@article{62861,
  author       = {{Laneve, Alessandro and Ronco, Giuseppe and Beccaceci, Mattia and Barigelli, Paolo and Salusti, Francesco and Claro-Rodriguez, Nicolas and De Pascalis, Giorgio and Suprano, Alessia and Chiaudano, Leone and Schöll, Eva and Hanschke, Lukas and Krieger, Tobias M. and Buchinger, Quirin and Covre da Silva, Saimon F. and Neuwirth, Julia and Stroj, Sandra and Höfling, Sven and Huber-Loyola, Tobias and Usuga Castaneda, Mario A. and Carvacho, Gonzalo and Spagnolo, Nicolò and Rota, Michele B. and Basso Basset, Francesco and Rastelli, Armando and Sciarrino, Fabio and Jöns, Klaus and Trotta, Rinaldo}},
  issn         = {{2041-1723}},
  journal      = {{Nature Communications}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Quantum teleportation with dissimilar quantum dots over a hybrid quantum network}}},
  doi          = {{10.1038/s41467-025-65911-9}},
  volume       = {{16}},
  year         = {{2025}},
}

@inproceedings{63193,
  abstract     = {{The integration of data-driven models and specifically machine learning for conditon monitoring and predictive maintenance into companies, especially small and medium-sized enterprises, offers significant opportunities in reducing costs, operating more sustainably, and maintaining long-term competitiveness. However, many small and medium-sized enterprises lack the necessary resources and expertise to derive knowledge from data and integrate their own machine learning based solutions. To address this challenge, a framework is presented that enables the automated generation of data-driven models with a particular focus on condition monitoring and predictive maintenance, but applicable to other use cases as well. Using a dataset from the 2022 data challenge of the prognostics and health management society, it is demonstrated that the framework can generate high-performing models, achieving F1-scores up to 0.998, exemplarily for a classification task.}},
  author       = {{Löwen, Alexander and Quirin, Dennis and Hesse, Marc and Aimiyekagbon, Osarenren Kennedy and Sextro, Walter}},
  booktitle    = {{2025 IEEE 30th International Conference on Emerging Technologies and Factory Automation (ETFA)}},
  location     = {{Porto}},
  publisher    = {{IEEE}},
  title        = {{{Facilitating the Automated Generation of Data-Driven Models for the Diagnostics and Prognostics of Technical Systems}}},
  doi          = {{10.1109/etfa65518.2025.11205799}},
  year         = {{2025}},
}

