# Geometric Stochastic Resonance in an Asymmetric T-Shaped Chamber

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## Abstract

**:**

## 1. Introduction

## 2. Model

## 3. Results and Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of T-shape chamber. (

**a**) Spout-like chamber; (

**b**) square-like chambers; and (

**c**) funnel-like chamber. Slope of side wall of the trapezoid cavity below is defined as $k=H/(W-{x}_{u})$.

**Figure 2.**Time series of the particle trajectory along x (top panel) and y (bottom panel) axes with noise strengths D $=0.0005$ (

**a**,

**d**), $=0.005$ (

**b**,

**e**) and $=0.05$ (

**c**,

**f**). Other parameters: ${F}_{0}=0.2$ and $\omega =0.01$, $h=0.02,$ $W=0.35,$ $H=0.2,$ $k=5$, and $L=0.75$.

**Figure 3.**Escape rate of Brownian particles versus $1/D$ for different values of AC drive strength ${F}_{0}$ with $\omega =0.01$ in (

**a**) upper and (

**b**) down cavities. Other parameters: $h=0.02$, $W=0.34$, $H=0.2$, and $L=0.75$.

**Figure 4.**Stochastic resonance in the T-shaped chamber. $\overline{x}\left(D\right)$ versus D for different values of AC drive strength ${F}_{0}$ at $\omega =0.1$ in (

**a**), and the frequency $\omega $ with ${F}_{0}=0.2$ in (

**c**). $\varphi \left(D\right)$ versus D for different values of AC drive strength ${F}_{0}$ at $\omega =0.1$ in (

**b**), and the frequency $\omega $ with ${F}_{0}=0.2$ in (

**d**). Other parameters: $h=0.02$, $W=0.34$, $H=0.2$, and $L=0.75$. The dashed curves represent the predicted asymptotic decay $\overline{x}\left(D\right)/{F}_{0}$ for $D\to \infty $; see text.

**Figure 5.**Dependence of SR on the geometry of the T-shaped chambers. $\overline{x}\left(D\right)$ versus D for different heights of upper cavity h (

**a**), depths of down cavity H (

**b**), widths of down cavity W (

**c**), and slopes of wall of down cavity (

**d**). ${F}_{0}=0.5$, $\omega =0.1$, and $L=0.75$. Other parameters: (

**a**) $W=0.35$, $H=0.2$, $k=5$; (

**b**) $W=0.35$, $h=0.02$, $k=5$; (

**c**) $h=0.02$, $H=0.2$, $k=5$; (

**d**) $W=0.35$, $h=0.02$, $H=0.2$.

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**MDPI and ACS Style**

Duan, S.; Fan, B.; Duan, Z.
Geometric Stochastic Resonance in an Asymmetric T-Shaped Chamber. *Symmetry* **2023**, *15*, 2183.
https://doi.org/10.3390/sym15122183

**AMA Style**

Duan S, Fan B, Duan Z.
Geometric Stochastic Resonance in an Asymmetric T-Shaped Chamber. *Symmetry*. 2023; 15(12):2183.
https://doi.org/10.3390/sym15122183

**Chicago/Turabian Style**

Duan, Shouhui, Bixuan Fan, and Zhenglu Duan.
2023. "Geometric Stochastic Resonance in an Asymmetric T-Shaped Chamber" *Symmetry* 15, no. 12: 2183.
https://doi.org/10.3390/sym15122183