arXiv subjects

Hongbo Zeng

Publications and source records attributed to Hongbo Zeng.

15 recordsLinked to original sources

arXiv2026

Devaney chaos in a Two-Dimensional Space with Weak Topology

It is well known that a finite-dimensional linear system cannot be chaotic. In this article, it shows that Devaney chaos with the weak topology can be generated by a linear map, where the weak topology into a two-dimensional Euclidean space is induced by a linear functional. Especially, it gives the equivalent conditions to be strongly transitive (weakly transitive, strongly sensitive,weakly sensitive, dense periodic points, respectively). Besides, we show that for a matrix with two conjugate complex eigenvalues, strong transitivity (sensitivity, respectively) is equivent to weak transitivity (sensitivity, respectively), which does not hold if we consider a matrix with two real eigenvalues. Finally, in two-dimensional space with weak topology, we show that weak transitivity and weak density of periodic points do not imply weak sensitivity and that weak transitivity and fixed point do not imply Li-Yorke chao, which show that there is a significant difference between the dynamic properties of weak topology and the dynamic properties of norm topology.

math.DS↗

arXiv2026

$\beta$-$n$-sensitivity and other stronger forms of sensitivity in dynamical systems

In this paper, we investigate the relationships between the $\beta$-$n$-sensitivity and other forms of sensitivity in discrete dynamical systems. And we present some different sufficient conditions (equivalent condition) to be (strongly) $\beta$-$n$-sensitive. These results improve and extend some existing ones. Moreover, we introduce and study the semi-strong $\beta$-$n$-sensitivity and (strong) multi-$\beta$-$n$-sensitivity with respect to $\alpha$. Besides, we proved that strongly multi-transitivity implies strongly multi-sensitivity, which improves some existing ones. Finally, we obtain that (semi-)strongly $\beta$-$n$-sensitivity is preserved under iterations but $\beta$-$n$-sensitivity fails.

math.DS↗

arXiv2025

Several stronger forms of transitivity in non-autonomous discrete dynamical systems

In this paper, we introduce and study the notions of $\Delta$-mixing, $\Delta$-transitivity, mildly mixing, strong multi-transitivity and multi-transitivity with respect to a vector in non-autonomous discrete dynamical systems (NDS). Firstly, we prove that multi-transitivity (strong multi-transitivity, multi-transitivity with respect to a vector, $\Delta$-transitivity, respectively) of NDS is iteration invariants. Then, necessary and sufficient conditions are obtained under which an NDS is strongly multi-transitive ($\Delta$-mixing, $\Delta$-transitive, respectively). Besides, we present some counterexamples to justify that the results related to stronger forms of transitivity which are true for autonomous discrete dynamical systems (ADS) but fail in NDS, which show that there is a significant difference between the theory of ADS and the theory of NDS, and establish a sufficient condition under which the results still hold in NDS. Finally, we give a sufficient condition under which multi-transitivity, weakly mixing, weakly mixing of all orders, thick transitivity, $\Delta$-transitivity and strongly multi-transitive are equivalent in NDS.

math.DS↗

arXiv2025

Sensitivity and transitivity for the induced maps on symmetric product suspensions of a topological space

Given a nondegenerate compact perfect and Hausdorff topological space $X$,$n\in \mathbb{N}$ and a function $f:X\rightarrow X$, we consider the $n$-fold symmetric product of $X$, $F_n(X)$ and the induced function $F_n(f):F_n(X)\rightarrow F_n(X)$. If $n\geq2$, we consider the $n$-fold symmetric product suspension of $X$, $SF_n(X)$ and the induced function$SF_n(f):SF_n(X)\rightarrow SF_n(X)$. In this paper, we study the relationships between the following statements: (1) $f\in \mathcal{M}$,(2) $F_n(f)\in \mathcal{M}$, and (3)$SF_n(f)\in \mathcal{M}$, where $\mathcal{M}$ is one of the following classes of map: sensitive, cofinitely sensitive, multi-sensitive, Z-transitive, quasi-periodic, accessible, indecomposable, multi-transitive, $\bigtriangleup$-transitive, $\bigtriangleup$-mixing, Martelli's chaos, Transitive, $F$-system, $TT_{++}$, Touhey, two-sided transitive, fully exact, strongly transitive. These results improve and extend some existing ones.

