Rigidity Properties Research Articles

An Overview of Microorganisms Immobilized in a Gel Structure for the Production of Precursors, Antibiotics, and Valuable Products.

Using free microorganisms for industrial processes has some limitations, such as the extensive consumption of substrates for growth, significant sensitivity to the microenvironment, and the necessity of separation from the product and, therefore, the cyclic process. It is widely acknowledged that confining or immobilizing cells in a matrix or support structure enhances enzyme stability, facilitates recycling, enhances rheological resilience, lowers bioprocess costs, and serves as a fundamental prerequisite for large-scale applications. This report summarizes the various cell immobilization methods, including several synthetic (polyvinylalcohol, polyethylenimine, polyacrylates, and Eudragit) and natural (gelatin, chitosan, alginate, cellulose, agar-agar, carboxymethylcellulose, and other polysaccharides) polymeric materials in the form of thin films, hydrogels, and cryogels. Advancements in the production of well-known antibiotics like penicillin and cephalosporin by various strains were discussed. Additionally, we highlighted cutting-edge research related to strain producers of peptide-based antibiotics (polymyxin B, Subtilin, Tyrothricin, varigomycin, gramicidin S, friulimicin, and bacteriocin), glusoseamines, and polyene derivatives. Crosslinking agents, especially covalent linkers, significantly affect the activity and stability of biocatalysts (penicillin G acylase, penicillinase, deacetoxycephalosporinase, L-asparaginase, β-glucosidase, Xylanase, and urease). The molecular weight of polymers is an important parameter influencing oxygen and nutrient diffusion, the kinetics of hydrogel formation, rigidity, rheology, elastic moduli, and other mechanical properties crucial for long-term utilization. A comparison of stability and enzymatic activity between immobilized enzymes and their free native counterparts was explored. The discussion was not limited to recent advancements in the biopharmaceutical field, such as microorganism or enzyme immobilization, but also extended to methods used in sensor and biosensor applications. In this study, we present data on the advantages of cell and enzyme immobilization over microorganism (bacteria and fungi) suspension states to produce various bioproducts and metabolites-such as antibiotics, enzymes, and precursors-and determine the efficiency of immobilization processes and the optimal conditions and process parameters to maximize the yield of the target products.

Improvement of Mechanical Properties of 3D Bioprinted Structures through Cellular Overgrowth

The common use of hydrogel materials in 3D bioprinting techniques is dictated by the unique properties of hydrogel bioinks, among which some of the most important in terms of sustaining vital cell functions in vitro in 3D cultures are the ability to retain large amounts of liquid and the ability to modify rigidity and mechanical properties to reproduce the structure of the natural extracellular matrix. Due to their high biocompatibility, non-immunogenicity, and the possibility of optimizing rheological properties and bioactivity at the same time, one of the most commonly used hydrogel bioink compositions are polymer solutions based on sodium alginate and gelatin. In 3D bioprinting techniques, it is necessary for hydrogel printouts to feature an appropriate geometry to ensure proper metabolic activity of the cells contained inside the printouts. The desired solution is to obtain a thin-walled printout geometry, ensuring uniform nutrient availability and gas exchange during cultivation. Within this study’s framework, tubular bioprinted structures were developed based on sodium alginate and gelatin, containing cells of the immortalized fibroblast line NIH/3T3 in their structure. Directly after the 3D printing process, such structures are characterized by extremely low mechanical strength. The purpose of this study was to perform a comparative analysis of the viability and spreading ability of the biological material contained in the printouts during their incubation for a period of 8 weeks while monitoring the effect of cellular growth on changes in the mechanical properties of the tubular structures. The observations demonstrated that the cells contained in the 3D printouts reach the ability to grow and spread in the polymer matrix after 4 weeks of cultivation, leading to obtaining a homogeneous, interconnected cell network inside the hydrogel after 6 weeks of incubation. Analysis of the mechanical properties of the printouts indicates that with the increasing time of cultivation of the structures, the degree of their overgrowth by the biological material contained inside, and the progressive degradation of the polymer matrix process, the tensile strength of tubular 3D printouts varies.

Sulphur Copolymers with Pyrrole Compounds as Crosslinking Agents of Elastomer Composites for High-Performance Tyres.

