Photomechanical coupling in photoactive nematic elastomers

Photoactive nematic elastomers are soft rubbery solids that undergo deformation when illuminated. They are made by incorporating photoactive molecules like azobenzene into nematic liquid crystal elastomers. Since its initial demonstration in 2001, it has received increasing interest with many recent studies of periodic and buckling behavior. However, theoretical models developed have focused on describing specific deformation modes (e.g., beam bending and uniaxial contraction) in the absence of mechanical loads, with only limited attention to the interplay between mechanical stress and light-induced deformation. This paper explores photomechanical coupling in a photoactive nematic elastomer under both light illumination and mechanical stress. We begin with a continuum framework built on the free energy developed by Corbett and Warner (Phys. Rev. Lett. 2006). Mechanical stress leads to nematic alignment parallel to a uniaxial tensile stress. In the absence of mechanical stress, in the photo-stationary state where the system reaches equilibrium, the nematic director tends to align perpendicular to the polarization of a linearly polarized light. However, sufficient illumination can destroy nematic order through a first-order nematic-isotropic phase transition which is accompanied by a snap through deformation. Combined illumination and mechanical stress can lead to an exchange of stability accompanied by stripe domains. Finally, the stress-intensity phase diagram shows a critical point that may be of interest for energy conversion

Almost sure well-posedness for incompressible Navier-Stokes equations with arbitrary regularity

In this paper, we study the random data problem for incompressible Navier-Stokes equations in Euclidean space. We prove that for any $s\in \mathbb{R}$, the almost sure local well-posedness holds in $H^s(\mathbb{R}^d)$ when $d\geq2$, and the almost sure global well-posedness holds in $H^s(\mathbb{R}^2)$. Our results have no regularity restriction, and thus can cover arbitrary rough data.Comment: 19 page

Finite time blow-up of non-radial solutions for some inhomogeneous Schr\"{o}dinger equations

This work studies the inhomogeneous Schr\"odinger equation $$i\partial_t u-\mathcal{K}_{s,\lambda}u +F(x,u)=0 , \quad u(t,x):\mathbb{R}\times\mathbb{R}^N\to\mathbb{C}.$$ Here, $s\in\{1,2\}$, $N>2s$ and $\lambda>-\frac{(N-2)^2}{4}$. The linear Schr\"odinger operator reads $\mathcal{K}_{s,\lambda}:= (-\Delta)^s +(2-s)\frac{\lambda}{|x|^2}$ and the focusing source term is local or non-local $$F(x,u)\in\{|x|^{-2\tau}|u|^{2(q-1)}u,|x|^{-\tau}|u|^{p-2}(J_\alpha *|\cdot|^{-\tau}|u|^p)u\}.$$ The Riesz potential is $J_\alpha(x)=C_{N,\alpha}|x|^{-(N-\alpha)}$, for certain $0<\alpha<N$. The singular decaying term $|x|^{-2\tau}$, for some $\tau>0$ gives a inhomogeneous non-linearity. One considers the inter-critical regime, namely $1+\frac{2(1-\tau)}N<q<1+\frac{2(1-\tau)}{N-2s}$ and $1+\frac{2-2\tau+\alpha}{N}<p<1+\frac{2-2\tau+\alpha}{N-2s}$. The purpose is to prove the finite time blow-up of solutions with datum in the energy space, non necessarily radial or with finite variance. The assumption on the data is expressed in terms of non-conserved quantities. This is weaker than the ground state threshold standard condition. The blow-up under the ground threshold or with negative energy are consequences. The proof is based on Morawetz estimates and a non-global ordinary differential inequality.Comment: 24 page

Application of DNA-based Nanofabrication in Nanoelectronics and Effect of Contaminations on the Surface Potential of Graphite