@article{63344,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>A Neumann-type initial-boundary value problem for <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \left\{ \begin{array}{l} u_{tt} = \nabla \cdot (\gamma (\Theta ) \nabla u_t) + a \nabla \cdot (\gamma (\Theta ) \nabla u) + \nabla \cdot f(\Theta ), \\ \Theta _t = D\Delta \Theta + \Gamma (\Theta ) |\nabla u_t|^2 + F(\Theta )\cdot \nabla u_t, \end{array} \right. \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mfenced>
                            <mml:mrow>
                              <mml:mtable>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:msub>
                                        <mml:mi>u</mml:mi>
                                        <mml:mrow>
                                          <mml:mi>tt</mml:mi>
                                        </mml:mrow>
                                      </mml:msub>
                                      <mml:mo>=</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>γ</mml:mi>
                                        <mml:mrow>
                                          <mml:mo>(</mml:mo>
                                          <mml:mi>Θ</mml:mi>
                                          <mml:mo>)</mml:mo>
                                        </mml:mrow>
                                        <mml:mi>∇</mml:mi>
                                        <mml:msub>
                                          <mml:mi>u</mml:mi>
                                          <mml:mi>t</mml:mi>
                                        </mml:msub>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>a</mml:mi>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>γ</mml:mi>
                                        <mml:mrow>
                                          <mml:mo>(</mml:mo>
                                          <mml:mi>Θ</mml:mi>
                                          <mml:mo>)</mml:mo>
                                        </mml:mrow>
                                        <mml:mi>∇</mml:mi>
                                        <mml:mi>u</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>f</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>Θ</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mrow/>
                                      <mml:msub>
                                        <mml:mi>Θ</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>=</mml:mo>
                                      <mml:mi>D</mml:mi>
                                      <mml:mi>Δ</mml:mi>
                                      <mml:mi>Θ</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>Γ</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>Θ</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:msup>
                                        <mml:mrow>
                                          <mml:mo>|</mml:mo>
                                          <mml:mi>∇</mml:mi>
                                          <mml:msub>
                                            <mml:mi>u</mml:mi>
                                            <mml:mi>t</mml:mi>
                                          </mml:msub>
                                          <mml:mo>|</mml:mo>
                                        </mml:mrow>
                                        <mml:mn>2</mml:mn>
                                      </mml:msup>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>F</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>Θ</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:msub>
                                        <mml:mi>u</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                              </mml:mtable>
                            </mml:mrow>
                          </mml:mfenced>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>is considered in a smoothly bounded domain <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\Omega \subset \mathbb {R}^n$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>Ω</mml:mi>
                    <mml:mo>⊂</mml:mo>
                    <mml:msup>
                      <mml:mrow>
                        <mml:mi>R</mml:mi>
                      </mml:mrow>
                      <mml:mi>n</mml:mi>
                    </mml:msup>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$n\ge 1$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>n</mml:mi>
                    <mml:mo>≥</mml:mo>
                    <mml:mn>1</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>. In the case when <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$n=1$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>n</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mn>1</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\gamma \equiv \Gamma $$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>γ</mml:mi>
                    <mml:mo>≡</mml:mo>
                    <mml:mi>Γ</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$f\equiv F$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>f</mml:mi>
                    <mml:mo>≡</mml:mo>
                    <mml:mi>F</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, this system coincides with the standard model for heat generation in a viscoelastic material of Kelvin-Voigt type, well-understood in situations in which <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\gamma =const$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>γ</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mi>c</mml:mi>
                    <mml:mi>o</mml:mi>
                    <mml:mi>n</mml:mi>
                    <mml:mi>s</mml:mi>
                    <mml:mi>t</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>. Covering scenarios in which all key ingredients <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\gamma ,\Gamma ,f$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>γ</mml:mi>
                    <mml:mo>,</mml:mo>
                    <mml:mi>Γ</mml:mi>
                    <mml:mo>,</mml:mo>
                    <mml:mi>f</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:italic>F</jats:italic> may depend on the temperature <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\Theta $$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>Θ</mml:mi>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> here, for initial data which merely satisfy <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$u_0\in W^{1,p+2}(\Omega )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>W</mml:mi>
                      <mml:mrow>
                        <mml:mn>1</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>p</mml:mi>
                        <mml:mo>+</mml:mo>
                        <mml:mn>2</mml:mn>
                      </mml:mrow>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>Ω</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$u_{0t}\in W^{1,p}(\Omega )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mrow>
                        <mml:mn>0</mml:mn>
                        <mml:mi>t</mml:mi>
                      </mml:mrow>
                    </mml:msub>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>W</mml:mi>
                      <mml:mrow>
                        <mml:mn>1</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>p</mml:mi>
                      </mml:mrow>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>Ω</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\Theta _0\in W^{1,p}(\Omega )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>Θ</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>W</mml:mi>
                      <mml:mrow>
                        <mml:mn>1</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>p</mml:mi>
                      </mml:mrow>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>Ω</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> with some <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p\ge 2$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>≥</mml:mo>
                    <mml:mn>2</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> such that <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p&gt;n$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>&gt;</mml:mo>
                    <mml:mi>n</mml:mi>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, a result on local-in-time existence and uniqueness is derived in a natural framework of weak solvability.</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{0095-4616}},
  journal      = {{Applied Mathematics &amp; Optimization}},
  number       = {{2}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}}},
  doi          = {{10.1007/s00245-025-10243-9}},
  volume       = {{91}},
  year         = {{2025}},
}

