Search for: All records

Field-theoretic simulations that rely on a partial saddle-point approximation have become powerful tools for studying complex polymer materials. The computational cost of such simulations depends critically upon the efficiency of the iterative algorithm used to identify a partial saddle-point field configuration during each step of a stochastic simulation. We introduce a new algorithm for this purpose that relies on a physically motivated approximation in which the linear response of the density to a small change in a pressure-like field is approximated by the response of a hypothetical homogeneous system. The computational cost of the resulting algorithm is significantly less than that of the commonly used Anderson mixing algorithm. 

We present a symmetric formulation of polymer field theory for incompressible systems containing any number M of monomer types, in which all monomers are treated on an equal footing. This is proposed as an alternative to the multispecies exchange formulation, which imposes incompressibility by eliminating one monomer type. The symmetric formulation is shown to correspond to the incompressible limit of a corresponding compressible model, and to reduce in the case M = 2 to the usual formulation of field theory for incompressible AB systems. An analysis of ABC systems (M = 3) identifies ranges of interaction parameter values in which a fully fluctuating field theory requires one, two or three imaginary-valued fields. ABC systems with parameters that satisfy the Hildebrand solubility parameter approximation are shown to require only one imaginary pressure-like field, much like AB systems. Generalization of the partial saddle-point approximation to M > 2 is discussed. 

The behavior of complex-Langevin field-theoretic simulations (CL-FTSs) of polymer liquids is sensitive to the nature of saddle-point field configurations, which are solutions of self-consistent field theory (SCFT). Recent work [Kang et al. Macromolecules 2024, 57, 3850] has shown that SCFT saddle-points with real fields are generally not isolated solutions but rather members of a low-dimensional family of continuously-connected complex-valued saddle-points sharing the same Hamiltonian value. We show that this behavior is a natural consequence of the analyticity and translational invariance of the Hamiltonian, which together demand its invariance under generalized translations by displacements with complex components. We also present a numerical algorithm that minimizes the deleterious effects of this generalized symmetry on the stability of CL-FTSs. 

Single-cell RNA sequencing (scRNA-seq) is a powerful technique for describing cell states. Identifying the spatial arrangement of these states in tissues remains challenging, with the existing methods requiring niche methodologies and expertise. Here, we describe segmentation by exogenous perfusion (SEEP), a rapid and integrated method to link surface proximity and environment accessibility to transcriptional identity within three-dimensional (3D) disease models. The method utilizes the steady-state diffusion kinetics of a fluores- cent dye to establish a gradient along the radial axis of disease models. Classification of sample layers based on dye accessibility enables dissociated and sorted cells to be characterized by transcriptomic and regional identities. Using SEEP, we analyze spheroid, organoid, and in vivo tumor models of high-grade serous ovarian cancer (HGSOC). The results validate long-standing beliefs about the relationship between cell state and position while revealing new concepts regarding how spatially unique microenvironments influence the identity of individual cells within tumors.