math.DS↗

arXiv2025

A note on multi-transitivity in non-autonomous discrete systems

This paper is concerned with some stronger forms of transitivity in non-autonomous discrete systems$(f_{ 1,\infty})$ generated by a uniformly convergent sequence of continuous self maps. Firstly, we present two counterexamples to show that Theorem 3.1 obtained by Salman and Das in [Multi-transitivity in nonautonomous discrete systems Topol. Appl. 278(2020)107237] is not true. Then, we introduce and study mildly mixing in non-autonomous discrete systems, which is stronger than mixing. We obtain that multi-transitivity implies Li-Yorke chaos and that mildly mixing implies multi-transitivity, which answer the open problems 1 and 2 in the paper above. Additionally, we give a counterexample which shows that Theorem 2.3 and Theorem 2.4 given by Sharma and Raghav in [On dynamics generated by a uniformly convergent sequence of maps Topol. Appl. 247 (2018)81-90] are both incorrect and give the correct proofs of them. Finally, some counterexamples are constructed justifying that some results related to stronger forms of transitivity which are true for autonomous systems but fail in non-autonomous systems, and establish a sufficient condition under which the results still hold in non-autonomous systems.

math.DS↗

arXiv2024

Sensitivity, transitivity and chaos in non-autonomous discrete systems

In this paper, we study properties of sensitivity, transitivity and chaos for non-autonomous discrete systems(NDS). Firstly, we present some different sufficient conditions for NDS to be chaotic. Then, we relate the transitivity with the sensitivity of NDS and give several sufficient conditions for NDS to be sensitive. We obtain that transitivity and dense periodic points imply sensitivity, and that transitive system is either sensitive or almost equicontinuous. The results improve and extend some existing ones. Besides, we give some examples to show that there is a significant difference between the theory of ADS and the theory of NDS. We get that almost periodic point and minimal point do not imply each other and that two definitions of minimal system are not equivalent for non-autonomous discrete systems. Finally, we introduce and study weakly sensitivity for non-autonomous discrete systems.

math.DS↗

arXiv2024

Mixing, Li-Yorke chaos, distributional chaos and Kato's chaos to multiple mappings

Let $(X,d)$ be a compact metric space and $F=\{f_1,f_2,...,f_m\}$ be an $m$-tuple of continuous maps from $X$ to itself. In this paper, we introduce the definitions of transitivity, weakly mixing and mixing of multiple mappings $(X,F)$ from a set-valued perspective, which is the semigroup generated by $F$ based on iterated function system. Firstly, we prove that for multiple mappings, mixing implies distributional chaos in a sequence, Li-Yorke chaos and Kato's chaos. Besides, we demonstrate that $F$ is Kato's chaos if and only if $F^k$ is Kato's chaos for any $k \in \mathbb{N}$. Finally, we construct a symbolic dynamical system to show that distributional chaos may be generated by only two strongly non-wandering points.

math.DS↗

arXiv2024

Iteration problem for several chaos in non-autonomous discrete system

In this paper we investigate the iteration problem for several chaos in non-autonomous discrete system. Firstly, we prove that the Li-Yorke chaos of a non-autonomous discrete dynamical system is preserved under iterations when $f_{1,\infty}$ converges to $f$, which weakens the condition in the literature that $f_{1,\infty}$ uniformly converges to $f$. Besides, we prove that both DC2' and Kato's chaos of a non-autonomous discrete dynamical system are iteration invariants. Additionally, we give a sufficient condition for non-autonomous discrete dynamical system to be Li-Yorke chaos. Finally, we give an example to show that the DC3 of a non-autonomous discrete dynamical system is not inherited under iterations, which partly answers an open question proposed by Wu and Zhu(Chaos in a class of non-autonomous discrete systems, Appl.Math.Lett. 2013,26:431-436).