@article{63242,
  abstract     = {{<jats:title>Abstract</jats:title>
                  <jats:p>
                    For
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$p&gt;2$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>p</mml:mi>
                            <mml:mo>&gt;</mml:mo>
                            <mml:mn>2</mml:mn>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    , the equation
                    <jats:disp-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$\begin{aligned} u_t = u^p u_{xx}, \qquad x\in \mathbb {R}, \ t\in \mathbb {R}, \end{aligned}$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mtable>
                              <mml:mtr>
                                <mml:mtd>
                                  <mml:mrow>
                                    <mml:msub>
                                      <mml:mi>u</mml:mi>
                                      <mml:mi>t</mml:mi>
                                    </mml:msub>
                                    <mml:mo>=</mml:mo>
                                    <mml:msup>
                                      <mml:mi>u</mml:mi>
                                      <mml:mi>p</mml:mi>
                                    </mml:msup>
                                    <mml:msub>
                                      <mml:mi>u</mml:mi>
                                      <mml:mrow>
                                        <mml:mi>xx</mml:mi>
                                      </mml:mrow>
                                    </mml:msub>
                                    <mml:mo>,</mml:mo>
                                    <mml:mspace/>
                                    <mml:mi>x</mml:mi>
                                    <mml:mo>∈</mml:mo>
                                    <mml:mi>R</mml:mi>
                                    <mml:mo>,</mml:mo>
                                    <mml:mspace/>
                                    <mml:mi>t</mml:mi>
                                    <mml:mo>∈</mml:mo>
                                    <mml:mi>R</mml:mi>
                                    <mml:mo>,</mml:mo>
                                  </mml:mrow>
                                </mml:mtd>
                              </mml:mtr>
                            </mml:mtable>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:disp-formula>
                    is shown to admit positive and spatially increasing smooth solutions on all of
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$\mathbb {R}\times \mathbb {R}$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>R</mml:mi>
                            <mml:mo>×</mml:mo>
                            <mml:mi>R</mml:mi>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    which are precisely of the form of an accelerating wave for
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$t&lt;0$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>t</mml:mi>
                            <mml:mo>&lt;</mml:mo>
                            <mml:mn>0</mml:mn>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    , and of a wave slowing down for
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$t&gt;0$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>t</mml:mi>
                            <mml:mo>&gt;</mml:mo>
                            <mml:mn>0</mml:mn>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    . These solutions satisfy
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$u(\cdot ,t)\rightarrow 0$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>u</mml:mi>
                            <mml:mo>(</mml:mo>
                            <mml:mo>·</mml:mo>
                            <mml:mo>,</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                            <mml:mo>→</mml:mo>
                            <mml:mn>0</mml:mn>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    in
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$L^\infty _{loc}(\mathbb {R})$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:msubsup>
                              <mml:mi>L</mml:mi>
                              <mml:mrow>
                                <mml:mi>loc</mml:mi>
                              </mml:mrow>
                              <mml:mi>∞</mml:mi>
                            </mml:msubsup>
                            <mml:mrow>
                              <mml:mo>(</mml:mo>
                              <mml:mi>R</mml:mi>
                              <mml:mo>)</mml:mo>
                            </mml:mrow>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    as
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$t\rightarrow + \infty $$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>t</mml:mi>
                            <mml:mo>→</mml:mo>
                            <mml:mo>+</mml:mo>
                            <mml:mi>∞</mml:mi>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    and as
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$t\rightarrow -\infty $$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>t</mml:mi>
                            <mml:mo>→</mml:mo>
                            <mml:mo>-</mml:mo>
                            <mml:mi>∞</mml:mi>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    , and exhibit a yet apparently undiscovered phenomenon of transient rapid spatial growth, in the sense that
                    <jats:disp-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$\begin{aligned} \lim _{x\rightarrow +\infty } x^{-1} u(x,t) \quad \text{ exists } \text{ for } \text{ all } t&lt;0, \end{aligned}$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mtable>
                              <mml:mtr>
                                <mml:mtd>
                                  <mml:mrow>
                                    <mml:munder>
                                      <mml:mo>lim</mml:mo>
                                      <mml:mrow>
                                        <mml:mi>x</mml:mi>
                                        <mml:mo>→</mml:mo>
                                        <mml:mo>+</mml:mo>
                                        <mml:mi>∞</mml:mi>
                                      </mml:mrow>
                                    </mml:munder>
                                    <mml:msup>
                                      <mml:mi>x</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>-</mml:mo>
                                        <mml:mn>1</mml:mn>
                                      </mml:mrow>
                                    </mml:msup>
                                    <mml:mi>u</mml:mi>
                                    <mml:mrow>
                                      <mml:mo>(</mml:mo>
                                      <mml:mi>x</mml:mi>
                                      <mml:mo>,</mml:mo>
                                      <mml:mi>t</mml:mi>
                                      <mml:mo>)</mml:mo>
                                    </mml:mrow>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>exists</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>for</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>all</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mi>t</mml:mi>
                                    <mml:mo>&lt;</mml:mo>
                                    <mml:mn>0</mml:mn>
                                    <mml:mo>,</mml:mo>
                                  </mml:mrow>
                                </mml:mtd>
                              </mml:mtr>
                            </mml:mtable>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:disp-formula>
                    that
                    <jats:disp-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$\begin{aligned} \lim _{x\rightarrow +\infty } x^{-\frac{2}{p}} u(x,t) \quad \text{ exists } \text{ for } \text{ all } t&gt;0, \end{aligned}$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mtable>
                              <mml:mtr>
                                <mml:mtd>
                                  <mml:mrow>
                                    <mml:munder>
                                      <mml:mo>lim</mml:mo>
                                      <mml:mrow>
                                        <mml:mi>x</mml:mi>
                                        <mml:mo>→</mml:mo>
                                        <mml:mo>+</mml:mo>
                                        <mml:mi>∞</mml:mi>
                                      </mml:mrow>
                                    </mml:munder>
                                    <mml:msup>
                                      <mml:mi>x</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>-</mml:mo>
                                        <mml:mfrac>
                                          <mml:mn>2</mml:mn>
                                          <mml:mi>p</mml:mi>
                                        </mml:mfrac>
                                      </mml:mrow>
                                    </mml:msup>
                                    <mml:mi>u</mml:mi>
                                    <mml:mrow>
                                      <mml:mo>(</mml:mo>
                                      <mml:mi>x</mml:mi>
                                      <mml:mo>,</mml:mo>
                                      <mml:mi>t</mml:mi>
                                      <mml:mo>)</mml:mo>
                                    </mml:mrow>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>exists</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>for</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>all</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mi>t</mml:mi>
                                    <mml:mo>&gt;</mml:mo>
                                    <mml:mn>0</mml:mn>
                                    <mml:mo>,</mml:mo>
                                  </mml:mrow>
                                </mml:mtd>
                              </mml:mtr>
                            </mml:mtable>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:disp-formula>
                    but that
                    <jats:disp-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$\begin{aligned} u(x,0)=K e^{\alpha x} \qquad \text{ for } \text{ all } x\in \mathbb {R}\end{aligned}$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mtable>
                              <mml:mtr>
                                <mml:mtd>
                                  <mml:mrow>
                                    <mml:mi>u</mml:mi>
                                    <mml:mrow>
                                      <mml:mo>(</mml:mo>
                                      <mml:mi>x</mml:mi>
                                      <mml:mo>,</mml:mo>
                                      <mml:mn>0</mml:mn>
                                      <mml:mo>)</mml:mo>
                                    </mml:mrow>
                                    <mml:mo>=</mml:mo>
                                    <mml:mi>K</mml:mi>
                                    <mml:msup>
                                      <mml:mi>e</mml:mi>
                                      <mml:mrow>
                                        <mml:mi>α</mml:mi>
                                        <mml:mi>x</mml:mi>
                                      </mml:mrow>
                                    </mml:msup>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>for</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mspace/>
                                    <mml:mtext>all</mml:mtext>
                                    <mml:mspace/>
                                    <mml:mi>x</mml:mi>
                                    <mml:mo>∈</mml:mo>
                                    <mml:mi>R</mml:mi>
                                  </mml:mrow>
                                </mml:mtd>
                              </mml:mtr>
                            </mml:mtable>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:disp-formula>
                    with some
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$K&gt;0$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>K</mml:mi>
                            <mml:mo>&gt;</mml:mo>
                            <mml:mn>0</mml:mn>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    and
                    <jats:inline-formula>
                      <jats:alternatives>
                        <jats:tex-math>$$\alpha &gt;0$$</jats:tex-math>
                        <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                          <mml:mrow>
                            <mml:mi>α</mml:mi>
                            <mml:mo>&gt;</mml:mo>
                            <mml:mn>0</mml:mn>
                          </mml:mrow>
                        </mml:math>
                      </jats:alternatives>
                    </jats:inline-formula>
                    .
                  </jats:p>}},
  author       = {{Hanfland, Celina and Winkler, Michael}},
  issn         = {{2296-9020}},
  journal      = {{Journal of Elliptic and Parabolic Equations}},
  number       = {{3}},
  pages        = {{2041--2063}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Exactly wave-type homoclinic orbits and emergence of transient exponential growth in a super-fast diffusion equation}}},
  doi          = {{10.1007/s41808-025-00316-9}},
  volume       = {{11}},
  year         = {{2025}},
}

