristic time constant. Slow viscous responses with 1.7 and 16 s characteristic times were observed during indentation. These results demonstrate that the locust flight system is adapted to both fast and slow mechanical processes. The fast highly elastic process is related to the flight function and the slow viscoelastic process may be related to the wing folding.

Certain arachnids exhibit complex coatings of their exoskeleton, consisting of globular structures with complex surface features. This, so-called, cerotegument is formed by a multi-component colloidal secretion that self-assembles and cures on the body surface, and leads to high water repellency. Previous ultrastructural studies revealed the involvement of different glandular cells that contribute different components to the secretion mixture, but the overall process of self-assembly into the complex regular structures observed remained highly unclear. Here we study this process from a theoretical point of view, starting from the so-called Tammes-problem. We show that slight changes of simple parameters lead to a variety of morphologies that are highly similar to the ones observed in the species specific cerotegument structures of whip-spiders. These results are not only important for our understanding of the formation of globular hierarchical structures in nature, but also for the fabrication of novel surface coatings by colloidal lithography.

Linear statistic N-isopropylacrylamide copolymer containing 16.8 mol % of methacrylic acid was studied using methods of static and dynamic light scattering and turbidimetry. The experiments were performed in aqueous solutions at the concentration c = 0.015 g cm-3 in a wide temperature region from 10 to 60 °C within pH interval from 1.7 to 11.2. The rapid increase of scattered light intensity and decrease of the transmitted light intensity at heating of the solution was observed, which implied phase separation in the solution. The phase separation was confirmed by intensive aggregation of macromolecules, which was evidenced by dramatic changes in the size of the dissolved species and their fraction in the solution. Thermoresponsiveness of the copolymer was strongly dependent on pH. The specific behavior of the N-isopropylacrylamide with methacrylic acid copolymer as compared to that with maleic acid was shown, which is caused by the presence of hydrophobic methyl group in the chemical structure of the methacrylic acid monomer.

Spatula is an individual adhesive element situated at the tip of an adhesive hair in geckos, spiders and some insects. Usually, the contact area and work of adhesion depends on the type of the substrate. It is interesting to note that the interaction of a spatula-like hair tip with the substrate is practically independent on the numerical approach by which the substrate is modeled. However, in the experiments on real animals, as well as in numerically-modeled adhesion of this type of contact systems, pull-off force drops at some particular substrate roughness. In this chapter, we present a numerical model, which is capable to explain experimentally found effect of the adhesion drop at the scale of spatula. Besides we apply our numerical approach to study dynamics of spatular tips during contact formation and show that the contact area of the tips increases under applied shear force, especially, when spatulae are misaligned prior to the contact formation. The shear force has an optimum, when maximal contact is formed, but no slip occurs. In such a state, maximal adhesion can be generated. Another factor influencing attachment is the pad secretion, which flow on rough substrates is studied numerically here. The obtained results demonstrate that an increase in the density of the substrate microstructures leads to an increase in fluid loss from the pad. Additional numerical study, discussed in this chapter, deals with adhesive properties of plant fruits used for dispersal. These fruits can readily stick using secretion provided by the set of glands arranged in a smart manner radially at the distal end of the cut-cone-shaped fruit.

Male and female genitalia usually evolve rather quickly and yield remarkable diversity in comparison with other characters. Since natural selection influences shapes indirectly through corresponding properties, links between genital features and their functional mechanisms are critically important, in order to understand evolutionary mechanisms of morphological diversity. In this chapter, we numerically modeled hyper-elongated male and female genitalia especially focusing on their physical properties previously observed in cassidine beetles. These male beetles bear an elongated flagellum and female genitalia have a helically coiled spermathecal duct including some reversal turns called knots. The flagellum was demonstrated to have stiffness gradient, which results in a specific mechanical behavior of the entire copulatory system, because the flagellum stiffness properties might influence its motion within the female spermathecal duct. These properties might be partially due to rubber-like protein resilin that is assumed to be an almost perfect elastomer in insects. Resilin is an ideal material for elastic joints that are subjected to repeated cyclical stress. During the lifetime of an insect, resilin shows neither tearing nor fatigue, when stressed within its natural limits. The resilin, almost unique among biological materials returns back to its original position, when the stress is relieved. In this chapter, the simple sphere-on-the-flat geometry was used in a microindentation experiment as one with the most precise determined boundary conditions. Then the mechanical response of resilin was simulated using a generalized Maxwell model with two characteristic time constants and alternatively using a 1D model with just one characteristic time constant. We also applied newly-developed method of dimension reduction allowing us utilization of functional model along with the generalized Maxwell model.