Reducing the critical feature size and lowering the overall fabrication cost are the keys to the future of semiconductor manufacturing. There is great interest in the development of novel electronic device manufacturing technologies compatible with high-resolution, low-cost, and large-scale fabrication. DNA-based nanofabrication technology developed in recent years is able to meet the above needs, due to its unique set of characteristics: designable patterns, nanometer-level resolution, low cost and scalability. Based on these advantages of DNA-based nanofabrication, this technology has broad prospects in the fields of electronic device manufacturing. This dissertation focuses on the application of DNA materials in the field of electronic device fabrication. Chapter 2 introduces the method of combining DNA-based nanofabrication technology with traditional doping technology. This method can realize n-type patterned doping by using DNA nanostructures as patterns and dopant carriers. Chapter 3 reports the use of DNA nanostructures as templates to deliver different dopants to achieve both n-type and p-type patterned doping, thereby expanding the usability of DNA materials for doping. Chapter 4 reports the application of DNA-based doping technology in the production of PN diodes, thus demonstrating the application of DNA nanomaterials in the production of analog electronic devices. Motivated by our interest to expand the doping study to 2D materials, Chapter 5 reports the changes in surface electrical properties of graphite materials over time in the air, allowing us to better understand the impact of air contaminations on the surface potential of graphite. I hope this dissertation can provide more insights into the application of DNA nanostructures in the production of electronic devices, and lay a steppingstone for the application of DNA nanotechnology in the field of electronic manufacturing

Photochemical-induced phase transitions in photoactive semicrystalline polymers

The emergent photoactive materials through photochemistry make it possible to directly convert photon energy to mechanical work. There is much recent work in developing appropriate materials and a promising new system is semi-crystalline polymers of the photoactive molecule azobenzene. We develop a phase field model with two order parameters for the crystal-melt transition and the trans-cis photo-isomerization to understand such materials, and the model describes the rich phenomenology. We find that the photo-reaction rate depends sensitively on temperature: at temperatures below the crystal-melt transition temperature, photoreaction is collective, requires a critical light intensity and shows an abrupt first order phase transition manifesting nucleation and growth; at temperatures above the transition temperature, photoreaction is independent and follows first order kinetics. Further, the phase transition depends significantly on the exact forms of spontaneous strain during the crystal-melt and trans-cis transitions. A non-monotonic change of photo-stationary cis ratio with increasing temperature is observed accompanied by a reentrant crystallization of trans below the melting temperature. A pseudo phase diagram is subsequently presented with varying temperature and light intensity along with the resulting actuation strain. These insights can assist the further development of these materials

Photochemical-induced phas transitions in photoactive semicrystalline polymers

The emergent photoactive materials obtained through photochemistry make it possible to directly convert photon energy to mechanical work. There has been much recent work in developing appropriate materials, and a promising system is semicrystalline polymers of the photoactive molecule azobenzene. We develop a phase field model with two order parameters for the crystal-melt transition and the trans-cis photoisomerization to understand such materials, and the model describes the rich phenomenology. We find that the photoreaction rate depends sensitively on temperature: At temperatures below the crystal-melt transition temperature, photoreaction is collective, requires a critical light intensity, and shows an abrupt first-order phase transition manifesting nucleation and growth; at temperatures above the transition temperature, photoreaction is independent and follows first-order kinetics. Further, the phase transition depends significantly on the exact forms of spontaneous strain during the crystal-melt and trans-cis transitions. A nonmonotonic change of photopersistent cis ratio with increasing temperature is observed accompanied by a reentrant crystallization of trans below the melting temperature. A pseudo phase diagram is subsequently presented with varying temperature and light intensity along with the resulting actuation strain. These insights can assist the further development of these materials

Non-radial Blow-up for a mass-critical fourth-order inhomogeneous nonlinear Schr\"odinger equation

We investigate the blow-up for fourth-order Schr\"odinger equation with a mas-critical focusing inhomogeneous nonliniearity. We prove the finite/infinite time blow-up of non-radial solutions with negative energy. Our result serves as a valuable complement to the existing literature, offering an improvement in our understanding of the subject matter

Optomechanics of Soft Materials

Some molecules change shape upon receiving photons of certain frequencies, but here we study light-induced deformation in ordinary dielectrics with no special optical effects. All dielectrics deform in response to light of all frequencies. We derive a dimensionless number to estimate when light can induce large deformation. For a structure made of soft dielectrics, with feature size comparable to the wavelength of light, the structure shapes the light, and the light deforms the structure. We study this two-way interaction between light and structure by combining the electrodynamics of light and the nonlinear mechanics of elasticity. We show that optical forces vary nonlinearly with deformation and readily cause optomechanical snap-through instability. These theoretical ideas may help to create optomechanical devices of soft materials, complex shapes, and small features.Engineering and Applied Science