Search Results (105)

Macrocyclic organic nanostructures have emerged as crucial components of functional supramolecular materials owing to their unique structural and chemical features, such as their distinctive “infinite” cyclic topology and tunable topology-dependent properties, attracting significant recent attention. However, the controlled synthesis of macrocyclic compounds with well-defined compositions and geometries remains a formidable challenge. On-surface synthesis, capable of constructing nanostructures with atomic precision on various substrates, has become a frontier technique for exploring novel macrocyclic architectures. This review summarizes the recent advances in the on-surface synthesis of macrocycles. It focuses on analyzing the synthetic mechanisms and conformational characterization of macrocycles formed through diverse bonding interactions, including both covalent and non-covalent linkages. This review elucidates the intricate interplay between the thermodynamic and kinetic factors governing macrocyclic structure formation across these bonding types and clarifies the critical influence of the reaction temperature and external conditions on the cyclization efficiency. Ultimately, this study offers design strategies for the precise on-surface synthesis of larger and more flexible macrocyclic compounds. Full article

Under cyclic moving load action, tensile-dominant structures are prone to crack initiation due to cumulative damage effects. The presence of cracks leads to structural stiffness degradation and nonlinear redistribution of dynamic characteristics, thereby compromising str18uctural integrity and service performance. The current research on the dynamic behavior of cracked structures predominantly focuses on transient analysis through high-fidelity finite element models. However, the existing methodologies encounter two critical limitations: computational inefficiency and a trade-off between model fidelity and practicality. Thus, this study presents an innovative analytical framework to investigate the dynamic response of cracked simply supported beams subjected to moving loads. The proposed methodology conceptualizes the cracked beam as a system composed of multiple interconnected sub-beams, each governed by the Euler–Bernoulli beam theory. At crack locations, massless rotational springs are employed to accurately capture the local flexibility induced by these defects. The transfer matrix method is utilized to derive explicit eigenfunctions for the cracked beam system, thereby facilitating the formulation of coupled vehicle–bridge vibration equations through modal superposition. Subsequently, dynamic response analysis is conducted using the Runge–Kutta numerical integration scheme. Extensive numerical simulations reveal the influence of critical parameters—particularly crack depth and location—on the coupled dynamic behavior of the structure subjected to moving loads. The results indicate that at a constant speed, neither crack depth nor position alters the shape of the beam’s vibration curve. The maximum deflection of beams with a 30% crack in the middle span increases by 14.96% compared to those without cracks. Furthermore, crack migration toward the mid-span results in increased mid-span displacement without changing vibration curve topology. For a constant crack depth ratio (γ_i = 0.3), the progressive migration of the crack position from 0.05 L to 0.5 L leads to a 26.4% increase in the mid-span displacement (from 5.3 mm to 6.7 mm). These findings highlight the efficacy of the proposed method in capturing the complex interactions between moving loads and cracked concrete structures, offering valuable insights for structural health monitoring and assessment. Full article

A graph’s minimum cycle basis is defined as the smallest collection of cycles that exhibit linear independence in the cycle space, serving as fundamental building blocks for constructing any cyclic structure within the graph. These bases are useful in various contexts, including the intricate analysis of electrical networks, structural engineering endeavors, chemical processes, and surface reconstruction techniques, etc. This study investigates the urban road networks of six Chinese cities to analyze their topological features, node centrality, and robustness (resilience to traffic disruptions) using motif analysis and minimum cycle bases methodologies. Some interesting conclusions are obtained: the frequency of motifs containing cycles exceeds that of random networks with equivalent degree sequences; the frequency distribution of minimum cycle lengths and surface areas obeys the power-law distribution. The cycle contribution rate is introduced to investigate the centrality of nodes within road networks, and has a significant impact on the total number of cycles in the robustness analysis. Finally, we construct two types of cycle-based dual networks for urban road networks by representing cycles as nodes and establishing edges between two cycles sharing a common node and edge, respectively. The results show that cycle-based dual networks exhibit small-world and scale-free properties. The research facilitates a comprehensive understanding of the cycle structure characteristics in urban road networks, thereby providing a theoretical foundation for both subsequent modeling endeavors of transportation networks and optimization strategies for existing road infrastructure. Full article

Conjugated polymer nanoparticles (CP NPs) attract attention as nanoscale materials used for a variety of applications. In relation to this, the internal structure of CP NPs is an important factor for their properties, and numerous investigations have been carried out to control their nanomorphology. Here, we report the formation of CP NPs from defect-free cyclic poly(3-hexylthiophene) (c-P3HT) using a microfluidic device, and the effect of polymer topology on their structural and solvatochromic properties was investigated. CP NPs from c-P3HT exhibited reduced particle sizes and hypsochromic shifts in the absorption spectrum when compared to CP NPs obtained from corresponding linear P3HT (l-P3HT). Furthermore, steady responses in the solvatochromism of CP NPs from c-P3HT were observed, while those from l-P3HT displayed molecular weight dependency. These topology effects were caused by the change in the conjugation length, solubility, and crystallinity upon cyclization. Grazing incidence X-ray scattering (GIXS) studies of spin-coated P3HT films further showed a reduced interchain order and a larger proportion of face-on molecular orientation on a substrate for c-P3HTs. The various distinct structures observed for c-P3HT indicate the use of polymer topology as a means of nanostructure regulation. Full article