Driving a car at extreme speeds, road holding, and sustainability do not go together well. Formula 1 racing is exciting but is not an example of sustainability. The aim of this work was to use materials, suitable for the treads of high-performance racing tyres, that can favour both high performance and sustainability. In particular, the objective was to achieve high dynamic rigidity at high temperatures (>100 °C) and a stable crosslinking network. A copolymer from an industrial waste such as sulphur and a comonomer from a circular biosourced material were used as the crosslinking agent of an elastomer composite based on poly(styrene-co-butadiene) from solution anionic polymerization and a carbon black with a high surface area. The biosourced circular material was 1,6-bis(2,5-dimethyl-1H-pyrrol-1-yl)hexane (HMDP), the di-pyrrole derivative of hexamethylenediamine. Two poly(S-co-HMDP) copolymers, with different S/HMDP ratios (6 and 8.9, Copolymer 1 and Copolymer 2) were carefully characterized by means of 1H-, 13C-, 2D1H-1H-COSY and 2D 1H-13C HSQC NMR. The comparison of the spectra highlighted the substitution with sulphur of the β-position of the pyrrole ring: mono-substitution largely prevailed in Copolymer 1 and also bi-substitution in Copolymer 2. The copolymers were used as additives in the vulcanization system. Compared with a reference composite, they allowed us to achieve more efficient vulcanization, a higher density of the crosslinking network, higher dynamic rigidity, better ultimate tensile properties, and better stability of the crosslinking network at high temperatures. Compared with a traditional oil-based crosslinking agent for elastomer composites with high rigidity and a stable structure at high temperatures, such as the perthiocarbamate 6-((dibenzylcarbamothioyl)disulfaneyl)hexyl 1,3-diphenylpropane-2-sulfinodithioate, the poly(S-co-HMDP) copolymers led to higher dynamic rigidity and better ultimate tensile properties. These improvements occurring simultaneously are definitely unusual. This work paves the way for the upcycling of circular materials in a large-scale application such as in tyres.

Upcycling PVC and PET as Volume-Enhancing Functional Fillers for the Development of High-Performance Bio-Based Rigid Polyurethane Foams

Polyvinyl chloride (PVC) and polyethylene terephthalate (PET) contribute significantly to global plastic waste, with only 9% recycled in recent years. In this work, these plastic wastes were upcycled as functional fillers to improve the rigid polyurethane foam (RPUF) properties. To attain this target, we leveraged the intrinsic polarity of the C=O and C-Cl groups of PVC and PET to induce intermolecular attractions with the N-H groups of the polyurethane matrix, evidenced by the observed IR peak shifts. This enhanced the nucleating effect during foaming, increasing the foams’ compressive strengths by 77% and 22% with the addition of 10% PVC and 5% PET filler, respectively. Furthermore, the addition of PVC and PET fillers increased the foam volume. Thus, the collective utilization of PPW and its corresponding impact on the CO-based RPUF’s properties signifies a reduction in carbon dioxide emissions by 14.15% and 17.52% for PVC and PET, respectively. Moreover, thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) revealed improved thermal stability and degradation profiles of the produced RPUFs. Overall, this work highlights potential advancement in environmentally responsible upcycling strategies for common end-of-life plastic wastes, while enhancing rigid foam properties.

A Review of Applications, Forms, Extraction, and Dissolution of Chitin

Background: Polymeric organic particles made by organisms or natural biopolymers, are considered as greener materials, more environmentally friendly and durable. Because of its exceptional structural properties, wide abundant, lack of toxicity, biocompatibility, simplicity of alteration and promised potentials, chitin is a sustainable material. It is composed of β(1,4)-linked N-acetyl-glucosamine units and represents the most abundant structural polysaccharide of invertebrates, including such marine phyla as sponges, corals, annelid worms, mollusks, and arthropods. This biopolymer is mostly found in the skeletal structures of invertebrates, and plays a crucial role in their rigidity, stiffness, and other mechanical properties. Chitin is recognized as one of the universal templates in biomineralization, with respect to both biocalcification and biosilicification. Conclusion: This review is concerned with chitin. For a set of uses, chitin with its derivatives are receiving more and more attention. The popularity of this plentiful biopolymer has skyrocketed in recent years. Studies on the use of chitin show that these biopolymers have a lot of potential for managing wounds, getting rid of toxic metals, farming, bone regenerative engineering, etc.