@article{63347,
  abstract     = {{<jats:p>Friction-spinning is an incremental thermomechanical forming process that has huge potential due to its simple yet effective mechanism of utilising friction between a rotating workpiece and a forming tool to increase the workpiece’s temperature, which reduces the required forces and increases formability during the forming process. Despite the simplicity of the process’s setup, the thermomechanical loads and high relative velocities involved, especially in the contact zone, make the application of classical methods for characterising friction inaccurate. It is therefore essential to find a way to describe the frictional behaviour under real process conditions to be able to gain a holistic understanding of the process and the effect of the adjustable parameters on the outcome, especially the temperature. To achieve this goal, an experimental setup that considers the actual process boundary conditions in forming tubes made of EN AW-6060 was used to measure in situ normal and frictional forces, in addition to process temperatures, under varying rotational speed and feed rate values.</jats:p>}},
  author       = {{Wiens, Eugen and Hijazi, Dina and Jüttner, Maik and Homberg, Werner and Kensy, Mark Dennis and Tillmann, Wolfgang}},
  issn         = {{2504-4494}},
  journal      = {{Journal of Manufacturing and Materials Processing}},
  number       = {{9}},
  publisher    = {{MDPI AG}},
  title        = {{{In Situ Investigation of the Frictional Behaviour in Friction-Spinning}}},
  doi          = {{10.3390/jmmp9090302}},
  volume       = {{9}},
  year         = {{2025}},
}