In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. Traditional methods for preparing PDMS flexible substrates with high porosity and high stability often require complex, costly processes. Breaking through the constraints of conventional material systems, this study innovatively combines the high elasticity of polydimethylsiloxane (PDMS) with the stochastically distributed porous topology of a sponge-derived biotemplate through biomimetic templating replication technology, fabricating a heterogeneous composite system with an architecturally asymmetric spatial network. After 5000 loading cycles, uncoated samples experienced a thickness reduction of 7.0 mm, while PDMS-coated samples showed minimal thickness changes (2.0–3.0 mm), positively correlated with curing agent content (5:1 to 20:1). The 5:1 ratio sample demonstrated exceptional mechanical stability. As evidenced, the PDMS film-encapsulated architecturally asymmetric spatial network demonstrates superior stress dissipation efficacy, effectively mitigating stress concentration phenomena inherent to symmetric configurations that induce matrix fracture, thereby achieving optimal mechanical stability. Compared to the pre-test resistance distribution of 10–248 Ω, after 5000 cyclic loading cycles, the uncoated samples exhibited a narrowed resistance range of 10–50 Ω, while PDMS-coated samples maintained a broader resistance range (10–240 Ω) as the curing agent ratio increased (from 20:1 to 5:1), demonstrating that increasing the curing agent ratio helps maintain conductive network stability. The 5:1 ratio sample displayed the lowest resistance variation rate attenuation—only 3% after 5000 cycles (vs. 80% for uncoated samples)—and consistently minimal attenuation at all stages, validating superior electrical stability. Under 0–6 kPa pressure, the 5:1 ratio device maintained a linear sensitivity of 0.157 kPa⁻¹, outperforming some existing works. Human motion monitoring experiments further confirmed its reliable signal output. Furthermore, the architecturally asymmetric spatial network of the device enables superior conformability to complex curvilinear geometries, leveraging its structural anisotropy to achieve seamless interfacial adaptation. By synergistically optimizing material composition and structural design, this study provides a novel technical method for developing highly durable flexible electronic devices. Full article

The quantity of wind and photovoltaic power-based distributed generators (DGs) is continually rising within the distribution network, presenting obstacles to its safe, steady, and cost-effective functioning. Active distribution network dynamic reconfiguration (ADNDR) improves the consumption rate of renewable energy, reduces line losses, and optimizes voltage quality by optimizing the distribution network structure. Despite being formulated as a highly dimensional and combinatorial nonconvex stochastic programming task, conventional model-based solvers often suffer from computational inefficiency and approximation errors, whereas population-based search methods frequently exhibit premature convergence to suboptimal solutions. Moreover, when dealing with high-dimensional ADNDR problems, these algorithms often face modeling difficulties due to their large scale. Deep reinforcement learning algorithms can effectively solve the problems above. Therefore, by combining the graph attention network (GAT) with the deep deterministic policy gradient (DDPG) algorithm, a method based on the graph attention network deep deterministic policy gradient (GATDDPG) algorithm is proposed to online solve the ADNDR problem with the uncertain outputs of DGs and loads. Firstly, considering the uncertainty in distributed power generation outputs and loads, a nonlinear stochastic optimization mathematical model for ADNDR is constructed. Secondly, to mitigate the dimensionality of the decision space in ADNDR, a cyclic topology encoding mechanism is implemented, which leverages graph-theoretic principles to reformulate the grid infrastructure as an adaptive structural mapping characterized by time-varying node–edge interactions Furthermore, the GATDDPG method proposed in this paper is used to solve the ADNDR problem. The GAT is employed to extract characteristics pertaining to the distribution network state, while the DDPG serves the purpose of enhancing the process of reconfiguration decision-making. This collaboration aims to ensure the safe, stable, and cost-effective operation of the distribution network. Finally, we verified the effectiveness of our method using an enhanced IEEE 33-bus power system model. The outcomes of the simulations demonstrate its capacity to significantly enhance the economic performance and stability of the distribution network, thereby affirming the proposed method’s effectiveness in this study. Full article