math.DS↗

arXiv2022

Growth Rates of Hydrogen Microbubbles in Reacting Femtoliter Droplets

Chemical reactions in small droplets are extensively explored to accelerate the discovery of new materials, increase efficiency and specificity in catalytic biphasic conversion and in high throughput analytics. In this work, we investigate the local rate of gas-evolution reaction within femtoliter droplets immobilized on a solid surface. The growth rate of hydrogen microbubbles (> 500 nm in radius) produced from the reaction was measured online by high-resolution confocal microscopic images. The growth rate of bubbles was faster in smaller droplets, and of bubbles near the three-phase boundary in the same droplet. The results were consistent for both pure and binary reacting droplets and on substrates of different wettability. Our theoretical analysis based on diffusion, chemical reaction, and bubble growth in a steady state predicted that the concentration of the reactant diffusing from the surrounding depended on the droplet size and the bubble location inside the droplet, in good agreement with experimental results. Our results reveal that the reaction rate may be spatially non-uniform in the reacting microdroplets. The findings may have implications for formulating chemical properties and uses of these droplets.

physics.chem-ph↗

arXiv2021

Interfacial Partitioning Enhances Microextractionby Multicomponent Nanodroplets

The sensitive and reliable in-droplet chemical analysis benefits from the enhanced partition of an analyte into the droplets. This work, we will show that chemical reactions in surface nanodroplets can shift the partition of analytes from a highly diluted solution to the droplets. Seven types of organic acids with partition coefficients (LgP) ranging from -0.7 to 1.87 are used as model analytes dissolved in an oil solution that are extracted from the flow into aqueous nanodroplets immobilized on a substrate. The timescale of integrated extraction and reaction in droplets was represented by the decoloration time of the droplets. Our results show that the effective distribution coefficient of the analyte can be decreased by 3 to 11 times of the distribution coefficient of the analyte in the bulk liquids. The principle behind the significantly shifted partition is proposed to be enhanced the transfer of the analyte across the droplet surface. The chemical reaction in the droplets enhances the partition of the analyte from a highly diluted solution. Our results show that the interfacial behavior of the analyte may be advantageous as it may improve extraction and partition. Such enhanced extraction may be leveraged for sensitive chemical detection using reactive droplets.

cond-mat.soft↗

arXiv2021

Size Effect on Reaction Rate of Surface Nanodroplets

Compartmentalizing reagents within small droplets is promising for highly efficient conversion and simplified procedures in many biphasic chemical reactions. In this work, surface nanodroplets (i.e., less than 100 nm in their maximal height) were employed to quantitatively understand the size effect on the chemical reaction rate of droplets. In our systems, a surface-active reactant in pure or binary nanodroplets reacted with the reactant in the bulk flow. Meanwhile, the product was removed from the droplet surface. The shrinkage rate of the nanodroplets was characterized by analyzing the lateral size as a function of time, where the droplet size was solely determined by chemical reaction rate at a given flow condition for the transport of the reactant and the product. We found that the overall kinetics increases rapidly with the decrease of droplets lateral radius R, as dR/dt ~ R^(-2). The faster increase in the concentration of the product in smaller droplets contributes to accelerating reaction kinetics. The enhancement of reaction rates from small droplet sizes was further confirmed when a non-reactive compound presented inside the droplets without reducing the concentrations of the reactant and the product on the droplet surface. The results of our study improve the understanding of chemical kinetics with droplets. Our findings highlight the effectiveness of small droplets for the design and control of enhanced chemical reactions in a broad range of applications.

cond-mat.soft↗

arXiv2020

Integrated nanoextraction and colorimetric reactions in surface nanodroplets for combinative analysis

A combinative approach for chemical analysis makes it possible to distinguish a mixture of a large number of compounds from other mixtures in a single step. This work demonstrates a combinative analysis approach by using surface nanodroplets for integrating nanoextraction and colorimetric reactions for the identification of multi-component mixtures. The model analytes are acidic compounds dissolved in oil that are extracted into aqueous droplets on a solid substrate. The proton from acid dissociation reacts with the halochromic chemical compounds inside the droplets, leading to the color change of the droplets. The rate of the colorimetric reaction exhibits certain specificity for the acid type, distinguishing acid mixtures with the same pH value. The underlying principle is that the acid transport rate is associated with the partition coefficient and the dissociation constant of the acid, in addition to the concentration in oil. As a demonstration, we showed that droplet-based combinative analysis can be applied for anti-counterfeiting of various alcoholic spirits by comparing decolor time of organic acid mixtures in the spirits. The readout can be done by using a common hand-hold mobile phone.

