Unconventional scattering of flexural waves in a tunable parity-time symmetric shunted piezoelectric beam (Conference Presentation)

Fri, 24 Apr 2020 00:00:00 +0000

Abstract: Inspired by the optical and acoustic non-Hermitian 𝒫𝒯 symmetric system, a 𝒫𝒯 symmetric metamaterial beam for flexural waves is proposed here, based on shunted piezoelectric patches. Positive and negative shunting resistances are the key to constructing the balanced loss and gain components. The associated asymmetric flexural wave scattering, 𝒫𝒯 phase transition and exceptional points are then investigated in both analytical and numerical ways. In addition, properties of exceptional points are tunable in our proposed system, simply owing to the variable shunting parameters. Our design may contribute to asymmetric wave control, enhanced sensing, amplification, and localization of flexural waves.
👉 Click the link here

Writing technical content in Markdown

Fri, 12 Jul 2019 00:00:00 +0000

Wowchemy is designed to give technical content creators a seamless experience. You can focus on the content and Wowchemy handles the rest.

Highlight your code snippets, take notes on math classes, and draw diagrams from textual representation.

On this page, you’ll find some examples of the types of technical content that can be rendered with Wowchemy.

Examples

Code

Wowchemy supports a Markdown extension for highlighting code syntax. You can customize the styles under the syntax_highlighter option in your config/_default/params.yaml file.

```python
import pandas as pd
data = pd.read_csv("data.csv")
data.head()
```

renders as

import pandas as pd
data = pd.read_csv("data.csv")
data.head()

Mindmaps

Wowchemy supports a Markdown extension for mindmaps.

Simply insert a Markdown markmap code block and optionally set the height of the mindmap as shown in the example below.

A simple mindmap defined as a Markdown list:


```markmap {height="200px"}
- Hugo Modules
- wowchemy
- wowchemy-plugins-netlify
- wowchemy-plugins-netlify-cms
- wowchemy-plugins-reveal
```

renders as

- Hugo Modules
- wowchemy
- wowchemy-plugins-netlify
- wowchemy-plugins-netlify-cms
- wowchemy-plugins-reveal

A more advanced mindmap with formatting, code blocks, and math:


```markmap
- Mindmaps
- Links
- [Wowchemy Docs](https://wowchemy.com/docs/)
- [Discord Community](https://discord.gg/z8wNYzb)
- [GitHub](https://github.com/wowchemy/wowchemy-hugo-themes)
- Features
- Markdown formatting
- **inline** ~~text~~ *styles*
- multiline
text
- `inline code`
-
```js
console.log('hello');
console.log('code block');
```
- Math: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$
```

renders as

- Mindmaps
- Links
- [Wowchemy Docs](https://wowchemy.com/docs/)
- [Discord Community](https://discord.gg/z8wNYzb)
- [GitHub](https://github.com/wowchemy/wowchemy-hugo-themes)
- Features
- Markdown formatting
- **inline** ~~text~~ *styles*
- multiline
text
- `inline code`
-
```js
console.log('hello');
console.log('code block');
```
- Math: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

Charts

Wowchemy supports the popular Plotly format for interactive charts.

Save your Plotly JSON in your page folder, for example line-chart.json, and then add the {{< chart data="line-chart" >}} shortcode where you would like the chart to appear.

Demo:

You might also find the Plotly JSON Editor useful.

Math

Wowchemy supports a Markdown extension for $\LaTeX$ math. You can enable this feature by toggling the math option in your config/_default/params.yaml file.

To render inline or block math, wrap your LaTeX math with {{< math >}}$...${{< /math >}} or {{< math >}}$$...$${{< /math >}}, respectively. (We wrap the LaTeX math in the Wowchemy math shortcode to prevent Hugo rendering our math as Markdown. The math shortcode is new in v5.5-dev.)

Example math block:

{{< math >}}
$$
\gamma_{n} = \frac{ \left | \left (\mathbf x_{n} - \mathbf x_{n-1} \right )^T \left [\nabla F (\mathbf x_{n}) - \nabla F (\mathbf x_{n-1}) \right ] \right |}{\left \|\nabla F(\mathbf{x}_{n}) - \nabla F(\mathbf{x}_{n-1}) \right \|^2}
$$
{{< /math >}}

renders as

$$\gamma_{n} = \frac{ \left | \left (\mathbf x_{n} - \mathbf x_{n-1} \right )^T \left [\nabla F (\mathbf x_{n}) - \nabla F (\mathbf x_{n-1}) \right ] \right |}{\left \|\nabla F(\mathbf{x}_{n}) - \nabla F(\mathbf{x}_{n-1}) \right \|^2}$$

Example inline math {{< math >}}$\nabla F(\mathbf{x}_{n})${{< /math >}} renders as $\nabla F(\mathbf{x}_{n})$.