A geometric framework for asymptoticity and expansivity in topological dynamics

In this paper we develop a geometric framework to address asymptoticity and nonexpansivity in topological dynamics when the acting group is second countable and locally compact. As an application, we show extensions of Schwartzman’s theorem in this context. Also, we get new results when the acting group is Z d {\mathbb Z}^d : any half-space of R d \mathbb {R}^d contains a vector defining a (oriented) nonexpansive direction in the sense of Boyle and Lind. Finally, we deduce rigidity properties of distal Cantor systems.

Research on the biophysical properties of circulating tumor cells

This article reviews the biophysical properties of circulating tumor cells (CTCs) and their significance in tumor metastasis and liquid biopsy. CTCs are tumor cells that have shed from solid tumors or metastatic foci and entered the bloodstream, possessing various biological markers. They may be cleared by the immune system, enter a dormant state, or form clusters to facilitate metastasis. The physical properties of CTCs, including cell size, density, rigidity, and dielectric properties, differ from normal blood cells, providing a theoretical basis for separation and detection. The biological characteristics of CTCs include epithelial cell properties, expression of specific surface marker proteins, and the characteristics of epithelial-mesenchymal transition, which are crucial for the aggressiveness and metastatic potential of tumors. The development of CTC detection technologies, such as the Cell Search system, has been clinically applied, but the heterogeneity of tumor cells remains a major challenge in research. The development of composite separation technologies that combine various properties of CTCs is expected to improve the sensitivity, specificity, and efficiency of CTC detection, thereby playing an important role in the personalized treatment and prognostic assessment of tumors.

Theory and Measurement of Heat Transport in Solids: How Rigidity and Spectral Properties Govern Behavior.

Models of heat transport in solids, being based on idealized elastic collisions of gas molecules, are flawed because heat and mass diffuse independently in solids but together in gas. To better understand heat transfer, an analytical, theoretical approach is combined with data from laser flash analysis, which is the most accurate method available. Dimensional analysis of Fourier's heat equation shows that thermal diffusivity (D) depends on length-scale, which has been confirmed experimentally for metallic, semiconducting, and electrically insulating solids. A radiative diffusion model reproduces measured thermal conductivity (K = DρcP = D × density × specific heat) for thick solids from ~0 to >1200 K using idealized spectra represented by 2-4 parameters. Heat diffusion at laboratory temperatures (conduction) proceeds by absorption and re-emission of infrared light, which explains why heat flows into, through, and out of a material. Because heat added to matter performs work, thermal expansivity is proportional to ρcP/Young's modulus (i.e., rigidity or strength), which is confirmed experimentally over wide temperature ranges. Greater uptake of applied heat (e.g., cP generally increasing with T or at certain phase transitions) reduces the amount of heat that can flow through the solid, but because K = DρcP, the rate (D) must decrease to compensate. Laser flash analysis data confirm this proposal. Transport properties thus depend on heat uptake, which is controlled by the interaction of light with the material under the conditions of interest. This new finding supports a radiative diffusion mechanism for heat transport and explains behavior from ~0 K to above melting.

Asymptotic stability of a finite sum of solitary waves for the Zakharov–Kuznetsov equation

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov–Kuznetsov equation in dimensions two and three. We also derive a qualitative version of the orbital stability result, which will be useful for studying the collision of two solitary waves in a forthcoming paper.The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by Côte, Muñoz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three.

Evaluation and optimization of esterified starch and Canna edulis ker fiber films for food packaging applications

Starch-based films reinforced with Canna edulis Ker fiber were developed by a reactive extrusion process in which an esterification reaction was generated using maleic anhydride as a modifying agent and glycerin as a plasticizer. A Box-Behnken experimental design and the response surface methodology allowed modeling of the mechanical and physicochemical properties and their subsequent optimization to obtain flexible or rigid materials with different approaches in food packaging. The optimal composition for the rigid and flexible material was 10 and 2 % (w/w) lignocellulosic fibers, 30 and 30 % (w/w) glycerol, and 4 and 4 % (w/w) maleic anhydride, respectively. Glycerol and maleic anhydride were the key variables that influenced the water solubility and water absorption of the materials. The values of the rigid and flexible material properties of elastic modulus, tensile strength, elongation at break, water solubility, and water absorption were 2.58 and 1.51 GPa, 112.04 and 104.56 Mpa, 6.58 and 10.44 %, 21.63 and 21.85 %, and 139.72 and 141.06, respectively.

