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Highly efficient and accurate numerical schemes for the anisotropic phase field crystal models by using the improved scalar auxiliary variable (iSAV) approach

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-04-24 DOI: 10.1016/j.cnsns.2025.108875

Xiaoli Wang, Zhengguang Liu

The two-dimensional anisotropic phase field crystal (APFC) model is a sixth-order nonlinear parabolic equation that can be used to simulate various phenomena such as epitaxial growth, material hardness, and phase transition. The scalar auxiliary variable method (SAV) is a common method to solve various nonlinear dissipative systems, and the improved SAV (iSAV) method is not only completely linear, but also strictly guarantees the original dissipation law. In this paper, we construct several efficient, accurate linear and original energy-stable numerical schemes of the APFC model based on the iSAV method. Firstly, a first-order iSAV scheme is considered to keep the original energy stability for the APFC model. Secondly, we propose a new stabilized iSAV scheme and give its rigorous energy stability analysis to keep its original dissipation law. Finally, several interesting numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed methods.

引用次数: 0

A curvature flow approach to the Lp chord Minkowski problem

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-04-24 DOI: 10.1016/j.na.2025.113825

Manli Cheng , Lan Tang

In this work, we mainly consider the

L_{p}

chord Minkowski problem and the existence results of solutions to this problem have been established by the method of flow governed by parabolic equations for the two cases: (1)

0 < p \leq n + q - 1

and

q > 2

; (2)

p > n

and

q > 2

引用次数: 0

Population dynamics of biological synchronous reproduction and the effects of synchronous reproductive cycle on population dynamics

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-04-24 DOI: 10.1016/j.chaos.2025.116438

Jian Gao , Bin Xu , Yaqi Zheng , Chuansheng Shen

Population dynamics and reproductive cycles are fundamental aspects of biological systems, with profound implications for species survival and ecosystem stability. Synchronous reproduction, a phenomenon observed across various taxa, optimizes breeding success and offspring survival but may also introduce complex dynamics under changing environmental conditions. However, there is a scarcity of reports on the impact of synchronous reproduction on population dynamics. This study investigates the influence of synchronous reproductive cycles on population dynamics, with a focus on bifurcation phenomena such as Hopf and period-doubling bifurcations. By employing a series of ordinary differential equation (ODE) models and their discrete difference equation (DDE) counterparts, we analyze the synergistic effects of the reproductive cycle and control parameters on population stability and oscillatory behavior. Numerical simulations demonstrate that synchronous reproduction induces systematic shifts in bifurcation diagrams within the parameter space. Specifically, an increase in reproductive cycle amplifies the displacement of bifurcation curves, revealing that reproductive cycle and control parameters jointly regulate population dynamics. Our results offer actionable guidance for ecosystem management by demonstrating that maintaining or adjusting reproductive synchrony could serve as a leverage point for stabilizing vulnerable populations. Specifically, conservation strategies targeting species with synchronized breeding cycles should prioritize habitat preservation during critical reproductive windows and incorporate climate-driven shifts in reproductive timing into adaptive management frameworks.

{"title":"Population dynamics of biological synchronous reproduction and the effects of synchronous reproductive cycle on population dynamics","authors":"Jian Gao , Bin Xu , Yaqi Zheng , Chuansheng Shen","doi":"10.1016/j.chaos.2025.116438","DOIUrl":"10.1016/j.chaos.2025.116438","url":null,"abstract":"<div><div>Population dynamics and reproductive cycles are fundamental aspects of biological systems, with profound implications for species survival and ecosystem stability. Synchronous reproduction, a phenomenon observed across various taxa, optimizes breeding success and offspring survival but may also introduce complex dynamics under changing environmental conditions. However, there is a scarcity of reports on the impact of synchronous reproduction on population dynamics. This study investigates the influence of synchronous reproductive cycles on population dynamics, with a focus on bifurcation phenomena such as Hopf and period-doubling bifurcations. By employing a series of ordinary differential equation (ODE) models and their discrete difference equation (DDE) counterparts, we analyze the synergistic effects of the reproductive cycle and control parameters on population stability and oscillatory behavior. Numerical simulations demonstrate that synchronous reproduction induces systematic shifts in bifurcation diagrams within the parameter space. Specifically, an increase in reproductive cycle amplifies the displacement of bifurcation curves, revealing that reproductive cycle and control parameters jointly regulate population dynamics. Our results offer actionable guidance for ecosystem management by demonstrating that maintaining or adjusting reproductive synchrony could serve as a leverage point for stabilizing vulnerable populations. Specifically, conservation strategies targeting species with synchronized breeding cycles should prioritize habitat preservation during critical reproductive windows and incorporate climate-driven shifts in reproductive timing into adaptive management frameworks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116438"},"PeriodicalIF":5.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Local bifurcation structure for a free boundary problem modeling tumor growth