Example multi-line math using the math linebreak (\\):

{{< math >}}
$$f(k;p_{0}^{*}) = \begin{cases}p_{0}^{*} & \text{if }k=1, \\
1-p_{0}^{*} & \text{if }k=0.\end{cases}$$
{{< /math >}}

renders as

$$ f(k;p_{0}^{*}) = \begin{cases}p_{0}^{*} & \text{if }k=1, \\ 1-p_{0}^{*} & \text{if }k=0.\end{cases} $$

Diagrams

Wowchemy supports a Markdown extension for diagrams. You can enable this feature by toggling the diagram option in your config/_default/params.toml file or by adding diagram: true to your page front matter.

An example flowchart:

```mermaid
graph TD
A[Hard] -->|Text| B(Round)
B --> C{Decision}
C -->|One| D[Result 1]
C -->|Two| E[Result 2]
```

renders as

graph TD A[Hard] -->|Text| B(Round) B --> C{Decision} C -->|One| D[Result 1] C -->|Two| E[Result 2]

An example sequence diagram:

```mermaid
sequenceDiagram
Alice->>John: Hello John, how are you?
loop Healthcheck
John->>John: Fight against hypochondria
end
Note right of John: Rational thoughts!
John-->>Alice: Great!
John->>Bob: How about you?
Bob-->>John: Jolly good!
```

renders as

sequenceDiagram Alice->>John: Hello John, how are you? loop Healthcheck John->>John: Fight against hypochondria end Note right of John: Rational thoughts! John-->>Alice: Great! John->>Bob: How about you? Bob-->>John: Jolly good!

An example Gantt diagram:

```mermaid
gantt
section Section
Completed :done, des1, 2014-01-06,2014-01-08
Active :active, des2, 2014-01-07, 3d
Parallel 1 : des3, after des1, 1d
Parallel 2 : des4, after des1, 1d
Parallel 3 : des5, after des3, 1d
Parallel 4 : des6, after des4, 1d
```

renders as

gantt section Section Completed :done, des1, 2014-01-06,2014-01-08 Active :active, des2, 2014-01-07, 3d Parallel 1 : des3, after des1, 1d Parallel 2 : des4, after des1, 1d Parallel 3 : des5, after des3, 1d Parallel 4 : des6, after des4, 1d

An example class diagram:

```mermaid
classDiagram
Class01 <|-- AveryLongClass : Cool
Class03 *-- Class04
Class05 o-- Class06
Class07 .. Class08
Class09 --> C2 : Where am i?
Class09 --* C3
Class09 --|> Class07
Class07 : equals()
Class07 : Object[] elementData
Class01 : size()
Class01 : int chimp
Class01 : int gorilla
Class08 <--> C2: Cool label
```

renders as

classDiagram Class01 <|-- AveryLongClass : Cool Class03 *-- Class04 Class05 o-- Class06 Class07 .. Class08 Class09 --> C2 : Where am i? Class09 --* C3 Class09 --|> Class07 Class07 : equals() Class07 : Object[] elementData Class01 : size() Class01 : int chimp Class01 : int gorilla Class08 <--> C2: Cool label

An example state diagram:

```mermaid
stateDiagram
[*] --> Still
Still --> [*]
Still --> Moving
Moving --> Still
Moving --> Crash
Crash --> [*]
```

renders as

stateDiagram [*] --> Still Still --> [*] Still --> Moving Moving --> Still Moving --> Crash Crash --> [*]

Todo lists

You can even write your todo lists in Markdown too:

- [x] Write math example
 - [x] Write diagram example
- [ ] Do something else

renders as

Write math example
- Write diagram example
Do something else

Tables

Save your spreadsheet as a CSV file in your page’s folder and then render it by adding the Table shortcode to your page:

{{< table path="results.csv" header="true" caption="Table 1: My results" >}}

renders as

Table 1: My results
customer_id	score
1	0
2	0.5
3	1

Callouts

Academic supports a shortcode for callouts, also referred to as asides, hints, or alerts. By wrapping a paragraph in {{% callout note %}} ... {{% /callout %}}, it will render as an aside.

{{% callout note %}}
A Markdown aside is useful for displaying notices, hints, or definitions to your readers.
{{% /callout %}}

renders as

A Markdown aside is useful for displaying notices, hints, or definitions to your readers.

Spoilers

Add a spoiler to a page to reveal text, such as an answer to a question, after a button is clicked.

{{< spoiler text="Click to view the spoiler" >}}
You found me!
{{< /spoiler >}}

renders as

Click to view the spoiler

You found me!

Icons

Academic enables you to use a wide range of icons from Font Awesome and Academicons in addition to emojis.

Here are some examples using the icon shortcode to render icons:

{{< icon name="terminal" pack="fas" >}} Terminal
{{< icon name="python" pack="fab" >}} Python
{{< icon name="r-project" pack="fab" >}} R

renders as

Terminal
Python
R

This is Singapore

Tue, 05 Feb 2019 00:00:00 +0000

Posts | Qian Wu (吳謙)

Unconventional scattering of flexural waves in a tunable parity-time symmetric shunted piezoelectric beam (Conference Presentation)

Writing technical content in Markdown

Examples

Code

Mindmaps

Charts

Math

Diagrams

Todo lists

Tables

Callouts

Spoilers

Icons

Did you find this page helpful? Consider sharing it 🙌

This is Singapore