A geometric Elliott invariant and noncommutative rigidity of mapping tori

We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, a leafwise homotopy equivalence of two mapping tori associated to Zd-actions on a compact space can be lifted to an isomorphism of their foliation C⁎-algebras. This property is a noncommutative analogue of topological rigidity in the context of foliated spaces whose space of leaves is singular, where isomorphism type of the C⁎-algebra replaces homeomorphism type. Our technique is to develop a geometric approach to the Elliott invariant that relies on topological and index-theoretic data from the mapping torus. We also discuss how our construction can be extended to slightly more general homotopy quotients arising from actions of discrete cocompact subgroups of simply connected solvable Lie groups, as well as how the theory can be applied to the magnetic gap-labelling problem for certain Cantor minimal systems.

Sums of Generalized Weighted Composition Operators from Weighted Bergman Spaces Induced by Doubling Weights into Bloch-Type Spaces

The single generalized weighted composition operator Du,ψn on various spaces of analytic functions has been investigated for decades, i.e., Du,ψnf=u·(f(n)∘ψ), where f∈H(D). However, the study of the finite sum of generalized weighted composition operators with different orders, i.e., PU,ψkf=u0·f∘ψ+u1·f′∘ψ+⋯+uk·f(k)∘ψ, is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of PU,ψk. Specifically, the boundedness and compactness of the sum PU,ψk is equivalent to those of each Dun,ψn, 0≤n≤k.

Crack growth in sandwich-structured foam core graphite epoxy laminate composite using a phase-field modelling approach

The laminated sandwich composites have wide structure-making applications in the automotive and aviation fields due to their lightweight and superior flexural rigidity properties. Making grooves or holes to assemble more than one structure induces crack discontinuities near the stress concentration region in these sandwich structures. The present work examines the effect of crack discontinuities on the mechanical performance and failure process of the sandwich structures under different loading conditions. Phase field method (PFM) has been presented and implemented using in-house developed MATLAB code. The effect of holes, multiple cracks, number of cores, and loading conditions are analyzed for the mechanical and fracture behavior of the structure. Load-carrying capacity, threshold displacement value for crack initiation, crack propagation trajectory, and energy absorption capacity are compared for various crack discontinuities under different loading conditions. Approximately 35% increase in load carrying capacity is observed in equivalent multiple core sandwich structures.

On neutral Tannakian subcategories of loop quiver representations

We explored the categories of (twisted) representations of a loop quiver. These representation categories have two choices of tensor structures: Kronecker tensor and Simpson tensor. By studying the rigidity properties, we have provided several examples of (semi-) Tannakian categories using the category of (twisted) representations of a loop quiver for both tensors.We have introduced the concept of essentially finite loop quiver bundles based on the work of Nori, Borne, and Vistoli. As an application, we have given some examples of (semi-) Tannakian categories of equivariant bundles and Hitchin pairs. Additionally, we have defined the notion of H-nflat twisted loop quiver bundles and have established Tannakian category structures for certain classes of varieties.

Super-rigidity for holomorphic Segre maps

Let H l n and H l , l ′ , n N be the complexifications of the real hyperquadrics in C n and C N of signatures l and l ′ , respectively. We study local holomorphic Segre maps sending a piece of H l n into H l , l ′ , n N with the degeneracy rank l 0 = 1 and N ≥ n . We show that these maps possess super rigidity properties.