@inproceedings{59091,
  abstract     = {{<jats:p>Abstract. Liquid Metal Embrittlement (LME) cracking is a well-documented issue encountered during resistance spot welding (RSW) of zinc-coated advanced high-strength steels (AHSS) in automotive manufacturing. Given that existing research has predominantly focused on laboratory-scale samples and lacks investigation into the load-bearing capacity of joints under crash conditions, this study aims to fill these gaps by analyzing third-generation zinc-coated AHSS. S-Rail components were produced through stamping to replicate real-world manufacturing conditions and geometries of automotive parts. To account for the disturbances typically encountered in production, samples with LME cracks were intentionally fabricated. Subsequently, a modified three-point bending test, assisted by numerical simulations, was developed to effectively apply loads to the weld spots of the S-Rail components. Results from crash tests demonstrated that observed light crack severity does not significantly compromise the joint's load-bearing capacity or lead to earlier joint failure.</jats:p>}},
  author       = {{Yang, Keke and Biegler, Max and Happe, Linus and Striewe, Marius and Olfert, Viktoria and Hein, David and Rethmeier, Michael  and Meschut, Gerson}},
  booktitle    = {{Materials Research Proceedings}},
  issn         = {{2474-395X}},
  publisher    = {{Materials Research Forum LLC}},
  title        = {{{Influence of Liquid metal embrittlement on load-bearing capacity of resistance spot welds under crash loads: A study based on S-Rail components}}},
  doi          = {{10.21741/9781644903551-42}},
  volume       = {{52}},
  year         = {{2025}},
}