Biological surfaces covered with micro- and nanostructures, oriented at some angle to the plain may cause strong mechanical anisotropy. Some of them also exhibit pronounced flexibility due to the material of the supporting layer or due to flexible connecting joints. Flexible systems have a wide range of functions including the transport of particles in insect cleaning devices and the propulsion generation during slithering locomotion of snakes. In this chapter, we study the dependence of the anisotropic friction on the slope of the structures, rigidity of their joints, and sliding speed. A system of this kind is the snake skin consisting of stiff scales embedded in a flexible supporting layer. Additionally, there is also microstructure with strongly anisotropic orientation on these scales, which provides frictional anisotropy of the skin. The main function of such hierarchical anisotropic structures is to generate low sliding friction in the forward sliding direction, and high propulsive force along the substrate. Snakes are also able to dynamically adapt their friction interactions by redistributing their local pressures and changing their winding angles, when either friction anisotropy is suppressed by the low friction substrate, or when the external force displacing snake overcomes friction resistance on inclines. In order to understand these biotribology problems, we develop a set of corresponding numerical models.

Microstructures responsible for temporary arresting of contacting surfaces are widely distributed on surfaces in different organisms. They have different density of outgrowths and surprisingly not ideal distribution patterns. This is why they are often called probabilistic fasteners. Their size, shape and the density of their outgrowths do not correspond exactly to each other and interact by generating strong resistance force against acting force without precise positioning of both surfaces. For example, this kind of attachment is of importance for functioning of some biomechanical systems in insects. One can suggest that different structure of the interlocking devices is optimized by natural selection to get appropriate mechanical arrest. In this chapter, we simulate such a system numerically, both in the frames of continuous and discrete dynamical models. The feathers of modern birds are waterproof, breathable, lightweight constructions combining thermo-isolation, rigidity and flexibility due to the feather’s ability to hold its parts together by a specific pattern of hooklets. The feather vane can be separated into two parts by pulling neighboring barbs apart, but original state can be re-established easily by lightly stroking through the feather. Hooklets responsible for holding vane barbs together are not damaged by multiple zipping and unzipping cycles. A model is developed which reproduces zipping and unzipping behavior in feathers similar to those observed in biomechanical experiments performed on real bird feathers.

Evolution of different systems can be described in terms of their relaxation to the minimums of some effective potential relief. This observation faces us with a question how to generate corresponding potential patterns which describe adequately various physical and biological systems. In this chapter, we present a number of different ways to generate such potentials demanded by the problems of different kinds. For example, we reproduce such a generation in the framework of a simple theory of phase transitions, automatic blocking of the growing phase nucleation and universal large scale structure. Being frozen at late stages of evolution, they form majority of meta-stable structures which we observe in real world. Counting on mentioned above universality of naturally-generated fractal structures and their further utilization in next chapters of this book, we reproduce also formal algorithms of generation of such structures based on random deposition technique and Fourier-transform approaches.

In this chapter, we will concentrate ourselves on the effect of so-called clusterization, which appears in biological and biologically-inspired fibrillar adhesion systems. If the arrays of fiber-like structures are flexible enough to allow efficient contact with natural rough surfaces, after few attachment-detachment cycles, the fibers tend to adhere one to another and form clusters which are much larger than original fibers. Due to this effect, they are less flexible and form much worse contacts with rough surfaces. Prevention of the clusterization is very important for the effectiveness of both natural and artificial adhesives. It is known that the arrays of setae of real gecko or beetle are much less susceptible to this problem than artificial ones. Here we provide numerical modeling of two different solutions of this problem that were previously experimentally studied in biological systems: gradients of the fiber stiffness and spatial structure of the fibers distributed in 3D space.

