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Abstract The absence of thermalization in certain isolated many-body systems is of great fundamental interest. Many-body localization (MBL) is a widely studied mechanism for thermalization to fail in strongly disordered quantum systems, but it is still not understood precisely how the range of interactions affects the dynamical behavior and the existence of MBL, especially in dimensionsD > 1. By investigating nonequilibrium dynamics in strongly disorderedD = 2 electron systems with power-law interactions ∝ 1/r^αand poor coupling to a thermal bath, here we observe MBL-like, prethermal dynamics forα = 3. In contrast, forα = 1, the system thermalizes, although the dynamics is glassy. Our results provide important insights for theory, especially since we obtained them on systems that are much closer to the thermodynamic limit than synthetic quantum systems employed in previous studies of MBL. Thus, our work is a key step towards further studies of ergodicity breaking and quantum entanglement in real materials. 

We present a quasi-incompressible Navier–Stokes–Cahn–Hilliard (q-NSCH) diffuse interface model for two-phase fluid flows with variable physical properties that maintains thermodynamic consistency. Then, we couple the diffuse domain method with this two-phase fluid model – yielding a new q-NSCH-DD model – to simulate the two-phase flows with moving contact lines in complex geometries. The original complex domain is extended to a larger regular domain, usually a cuboid, and the complex domain boundary is replaced by an interfacial region with finite thickness. A phase-field function is introduced to approximate the characteristic function of the original domain of interest. The original fluid model, q-NSCH, is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the solid surface. We show that the q-NSCH-DD system converges to the q-NSCH system asymptotically as the thickness of the diffuse domain interface introduced by the phase-field function shrinks to zero ( $$\epsilon \rightarrow 0$$ ) with $$\mathcal {O}(\epsilon )$$ . Our analytic results are confirmed numerically by measuring the errors in both $$L^{2}$$ and $$L^{\infty }$$ norms. In addition, we show that the q-NSCH-DD system not only allows the contact line to move on curved boundaries, but also makes the fluid–fluid interface intersect the solid object at an angle that is consistent with the prescribed contact angle. 

Abstract The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case where the upper wall is with an amount of flow injection and the lower wall with a different amount of suction. The numerical results suggest that there exist three solutions designated as type $$I$$, type $II$ and type $III$ for the asymmetric case, type $$I$$ solution exists for all non-negative Reynolds number and types $II$ and $III$ solutions appear simultaneously at a common Reynolds number that depends on the value of asymmetric parameter $$a$$ and with the increase of $$a$$ the common Reynolds numbers are decreasing. We also theoretically show that there exist three solutions. The corresponding asymptotic solution for each of the multiple solutions is constructed by the method of boundary layer correction or matched asymptotic expansion for the most difficult high Reynolds number case. These asymptotic solutions are all verified by their corresponding numerical solutions. 

Abstract Almost all commercial proteins are purified using ammonium sulfate precipitation. Protein-polymer conjugates are synthesized from pure starting materials, and the struggle to separate conjugates from polymer, native protein, and from isomers has vexed scientists for decades. We have discovered that covalent polymer attachment has a transformational effect on protein solubility in salt solutions. Here, protein-polymer conjugates with a variety of polymers, grafting densities, and polymer lengths are generated using atom transfer radical polymerization. Charged polymers increase conjugate solubility in ammonium sulfate and completely prevent precipitation even at 100% saturation. Atomistic molecular dynamic simulations show the impact is driven by an anti-polyelectrolyte effect from zwitterionic polymers. Uncharged polymers exhibit polymer length-dependent decreased solubility. The differences in salting-out are then used to simply purify mixtures of conjugates and native proteins into single species. Increasing protein solubility in salt solutions through polymer conjugation could lead to many new applications of protein-polymer conjugates.