@inproceedings{60604,
  abstract     = {{<jats:p>Abstract. In the field of online condition monitoring, non-destructive testing methods using active acoustic testing [1] emerged as innovative tools. These techniques are particularly effective because damage in joined structures leads to significant changes in their vibrational characteristics. However, the consistent use of online condition monitoring through active acoustic testing combined with complex pattern recognition for early crack detection in joined components has not yet been fully established. This research aims to develop an online crack detection system employing pattern recognition techniques under cyclic loading during fatigue tests, utilizing non-contact active acoustic testing with laser vibrometry. Due to the wide range of materials that can be joined, mechanical joining processes can be used in many different industry branches. Self-pierce riveting (SPR), in particular, is a well-established joining process. Therefore, the investigations for online crack detection initially focus on SPR joints. To achieve this, the fatigue behavior of SPR joints in a lap-shear configuration was characterized. Experimental fatigue testing demonstrated that SPR joint failure occurs either through cracks propagating in the sheet material away from the rivet or in the rivet foot, depending on the material combination. Laser vibrometry has been successfully used as a crack detection system and has proven to be effective in detecting crack initiation in SPR joints. Cracks can be detected without contact regardless of the material combination, the damage location, the size of the damage, or the type of damage.  The optimization of the crack detection system involved several key enhancements, including adjusting data acquisition to improve crack detection, incorporating principal component analysis (PCA) to reduce dimensionality, and implementing a classification model based on a global training dataset. An intuitive, problem-specific software demonstrator for analyzing the crack initiation behavior of SPR joints under cyclic loading was developed and iteratively optimized. Future work will focus on the implementation of an autoencoder network to further enhance crack detection capabilities.</jats:p>}},
  author       = {{Olfert, Viktoria and Yang, Keke and Gollnick, Maik and Krause, Jacob and Hein, David and Meschut, Gerson}},
  booktitle    = {{Materials Research Proceedings}},
  issn         = {{2474-395X}},
  publisher    = {{Materials Research Forum LLC}},
  title        = {{{Analysis of fatigue behaviour of self-piercing riveted joints under cyclic loading using laser vibrometry}}},
  doi          = {{10.21741/9781644903599-154}},
  volume       = {{54}},
  year         = {{2025}},
}

@inproceedings{62299,
  author       = {{Friesen, Olga and Scheidemann, Claus and Claes, Leander and Hemsel, Tobias and Henning, Bernd}},
  booktitle    = {{2025 International Congress on Ultrasonics}},
  pages        = {{138–141}},
  publisher    = {{AMA Service GmbH}},
  title        = {{{Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer}}},
  doi          = {{10.5162/ultrasonic2025/a18-a4}},
  year         = {{2025}},
}

@inbook{63461,
  author       = {{Bartmann, Finn and Riedl, Alexander and Moritzer, Elmar}},
  booktitle    = {{Lecture Notes in Mechanical Engineering}},
  isbn         = {{9783032073914}},
  issn         = {{2195-4356}},
  publisher    = {{Springer Nature Switzerland}},
  title        = {{{Creep Effects of Thermoplastic Flange Systems}}},
  doi          = {{10.1007/978-3-032-07392-1_39}},
  year         = {{2025}},
}

@article{63444,
  author       = {{Moritzer, Elmar and Rauen, Dennis and Hoppe, Justin}},
  journal      = {{Magazin für Oberflächentechnik}},
  keywords     = {{Plasma, Plasmaaktivierung, Werkzeugstahl}},
  number       = {{10}},
  title        = {{{Atmosphärendruckplasma: Grenzflächenmodifikation von Werkzeugstahl: Plasma trifft Stahl: Möglichkeiten zur Modifikation und Verbesserung von Oberflächeneigenschaften}}},
  volume       = {{2025}},
  year         = {{2025}},
}

@inproceedings{63442,
  author       = {{Moritzer, Elmar and Brandes, Philipp and Wittler, Maurice and Westphal, Max Siegfried}},
  booktitle    = {{Annual Technical Conference of the Society of Plastics Engineers (ANTEC 2025)}},
  keywords     = {{Faser-Kunststoff-Verbunde (FKV), Faserverstärkte Kunststoffe (FVK), Organobleche}},
  title        = {{{A COMPARISON OF USING FILM INSTEAD OF POLYMER POWDER FOR POLYPROPYLENE GLASS-FIBER COMPOSITE LAMINATES}}},
  year         = {{2025}},
}