Linear and star-shaped poly(2-ethyl-2-oxazine)s have been synthesized. The star core was a calix[4]arene. The linear polymers and star arms were prepared by the cationic ring-opening polymerization of 2-ethyl-2-oxazine. The grafting-onto approach was used to synthesize the polymer stars. Molar masses were in the range from 2500 to 38,000 g⋅mol−1 for linear samples and from 5100 to 23,000 g⋅mol−1 for stars. Hydrodynamic and conformational behavior of synthesized polymers were investigated by molecular hydrodynamics and optics methods in dilute solutions in 2-nitropropane. It was shown that linear poly(2-ethyl-2-oxazine) is a flexible-chain polymer with length of statistical Kuhn segment 1.5 nm and macromolecular diameter 0.5 nm. The molecules of star-shaped poly(2-ethyl-2-oxazine) are characterized by compact structure and high intramolecular density. The arms are coiled to shield the calix[4]arene core from the solvent. The arm lengthening leads to a decrease in the intramolecular density and shape symmetry of the star-shaped molecules.

Star-shaped polymers with arms of block and gradient copolymers of 2-ethyl- and 2-isopropyl-2-oxazolines grafted to the upper rim of calix[8]arene were synthesized by the “grafting from” method. The ratio of 2-ethyl- and 2-isopropyl-2-oxazoline units was 1:1. Molar masses and hydrodynamic characteristics were measured using molecular hydrodynamics and optics methods in 2-nitropropane. The arms of the synthesized stars were short and the star-shaped macromolecules were characterized by compact dimensions and heightened intramolecular density. The influence of the arm structure on the conformation of star molecules was not observed. At low temperatures, the aqueous solutions of the studied stars were not molecular dispersed but individual molecules prevailed. One phase transition was detected for all solutions. The phase separation temperatures decreased with a growth of the content of more hydrophobic 2-isopropyl-2-oxazoline units. It was shown that the way of arms grafting to the calix[8]arene core affects the behavior of aqueous solutions of star-shaped poly-2-alkyl-2-oxazoline copolymers. In the case of upper rim functionalization, the shape of calix[8]arene resembles a plate. Accordingly, the core is less shielded from the solvent and the phase separation temperatures are lower than those for star-shaped poly-2-alkyl-2-oxazolines with lower rim functionalization of the calix[8]arene.

The majority of biologically inspired dynamic problems are essentially defined by the complexity of the contact surface where such motion takes place. From a statistical point of view, such a surface in many biological problems is typically a combination of a universal scale invariant (fractal) component and a well-defined component having a characteristic scale. If the biological object, here a dung ball, or its parts have a size comparable to the dimensions of the surface peculiarities, one can expect a strong influence on the motion. To avoid competition for the same food resource, some dung-feeding insect species form a dung ball and roll it away from the dung pile. In order to quickly escape competition, dung beetles seem to strictly follow an initial bearing. On flat terrain, they manage to roll a dung ball along a nearly perfect straight path. However, on a more realistic terrain, which normally includes both components mentioned above, the motion is more complex. In this study, we numerically model the ball transportation on terrain with different scales of surface profile. A strong correlation is observed between effective ball transportation (time, distance, work) and the ratio of the size of the ball relative to the size of the terrain roughness. Surface irregularities, with a characteristic size comparable to the ball diameter, are negatively correlated to the efficiency of ball transportation. In addition a strong correlation is found between the quasi random noise, numerically simulating the activity of a dung beetle trying to escape from a valley in which it is trapped, and the success in ball transportation.

Four-arm star-shaped poly(2-isopropyl-2-oxazoline) (PiPrOx4-S) with short arms was studied by turbidimetry and light scattering in aqueous solutions at concentrations ranging from 0.00024 to 0.0326 g cm−3. The molar mass M of the sample investigated was 5700 g mol−1. In order to reveal the influence of arm length on solution properties, the results obtained for PiPrOx4-S were compared with the characteristics of four-arm star PiPrOx4-L with long arms and M = 13,000 g mol−1. Arm shortening leads to appearance of the new type of particles and growth of the aggregation number. Stronger concentration dependences of phase transition temperatures and double widening of this interval are observed for PiPrOx4-S as compared to long-arm star. It is shown that arm lengthening causes more remarkable changes in solution behavior than the variation of arm number.