Scholarlink

<p>We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes <i>N</i> Brownian motions up to time <i>T</i>, started at the origin and subject to exponential penalization based on the amount of time they spend close to each other, or close to themselves. The effective radius measures the typical distance from the origin. Our main result gives estimates for the effective radius where in two and three dimensions we impose the restriction that <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3444_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(T \le N\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>≤</mo> <mi>N</mi> </mrow> </math></EquationSource> </InlineEquation>. One of the highlights of our results is that in two dimensions, we find that the radius is proportional to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3444_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(T^{3/4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>T</mi> <mrow> <mn>3</mn> <mo stretchy="false">/</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, up to logarithmic corrections.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Radius of a Self-repelling Star Polymer

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月6日

查看全文
  • Carl Mueller,
  • Eyal Neuman

摘要

We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes N Brownian motions up to time T, started at the origin and subject to exponential penalization based on the amount of time they spend close to each other, or close to themselves. The effective radius measures the typical distance from the origin. Our main result gives estimates for the effective radius where in two and three dimensions we impose the restriction that \(T \le N\) T ≤ N . One of the highlights of our results is that in two dimensions, we find that the radius is proportional to \(T^{3/4}\) T 3 / 4 , up to logarithmic corrections.