A Topology Optimization Based Design of Space Radiator for Focal Plane Assemblies

In this paper, to improve the heat dissipation efficiency of a radiator for focal plane assemblies, a topology optimization method is introduced into the design process. For the realization of the optimization, an objective of maximal thermal stiffness concerning the radiator is formulated. The topology optimization is performed under the same mass constraint of 2.05 kg as the initial design. To improve the manufacturability of topology optimization result, an inverse design is conducted to reconstruct a new model. In transient thermal simulation, the average maximal temperature on focal plane assemblies with a reconstructed radiator is 8.626 °C, while the average maximal temperature with the initial design is 9.793 °C. Compared to the initial design, a decrease of 1.167 °C on maximal temperature is achieved. As the heat dissipation efficiency of the proposed radiator design is improved compared to the initial design, it is meaningful in future applications.

Evolutionary Discrete Multi-Material Topology Optimization Using CNN-Based Simulation Without Labeled Training Data

Multi-material topology optimization problem under total mass constraint is a challenging problem owning to the incompressibility constraint on the summation of the usage of the total materials. A novel optimization approach is proposed here that utilizes the wide search space of the genetic algorithm, and greatly reduced computational effects achieved from the direct structure-performance mapping. The former optimization is carefully designed based on our recent theoretical insights, while the latter simulation is derived via a novel convolutional neural network based simulation which does not rely on any labeled simulation data but is instead designed based on a physics-informed loss function. As compared with results obtained using latest approach based on density interpolation, structures of better compliances are observed under acceptable computational costs, as demonstrated by our numerical examples.

A Constrained Data Assimilation Algorithm Based on GSI Hybrid 3D-EnVar and Its Application

Data assimilation (DA) at mesoscales is important for severe weather forecasts, yet the techniques of data assimilation at this scale remain a challenge. This study introduces dynamical constraints in the Gridpoint Statistical Interpolation (GSI) three-dimensional ensemble variational (3D-EnVar) data assimilation algorithm to enable the use of high-resolution surface observations of precipitation to improve atmospheric analysis at mesoscales. The constraints use the conservations of mass and moisture. Mass constraint suppresses the unphysical high-frequency oscillation, while moisture conservation constrains the atmospheric states to conform with the observed high-resolution precipitation. We show that the constrained data assimilation (CDA) algorithm significantly reduced the spurious residuals of the mass and moisture budgets compared to the original data assimilation (ODA). A case study is presented for a squall line over the Southern Great Plains on 20 May 2011 during Midlatitude Continental Convective Clouds Experiment (MC3E) of the Atmospheric Radiation Measurement (ARM) program by using ODA or CDA analysis as initial condition of forecasts. The state variables, and the location and intensity of the squall line are better simulated in the CDA experiment. Results show how surface observation of precipitation can be used to improve atmospheric analysis through data assimilation by using the dynamical constraints of mass and moisture conservations.

STABILITYANALYSIS OF SCHWARZSCHILD-DAMOUR-SOLODUKHIN WORMHOLE

The equations of general relativity are nonlinear second-order partial differential equations, and, as a consequence, obtaining the exact solutions is a difficult problem. One of the solutions to this problem is to obtain models with a thin self-gravitating shell. This method is used to study most of the phenomena in the theory of gravity, where the reverse effect of matter on the geometry of space-time is a key factor. Another interesting problem that can be studied using the thin shell method is the «simulation» of a black hole. Consider a system consisting of a spherically symmetric Schwarzschild black hole and a thin shell surrounding it, located at a certain fixed distance from the black hole. From the viewpoint of gravitational physics, an observer at infinity is unable to distinguish a real black hole from a wormhole with a thin shell, in which the simulation condition is satisfied. Simulation of a black hole is possible only under sufficiently stringent conditions for the parameters of the model. In particular, the shell needs to be held at a fixed radius. In the general case, such a movement of the shell is non-geodesic, and external forces are required to hold it. The radius of the shell is also a parameter that determines the possibility / impossibility of simulation. In this paper, the radius is found for the case of a Schwarzschild black hole. In particular, the paper considers a model of a wormhole obtained as a result of gluing two space-times: a Schwarzschild black hole and a Damour-Solodukhin wormhole. The latter solution differs from the Schwarzschild black hole in the parameter of the dimensionless real deviation λ and is a twice asymptotically flat regular space-time. It is shown that they can be glued along a given radius. As a result, a thin shell is formed between two glued manifolds consisting of exotic matter. Cases are considered when the thin shell is stable. It turns out that zones corresponding to the «force» constraint are more restrictive than those corresponding to the «mass» constraint.

Local minimizers in absence of ground states for the critical NLS energy on metric graphs

We consider the mass-critical non-linear Schrödinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass constraint, is provided by Adami, Serra and Tilli in [R. Adami, E. Serra and P. Tilli. Negative energy ground states for the L2-critical NLSE on metric graphs. Comm. Math. Phys. 352 (2017), 387–406.] , where it is proved that existence and properties of ground states depend in a crucial way on both the value of the mass, and the topological properties of the underlying graph. In this paper we address cases when ground states do not exist and show that, under suitable assumptions, constrained local minimizers of the energy do exist. This result paves the way to the existence of stable solutions in the time-dependent equation in cases where the ground state energy level is not achieved.

Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials

We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional non-linear Schrödinger equation with periodic potentials. Using the concentration-compactness principle, we show a complete classification for the existence and non-existence of minimizers for the problem. In the mass-critical case, under a suitable assumption of the potential, we give a detailed description of blow-up behaviour of minimizers once the mass tends to a critical value.

Improving dynamical mass constraints for intermediate-period substellar companions using Gaia DR2

The relationship between luminosity and mass is of fundamental importance for direct imaging studies of brown dwarf and planetary companions to stars. In principle this can be inferred from theoretical mass-luminosity models; however, these relations have not yet been thoroughly calibrated, since there is a lack of substellar companions for which both the brightness and mass have been directly measured. One notable exception is GJ 758 B, a brown dwarf companion in a ~20 AU orbit around a nearby Sun-like star, which has been both directly imaged and dynamically detected through a radial velocity trend in the primary. This has enabled a mass constraint for GJ 758 B of 42+19−7 MJup. Here, we note that Gaia is ideally suited for further constraining the mass of intermediate-separation companions such as GJ 758 B. A study of the differential proper motion, Δμ, with regards to HIPPARCOS is particularly useful in this context, as it provides a long time baseline for orbital curvature to occur. By exploiting already determined orbital parameters, we show that the dynamical mass can be further constrained to 42.4+5.6−5.0 MJup through the Gaia-HIPPARCOS Δμ motion. We compare the new dynamical mass estimate with substellar evolutionary models and confirm previous indications that there is significant tension between the isochronal ages of the star and companion, with a preferred stellar age of ≤5 Gyr while the companion is only consistent with very old ages of ≥8 Gyr.

An MBO Scheme for Minimizing the Graph Ohta–Kawasaki Functional

We study a graph-based version of the Ohta–Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph-based problems inspired by partial differential equations (PDEs) and variational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph-based problems to pattern-forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman–Bence–Osher (MBO) scheme for minimizing the graph Ohta–Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme $$\Gamma $$ Γ -converge to the Ohta–Kawasaki functional (which includes the standard graph-based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta–Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta–Kawasaki functional with a mass constraint.