On rigidity properties of time-changes of unipotent flows

On rigidity properties of time-changes of unipotent flows

Synthesis of Biodegradable Plastic Film from Chitosan-Glycerol with Cellulose Nanowhiskers of Coconut Coir as Reinforcing Agent

Abstract This research was conducted to synthesize biodegradable plastic films from chitosan and glycerol with the addition of cellulose nanowhiskers as a reinforcing agent. Cellulose synthesis of nanowhiskers from coconut husks was carried out with 3 phases, i.e., pre-treatment, bleaching, and sulphuric acid hydrolysis with a concentration of 55%. The result of cellulose hydrolysis in the form of needle-like nanowhiskers with an average of 223.6 nm particle size and a crystallinity index of 34.27% were shown through the results of FTIR, SEM, PSA, and XRD. Plastic film was made by blending method, which was mixing whole material then stirred until homogeneous and printed at room temperature. This study showed that the addition of cellulose nanowhiskers 3% can increase the tensile strength value up to 50 MpA, water resistance by 88.86%, and the biodegradation rate by 0.51 mg/day, but the value decreased if the addition of cellulose nanowhiskers was more than 3%. This was influenced by the rigid properties of cellulose nanowhiskers and experienced aggregation if it was added in excess. In conclusion, the addition of cellulose nanowhiskers with precise concentration can increase the tensile strength, water resistance, and the rate of biodegradation in the plastic film from chitosan-glycerol.

Groups of profinite type and profinite rigidity

Abstract We say that a group 𝐺 is of profinite type if it can be realized as a Galois group of some field extension. Using Krull’s theory, this is equivalent to 𝐺 admitting a profinite topology. We also say that a group of profinite type is profinitely rigid if it admits a unique profinite topology. In this paper, we study when abelian groups and some group extensions are of profinite type or profinitely rigid. We also discuss the connection between the properties of profinite type and profinite rigidity to the injectivity and surjectivity of the cohomology comparison maps, which were studied by Sury and other authors.

Development of a plugging material featuring external flexibility and internal rigidity

Recognizing the challenges of low strength, inadequate cementation, significant pore development, and excellent connectivity of reef limestone, as well as the persistent issues of ‘re-leakage’ and increasing leaks when using rigid bridge plugs, this paper posits the use of materials possessing both flexible and rigid properties for the prevention of leaks and plugging in reef limestone formations. Consequently, a plugging material exhibiting external flexibility and internal rigidity is developed (EFIR Material). This synergistic approach employs the deformability of flexible materials and the skeletal support of rigid materials to create a high-strength, dense plugging section. The new design enhances the formation’s pressure-bearing capacity while effectively addressing leakage issues. The material’s functional structure design, a core-shell structure of EFIR, is achieved by reverse-phase suspension polymerization of acrylamide (AM), 2-acrylamide-2-methylpropanesulfonic acid (AMPS), and alkyl ketone polymer (NVP), water-soluble monomers functioning as the shell and modified sand as the core. The results indicate that EFIR retains significant flexibility and strength upon water absorption and expansion. A sand bed made from 10 to 18 mesh calcareous sand exhibits excellent sealing properties. The optimal dosage of 3%-4% produces robust sealing effects, withstands pressures up to 7 MPa, and results in a tightly cemented, high-strength sand bed post-sealing with reef tuff, displaying high-quality sealing that is resistant to re-leakage.

Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds

We prove two rigidity results on holomorphic isometries into homogeneous Kähler manifolds. The first shows that a Kähler-Ricci soliton induced by the homogeneous metric of the Kähler product of a special generalized flag manifold (i.e. a flag of classical type or integral type) with a bounded homogeneous domain is trivial, i.e. Kähler-Einstein. In the second one we prove that: (i) a flat space is not relative to the Kähler product of a special generalized flag manifold with a homogeneous bounded domain, (ii) a special generalized flag manifold is not relative to the Kähler product of a flat space with a homogeneous bounded domain and (iii) a homogeneous bounded domain is not relative to the Kähler product of a flat space with a special generalized flag manifold. Our theorems strongly extend the results of Cheng and Hao [Ann. Global Anal. Geom. 60 (2021), pp. 167–180], Cheng, Di Scala, and Yuan [Internat. J. Math. 28 (2017), p. 1750027], Loi and Mossa [Proc. Amer. Math. Soc. 149 (2021), pp. 4931–4941], Loi and Mossa [Proc. Amer. Math. Soc. 151 (2023), pp. 3975–3984] and Umehara [Tokyo J. Math. 10 (1987), pp. 203–214].