We performed extensive molecular dynamics simulations using a bead–spring model to investigate the interfacial behavior of blends of linear and cyclic polymer chains confined between two planar, attractive substrates. The model system was studied over a range of chain lengths spanning an order of magnitude in the number of beads for varying blend compositions and for two different levels of substrate affinity. For short chains, we observed the preferential adsorption of linear chains at the substrate interface when they are the majority component (10% cyclic chains) as well as at equimolar composition. In contrast, for longer chains, cyclic chains are preferentially enriched at the interface. These results extend recent findings from neutron reflectivity experiments—where the enrichment of cyclic polystyrene chains at low-energy surfaces was demonstrated—to systems under solid confinement, providing deeper insight into the structural behavior of topologically distinct polymers near interfaces. This work highlights the potential for tuning interfacial composition and properties in polymer blends through topological design, with implications for advanced coatings, membranes, and nanostructured materials. Full article

Materials for heat storage are important to fully utilize renewable energy sources and to realize a constant, on-demand supply. Organic phase change materials (PCMs) can play a crucial role in heat storage, as they have many advantages; however, their widespread commercial adoption is hindered by their low thermal conductivity and lack of cyclic stability. To enhance performance, highly thermally conductive fillers such as graphene nanoplatelets (GNPs) have been used; however, the role of the filler network has not been investigated. Here, we present, from a colloidal perspective, an in-depth study of GNP networks in paraffin PCMs. We investigate how GNP size, aspect ratio, and network topology determine thermal conductivity and cyclic stability of the composite. Our results show that the best-performing GNP network is random, with an optimized GNP aspect ratio. Filler fractions should be such that overlap between GNPs is guaranteed, which prevents leakage of paraffin from the composite, ensuring cyclic stability. These results not only contribute valuable insights into the design of new PCM composites but also emphasize the significance of considering filler geometry and network topology alongside filler type and fraction for optimizing thermal performance and cyclic stability. Full article

Inverse topological index problems involve determining whether a graph exists with a given integer as its topological index. One such index, the Mostar index, $Mo\left(G\right)$, is defined as $Mo\left(G\right)={\sum }_{uv\in E\left(G\right)}|n_u\left(e\right|G)-n_v\left(e\right|G)|,$ where $n_u\left(e\right|G)$ and $n_v\left(e\right|G)$ represent the number of vertices closer to vertex u than v and closer to v than u, respectively, for an edge $e=uv$. The inverse Mostar index problem has gained significant attention recently. In their work, Alizadeh et al. [Solving the Mostar index inverse problem, J. Math. Chem. 62 (5) (2024) 1079–1093] proposed the following open problem: “Which nonnegative integers can be realized as Mostar indices of c-cyclic graphs, for a given positive integer c?”. Subsequently, one of the present authors [On the inverse Mostar index problem for molecular graphs, Trans. Comb. 14 (1) (2024) 65–77] conjectured that, except for finitely many positive integers, all other positive integers can be realized as the Mostar index of a c-cyclic graph, where $c\ge 3$. In this paper, we address the inverse Mostar index problem for c-cyclic graphs. Specifically, we construct infinitely many families of symmetric c-cyclic structures, thereby demonstrating a solution to the inverse Mostar index problem using an infinite family of such symmetric structures. By providing a comprehensive proof of the conjecture, we fully resolve this longstanding open problem. Full article

In this article, the solvability of the equilibrium problem (EP), Minty equilibrium problem (MEP), and quasi-equilibrium problem (QEP) by using the notions of cyclically monotone and cyclically antimonotone in the setting of topological vector spaces and metric spaces is investigated. Also, the concepts transfer lower continuity, transfer weakly lower continuity, lower semicontinuity, from above, and sequentially weakly lower semicontinous which are weaker notions than the lower semicontinuity for establishing the existence results for EP and QEP, and the other forms of them are applied. Moreover, by using the famous results for the minimum points of a function, some existence theorems, by using the triangle property, of solutions for EP and QEP are given when the domains of bifunctions are compact and not compact. The results of this paper can be viewed as new versions of the corresponding published results with new and mild assumptions. Full article

There is relatively little research on cyclic amphiphilic block polymers, having both hydrophilic and hydrophobic segments placed in the ring and thus resulting in a higher degree of topological restriction, as drug vehicles. Cyclic amphiphilic binary block polymer is synthesized by the click coupling reaction of bimolecular homodifunctional precursors. The results indicate that cyclization between linear polymer precursors is successful if the trace linear by-products generated are ignored, which also suggests that the small molecule bifunctional terminating agent applied in traditional bimolecular homodifunctional ring-closure process can be extended to large molecule. Moreover, the study on the self-assembly behavior of polymers shows that, compared with linear counterparts, the stability and drug loading capacity of micelles based on the resultant cyclic polymer are not significantly improved due to the influence of topological structure and linear impurities. Nevertheless, drug loaded micelles formed by the obtained cyclic polymers still exhibit superior cellular uptake ability. It can be seen that topological effects do play an irreplaceable role in the application performance of polymers. Therefore, the construction and synthesis of cyclic and its derivative polymers with moderate topological confinement and high purity may be a key direction for future exploration of polymer drug delivery carriers. Full article