cond-mat.soft↗

arXiv2020

Speeding up biphasic reactions with surface nanodroplets

Biphasic chemical reactions compartmentalized in small droplets offer advantages, such as streamlined procedures for chemical analysis, enhanced chemical reaction efficiency and high specificity of conversion. In this work, we experimentally and theoretically investigate the rate for biphasic chemical reactions between acidic nanodroplets on a substrate surface and basic reactants in a surrounding bulk flow. The reaction rate is measured by droplet shrinkage as the product is removed from the droplets by the flow. In our experiments, we determine the dependence of the reaction rate on the flow rate and the solution concentration. The theoretical analysis predicts that the life time $τ$ of the droplets scales with Peclet number $Pe$ and the reactant concentration in the bulk flow $c_{re,bulk}$ as $τ\propto Pe^{-3/2}c_{re,bulk}^{-1}$, in good agreement with our experimental results. Furthermore, we found that the product from the reaction on an upstream surface can postpone the droplet reaction on a downstream surface, possibly due to the adsorption of interface-active products on the droplets in the downstream. The time of the delay decreases with increasing $Pe$ of the flow and also with increasing reactant concentration in the flow, following the scaling same as that of the reaction rate with these two parameters. Our findings provide insight for the ultimate aim to enhance droplet reactions under flow conditions.

cond-mat.soft↗

arXiv2018

Spontaneous Repairing Liquid Metal/Si Nanocomposite as a Smart Conductive-Additive-Free Anode for Lithium-ion Battery

Silicon is a promising candidate for negative electrodes due to its high theoretical specific capacity (~3579 mAh g-1) and low lithiation potential (~0.40 V vs Li). However, its practical applications in battery have been inhibited by the large volume change (~400%) induced by Li+-insertion into Si lattices. Here, we attempt to resolve this issue at a fundamental level, and report for the first time a novel liquid metal (LM)-mediated spontaneous repairing conductive-additive-free Si anode for Li-ion battery. The fluidity of LM ensures the eternal contact between Si and the conducting-network during its repeated electrochemical reactions. The as-prepared nano-composite of LM/Si leads to superior performances as characterized by high capacity utilization (2300 mAh g-1 at 500 mA g-1), long-term stability (968 mAh g-1 after 1500 charge-discharge cycles at 8 A g-1 with 81.3% retention), high rate capability (360 mAh g-1 at 20 A g-1, equivalence of 55 C, or full charge/discharge in 65 seconds), and, in particular, an extra-ordinarily high initial coulombic efficiency (95.92%), which is not only the highest reported for Si to the best of our knowledge, but also higher than the mature graphitic carbon anodes. The unique approach described in this work not only resolves the basic stress challenges faced by the promising but often problematic alloy-type materials; in broader context it also provides a universal inspiration to all electrode materials whose electric properties suffer from extreme mechanic upheavals induced by the electrochemical strains during the cell reactions.

physics.app-ph↗

arXiv2010

Reversible shear thickening at low shear rates of electrorheological fluids under electric fields

Shear thickening is a phenomenon of significant viscosity increase of colloidal suspensions. While electrorheological (ER) fluids can be turned into a solid-like material by applying an electric field, their shear strength is widely represented by the attractive electrostatic interaction between ER particles. By shearing ER fluids between two concentric cylinders, we show a reversible shear thickening of ER fluids above a low critical shear rate (<1 s-1) and a high critical electric field strength (>100 V/mm), which could be characterized by a modified Mason number. Shear thickening and electrostatic particle interaction-induced inter-particle friction forces is considered to be the real origin of the high shear strength of ER fluids, while the applied electric field controls the extent of shear thickening. The electric field-controlled reversible shear thickening has implications for high-performance ER/magnetorheological (MR) fluid design, clutch fluids with high friction forces triggered by applying local electric field, other field-responsive materials and intelligent systems.

cond-mat.soft↗