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-04-24 DOI: 10.1016/j.nonrwa.2025.104383

Wenhua He, Ruixiang Xing

There are many papers in the literature studying a classic free boundary problem modeling 3-dimensional tumor growth, initiated by Byrne and Chaplain. One of the most important parameters is the tumor aggressiveness constant

μ

. Friedman and Reitich (1999) showed the problem admits a unique radially symmetric solution with the free boundary

r = R_{S}

when the external nutrient concentration is greater than the threshold concentration for proliferation. A sequence of papers, Fontelos and Friedman (2003), Friedman and Hu (2008) and Pan and Xing (2022) derived a sequence of symmetry-breaking branches bifurcating from the spherical state

r = R_{S}

at an increasing sequence of

μ = μ_{n}

(

n \geq 2

). Friedman and Hu (2008) studied the structure of the branching solution at

μ = μ_{2}

. These bifurcation results cover only the direction of spherical harmonic function

Y_{2, 0}

. In this paper, we determine a plethora of new local bifurcation structures at

μ = μ_{n}

for even

n \geq 2

in directions involving combinations of

Y_{n, m}

for

m \neq 0

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引用次数: 0

Numerical steepest descent method for computing oscillatory-type Bessel integral transforms

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-04-24 DOI: 10.1016/j.matcom.2025.04.016

Ruyun Chen, Yu Li, Yongxiong Zhou

In this paper, numerical steepest descent method is implemented to approximate highly oscillatory Bessel-type integral transforms. We begin our analysis by utilizing an important relationship between Bessel function of the first kind and modified Bessel function of the second kind. Subsequently, we transform new integrals into the forms on the interval

[0, + \infty)

, where the integrands do not oscillate and decay exponentially fast. These integrals can then be efficiently computed using Gauss–Laguerre quadrature rule. Furthermore, we derive the theoretical error estimates that depend on the frequency

ω

and the number of nodes

n

. Numerical examples based on the theoretical results are provided to demonstrate the effectiveness of these methods.

引用次数: 0

Walking dynamics of a bipedal robot with impulsive actuation

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-04-24 DOI: 10.1016/j.physd.2025.134677

Tengfei Long , Xianfei Hui , Guirong Jiang

Impulsive actuation, which includes hip joint pulse torque and heel pulse thrust, is introduced to build a walking model of a bipedal robot on level ground in this study. The impulsive actuation configuration and the mechanism of stable walking motion are investigated. The existence and stability of period

- 1

and 2 gaits are investigated by means of the discrete map. The conditions for flip bifurcation and inverse flip bifurcation of period

- 1

gait are derived. The complex walking dynamics, such as period

- 4

gait, flip bifurcation and inverse flip bifurcation of period

- n (n = 2, 4)

gait, and chaotic gait, are obtained by numerical simulations. By using period

- 1

gait, theoretical analysis is conducted on the energy consumption of applying pulse torque and constant torque to the hip joint under the same conditions. Numerical results show that the energy consumption of pulse torque is less than that of constant torque. The superiority and walking dynamics caused by impulsive actuation can provide theoretical reference for designing bipedal robots with stable and efficient walking.