@inproceedings{63457,
  author       = {{Moritzer, Elmar and Völklein, Paul Leonhard}},
  booktitle    = {{Technomer 2025 29. Fachtagung}},
  isbn         = {{978-3-939382-17-1}},
  keywords     = {{Faserverstärkte Kunststoffe (FVK), mechanischens Fügen, Nieten, Organobleche}},
  title        = {{{Untersuchung des Erwärmverhaltens von Organoblechen mittels IR-Strahlung für das Fügen im Stempelnietverfahren}}},
  year         = {{2025}},
}

@article{63455,
  author       = {{Arndt, Theresa and Schöppner, Volker}},
  journal      = {{Joining Plastics}},
  keywords     = {{Schweißen, Ultraschall, weld seam quality}},
  number       = {{3-4}},
  pages        = {{166–174}},
  title        = {{{Ambossfreies Ultraschallschweißen für nur einseitig zugängliche Schweißsituationen}}},
  volume       = {{19}},
  year         = {{2025}},
}

@article{63456,
  abstract     = {{Externer Doktorand von Moritzer}},
  author       = {{Moritzer, Elmar and Bartmann, Finn and Riedl, Alexander}},
  journal      = {{1. XXIV Dichtungskolloquium (Essen Juni 2025)}},
  title        = {{{Berücksichtigung des Kriechverhaltens bei numerischen Simulationen von Thermoplastflanschverbindungen}}},
  year         = {{2025}},
}

@inproceedings{63443,
  author       = {{Moritzer, Elmar and Lingnau, Kai}},
  booktitle    = {{Annual Technical Conference of the Society of Plastics Engineers (ANTEC 2025)}},
  keywords     = {{Lackierung, Pulverlack, Spritzgießen}},
  title        = {{{PROCESS DEVELOPMENT OF A POWDER-BASED DIRECT COATING IN THE INJECTION MOLDING PROCESS}}},
  year         = {{2025}},
}

@article{58116,
  author       = {{Mohammadian, Noushin and Fatahi Valilai, Omid and Schlüter, Alexander}},
  issn         = {{2199-8531}},
  journal      = {{Journal of Open Innovation: Technology, Market, and Complexity}},
  number       = {{1}},
  publisher    = {{Elsevier BV}},
  title        = {{{Sustainable design and repair: Leveraging circular economy and machine learning for product development}}},
  doi          = {{10.1016/j.joitmc.2025.100469}},
  volume       = {{11}},
  year         = {{2025}},
}

@inproceedings{63019,
  author       = {{Donner, Johannes Aurelius Tamino and Schlüter, Alexander}},
  booktitle    = {{SDEWES Conference 2025}},
  keywords     = {{5GDHC, district heating, DHC, waste heat, AI-Driven}},
  location     = {{Dubrovnik}},
  title        = {{{Development of an AI-driven decentralized control for fifth generation district heating and cooling networks}}},
  year         = {{2025}},
}

@article{59056,
  author       = {{Seeger, Karl and Genovese, Matteo and Schlüter, Alexander and Kockel, Christina and Corigliano, Orlando and Díaz Canales, Edith Benjamina and Praktiknjo, Aaron and Fragiacomo, Petronilla}},
  issn         = {{0360-3199}},
  journal      = {{International Journal of Hydrogen Energy}},
  pages        = {{558--576}},
  publisher    = {{Elsevier BV}},
  title        = {{{Techno-economic analysis of hydrogen and green fuels supply scenarios assessing three import routes: Canada, Chile, and Algeria to Germany}}},
  doi          = {{10.1016/j.ijhydene.2025.02.379}},
  volume       = {{116}},
  year         = {{2025}},
}