Ladder oligomers containing calixarene skeletons in the main chain—calix[4]resorcinarene (CRA) ladder macromolecules with open chain and cyclic macromolecules with double ring-like (Noria-type) topologies—bring particular research attention as functional materials with various applications. However, there is still a remarkable lack of studies into the synthesis of fully water-soluble derivatives of these interesting macromolecules. Research on this topic would allow their bio-based research and application niche to be at least revealed. In the present study, a strategy for the synthesis of water-soluble polyglycidol-derivatized calix resorcinarene ladder oligomers with open chain and cyclic structures is introduced. A grafting from approach was used to build branched or linear polyglycidol chains from the ladder scaffolds. The novel structures were synthesized in quantitative yields and fully characterized by NMR, FTIR and UV–vis spectroscopy, gel permeation chromatography, MALDI-TOF mass spectrometry, analytical ultracentrifugation, and static light scattering to obtain the molar mass characteristics and composition. The biocompatibility and toxicity of the two polyglycidol-derivatized oligomers were investigated and the concentration dependence of the survival of three cell lines of human origin determined. The selective apoptosis effect at relatively low dissolve concentrations toward two kinds of cancerous cell lines was found. Full article

Mimicking nature, the reversible isomerization of hydrophobic dyes in aqueous solutions is appealing for bio-applications. Here, we report on the reversible isomerization of first-generation solvatochromic donor-acceptor Stenhouse adducts (DASAs) in water within dendritic matrices, realized either through the dendronization of DASAs or the incorporation of DASA pendants into dendronized copolymers. These dendritic macromolecules contain three-fold dendritic oligoethylene glycols (OEGs), which afford the macromolecules water-solubility and unprecedented thermoresponsive behavior. The thermoresponsive behavior of both dendronized DASAs and dendronized copolymers is dominated by the peripherals of dendritic OEGs. However, the hydrophilicity of the acceptor from DASA moieties also play a role in mediating their thermal phase transitions, and more importantly, tailor the hydrophobic interactions between dendritic OEGs and DASA moieties. Intriguingly, dendritic topologies contribute confinement to encapsulate the DASA moieties through crowding effects, and cooperative interactions from the crowded dendritic OEGs modulate the DASA moieties with different isomerization in aqueous media. The thermally induced collapse of dendritic OEGs, accompanied by the aggregation of dendritic macromolecules, leads to the formation of hydrophobic domains, which exert enhanced crowding effects to efficiently encapsulate the DASA moieties. Compared to the low molar mass of dendronized DASAs, thermally collapsed dendronized copolymers can efficiently retard the hydration of DASA pendants through cooperation between neighboring dendritic OEGs and afford the DASA pendants with better confined microenvironments to mediate their isomerization recovery by up to 90% from a cyclic charged (hydrophilic) state into a noncharged (hydrophobic) linear state in water. This dendritic confinement exhibits excellent fatigue resistance after several cycles of alternating photo-irradiation and thermal annealing at elevated temperatures. Full article

This review paper investigates the relationship between symmetries of knots and links in the three-dimensional sphere, with a focus on cyclic symmetries, and their associated polynomial invariants. It examines the behavior of these polynomials in the case where the knot is set-wise fixed by the action of finite cyclic group on the 3-sphere. The study highlights how these invariants can obstruct the existence of such symmetries, providing valuable insights into the topological properties of these knots. The paper reviews established results on polynomial criteria for periodicity and their extensions to freely periodic links. It also explores generalizations to study the symmetries of virtual knots and spatial graphs. Full article

This work presents a novel compact CMOS potentiostat-designed circuit for an electrochemical cell. The proposed topology functions as a circuit interface, controlling the polarization of voltage signals at the sensor electrodes and facilitating current measurement during the oxidation–reduction process of an analyzed solution. The potentiostat, designed for CMOS technology, comprises a two-stage amplifier, two current mirror blocks coupled to this amplifier, and a CMOS push–pull output stage. The electrochemical method of cyclic voltammetry is employed, operating within a voltage range of ±0.8 V and scan rates of 10 mV/s, 25 mV/s, 100 mV/s, and 250 mV/s. The circuit is capable of reading currents ranging from 10 µA to 500 µA. Experimental results were obtained using a potassium ferrocyanide K₃[Fe(CN)₆] redox solution with concentrations of 10, 15, and 20 mmol/L, and their corresponding voltammograms were evaluated. The experimental results from a discrete circuit demonstrate that the proposed potentiostat topology produces outcomes consistent with those of classical topologies presented in the literature and industrial equipment. Full article