{"title":"Walking dynamics of a bipedal robot with impulsive actuation","authors":"Tengfei Long , Xianfei Hui , Guirong Jiang","doi":"10.1016/j.physd.2025.134677","DOIUrl":"10.1016/j.physd.2025.134677","url":null,"abstract":"<div><div>Impulsive actuation, which includes hip joint pulse torque and heel pulse thrust, is introduced to build a walking model of a bipedal robot on level ground in this study. The impulsive actuation configuration and the mechanism of stable walking motion are investigated. The existence and stability of period<span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> and 2 gaits are investigated by means of the discrete map. The conditions for flip bifurcation and inverse flip bifurcation of period<span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> gait are derived. The complex walking dynamics, such as period<span><math><mrow><mo>−</mo><mn>4</mn></mrow></math></span> gait, flip bifurcation and inverse flip bifurcation of period<span><math><mrow><mo>−</mo><mi>n</mi><mspace></mspace><mrow><mo>(</mo><mi>n</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow></mrow></math></span> gait, and chaotic gait, are obtained by numerical simulations. By using period<span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> gait, theoretical analysis is conducted on the energy consumption of applying pulse torque and constant torque to the hip joint under the same conditions. Numerical results show that the energy consumption of pulse torque is less than that of constant torque. The superiority and walking dynamics caused by impulsive actuation can provide theoretical reference for designing bipedal robots with stable and efficient walking.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134677"},"PeriodicalIF":2.7,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Restricted Hausdorff spectra of q-adic automorphisms

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-04-24 DOI: 10.1016/j.aim.2025.110294

Jorge Fariña-Asategui

Firstly, we completely determine the self-similar Hausdorff spectrum of the group of q-adic automorphisms where q is a prime power, answering a question of Grigorchuk. Indeed, we take a further step and completely determine its Hausdorff spectra restricted to the most important subclasses of self-similar groups, providing examples differing drastically from the previously known ones in the literature. Our proof relies on a new explicit formula for the computation of the Hausdorff dimension of closed self-similar groups and a generalization of iterated permutational wreath products.

Secondly, we provide for every prime p the first examples of just infinite branch pro-p groups with zero Hausdorff dimension in

Γ_{p}

, giving strong evidence against a well-known conjecture of Boston.

引用次数: 0

Vortex droplets and lattice patterns in two-dimensional traps: A photonic spin–orbit-coupling perspective

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-04-24 DOI: 10.1016/j.chaos.2025.116441

S. Sanjay , S. Saravana Veni , Boris A. Malomed

In the context of the mean-field exciton-polariton (EP) theory with balanced loss and pump, we investigate the formation of lattice structures built of individual vortex-antivortex (VAV) bound states under the action of the two-dimensional harmonic-oscillator (HO) potential trap and effective spin–orbit coupling (SOC), produced by the TE-TM splitting in the polariton system. The number of VAV elements (“pixels”) building the structures grow with the increase of self- and cross-interaction coefficients. Depending upon their values and the trapping frequency, stable ring-shaped, circular, square-shaped, rectangular, pentagonal, hexagonal, and triangular patterns are produced, with the central site left vacant or occupied in the lattice patterns of different types. The results suggest the experimental creation of the new patterns and their possible use for the design of integrated circuits in EP setups, controlled by the strengths of the TE-TM splitting, nonlinearity, and HO trap.

引用次数: 0

On the third largest eigenvalue of eccentricity matrices of graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-04-24 DOI: 10.1016/j.dam.2025.04.039

Yuanfen Song , Yuxia Li , Maurizio Brunetti , Jianfeng Wang

Let

D (G)

denote the distance matrix of a connected graph

G

. The eccentricity matrix (or anti-adjacency matrix) of

G

is obtained from

D (G)

by retaining in each row and each column only the maximal entries. In this paper, all the graphs with third largest eccentricity eigenvalue in the interval

(- 1, 0)

are detected. It turns out that these graphs are all found among the chain graphs with (nonempty) four cells and the graphs of type

K_{t} \lor (G \cup k K_{1})

, where

k ⩾ 0

and

G

is a chain graph with at most ten cells.

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引用次数: 0

An analogue of Koebe’s theorem and the openness of a limit map in one class

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics

Pub Date : 2025-04-24 DOI: 10.1007/s13324-025-01058-6

Evgeny Sevost’yanov, Valery Targonskii

We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class. This statement can be interpreted as the well-known analogue of Koebe’s theorem for analytic functions. As an application of the obtained result, we show that, if a sequence of mappings belonging to the specified class converges locally uniformly, then the limit mapping is open.

引用次数: 0

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