@article{60837,
  abstract     = {{In light of growing demands for resource efficiency and sustainability in vehicle engineering, the environmentally compatible separation of structural adhesive joints is gaining increasing relevance. This study presents a comparative analysis of two physically based debonding methods: the established hot-air process and a cryogenic cold process based on liquid nitrogen (LN2). The primary objective is to assess the ecological impact and process-related sustainability of both approaches.
Experimental investigations were conducted on a component-representative triple-sheet structure that simulates common automotive flange joints. Thermal input was applied either by convective heating using a hot air gun or by direct cooling through a contact-based LN2 tool. The resulting temperature profiles were recorded using spatially distributed thermocouples. Subsequently, the outer panel was selectively debonded to replicate a repair scenario, and the mechanical integrity of the remaining adhesive joint was evaluated through Mode I testing of L-shaped specimens. Process data served as input for an Life Cycle Assessment (LCA) according to DIN EN ISO 14040.
The cryogenic method achieved a 40% reduction in carbon footprint compared to the hot-air process (0.337 kg vs. 0.559 kg CO2-equivalents), primarily due to its shorter process time and more efficient heat transfer. While the hot-air method’s impact is mainly driven by electrical energy use, that of the cold method stems from cryogenic media consumption. Notwithstanding certain disadvantages in specific impact categories, the LN2-based process exhibits a superior overall ecological performance and signifies a promising solution for repair- and recycling-oriented adhesive separation in structural vehicle applications.}},
  author       = {{Jordan, Alex and Hermelingmeier, Lucas and Gilich, Julian and Meschut, Gerson and De Santis, Marco Sebastian and Schlüter, Alexander}},
  issn         = {{2666-3309}},
  journal      = {{Journal of Advanced Joining Processes}},
  keywords     = {{Sustainable debonding, Structural adhesives, Sustainable joining technologies, Life Cycle Assessment (LCA), Automotive repair process, Economically efficient debonding}},
  publisher    = {{Elsevier}},
  title        = {{{Comparison of the economic efficiency and sustainability of two debonding processes for structurally bonded sills}}},
  doi          = {{10.1016/j.jajp.2025.100332}},
  volume       = {{12}},
  year         = {{2025}},
}

@techreport{63209,
  abstract     = {{Die DFG-Projekte AddFeRo-PM (406108415) und AddFeRo-SR (465089065) untersuchten die Potenziale des LB-PBF/M-Verfahrens zur Herstellung von Rotoren für unterschiedliche elektrische Maschinen. Im interdisziplinären Ansatz wurden Materialentwicklung und mechanische sowie elektromagnetische Optimierung verbunden. Im Projekt „AddFeRo-PM“ wurde der Rotor einer permanentmagneterregten Synchron- maschine (PMSM) untersucht. FeSi erwies sich als geeignete Legierung, konnte aber wegen Spannungsrissen nur bis zu 3 % Siliziumanteil (kurz: FeSi3) verarbeitet werden. Mechanische und elektromagnetische Untersuchungen ermöglichten eine 3D-Optimierung der Rotorgeometrie und -struktur. Der Demonstrator wurde additiv gefertigt und zeigt Leicht-baupotenziale sowie reduzierte Drehmomentwelligkeit. Im Folgeprojekt „AddFeRo-SR“ kam eine Hochtemperatur-Bauraumheizung (HTBH) zum Einsatz, die FeSi mit 6,5 % Siliziumanteil verarbeitbar machte, welches bessere elektro- magnetische Eigenschaften bietet. Sie wurde bei einer Synchron-Reluktanzmaschine (SynRM) getestet. Eine hybride Rotorfertigung erwies sich jedoch aufgrund von HTBH-Einschränkungen als ungeeignet, weshalb eine einteilige Fertigung mit FeSi3 umgesetzt wurde. Experimente bestätigten vergleichbare Betriebsergebnisse zur konventionellen Fertigung bei reduzierter Rotormasse. Zusätzlich wurde eine Methodik entwickelt, um additive Verfahren als Ergänzung zur konventionellen Fertigung zu integrieren. Beide Projekte zeigen das Potenzial additiver Fertigung für Leichtbau und Wirkungsgradsteigerung im Elektromaschinenbau und bieten wertvolle Grundlagen für industrielle Anwendungen.}},
  author       = {{Haase, Michael and Behrendt, Marius and Hengsbach, Florian and Kunnathully Sathees Kumar, Vinay and Magerkohl, Sebastian and Magyar, Balázs and Ponick, Bernd and Schaper, Mirko and Zimmer, Detmar}},
  keywords     = {{Additive Fertigung, Elektromotor, Leichtbau, Synchronmotor, DFG}},
  publisher    = {{Technische Informationsbibliothek}},
  title        = {{{Additive Fertigung im Elektromaschinenbau: Erforschung von Potentialen der additiven Fertigung in Rotoren permanentmagneterregter Synchronmaschinen}}},
  doi          = {{10.34657/26753}},
  year         = {{2025}},
}

