Synthesis and design of polyurethane and its nanocomposites derived from canola-castor oil: Mechanical,thermal and shape memory properties

The recent global pandemic and its tremendous effect on the price fluctuations of crude oil illustrates the side effects of petroleum dependency more evident than ever. Over the past decades, both academic and industrial communities spared endless efforts in order to replace petroleum-based materials with bio-derived resources. In the current study, a series of shape memory polymer composites (SMPC's) was synthesized from epoxidized vegetable oils, namely canola oil and castor oil fatty acids (COFA's) as a 100% bio-based polyol and isophorone diisocyanate (IPDI) as an isocyanate using a solvent/catalyst-free method in order to eventuate polyurethanes (PU's). Thereafter, graphene oxide (GO) nanoplatelets were synthesized and embedded in the neat PU in order to overcome the thermomechanical drawbacks of the neat matrix. The chemical structure of the synthesized components, as well as the dispersion and distribution levels of the nanoparticles, was characterized. In the following, thermal and mechanical properties as well as shape memory behavior of the specimens were comprehensively investigated. Likewise, the thermal conductivity was determined. This study proves that synthesized PU's based on vegetable oil polyols, including graphene nanoparticles, exhibit proper thermal and mechanical properties, which make them stand as a potential candidate to compete with traditional petroleum-based SMPC's.     

An optimal reinsurance problem in the Cramér–Lundberg model

In this article we consider the surplus process of an insurance company within the Cramér–Lundberg framework with the intention of controlling its performance by means of dynamic reinsurance. Our aim is to find a general dynamic reinsurance strategy that maximizes the expected discounted surplus level integrated over time. Using analytical methods we identify the value function as a particular solution to the associated Hamilton–Jacobi–Bellman equation. This approach leads to an implementable numerical method for approximating the value function and optimal reinsurance strategy. Furthermore we give some examples illustrating the applicability of this method for proportional and XL-reinsurance treaties.     

Regularity and Singularities of Optimal Convex Shapes in the Plane

We focus here on the analysis of the regularity or singularity of solutions Ω ₀ to shape optimization problems among convex planar sets, namely:

$J(\Omega_{0})={\rm min} \{J(\Omega), \Omega \quad {\rm convex},\Omega \in \mathcal{S}_{\rm ad}\},$

where \({\mathcal{S}_{\rm ad}}\) is a set of 2-dimensional admissible shapes and \({J:\mathcal{S}_{\rm ad}\rightarrow\mathbb{R}}\) is a shape functional. Our main goal is to obtain qualitative properties of these optimal shapes by using first and second order optimality conditions, including the infinite dimensional Lagrange multiplier due to the convexity constraint. We prove two types of results:

1. i)
   under a suitable convexity property of the functional J, we prove that Ω ₀ is a W ^2,p -set, \({p\in[1, \infty]}\). This result applies, for instance, with p = ∞ when the shape functional can be written as J(Ω) = R(Ω) + P(Ω), where R(Ω) = F(|Ω|, E _f (Ω), λ₁(Ω)) involves the area |Ω|, the Dirichlet energy E _f (Ω) or the first eigenvalue of the Laplace–Dirichlet operator λ₁(Ω), and P(Ω) is the perimeter of Ω;
    

1. ii)
   under a suitable concavity assumption on the functional J, we prove that Ω ₀ is a polygon. This result applies, for instance, when the functional is now written as J(Ω) = R(Ω) ? P(Ω), with the same notations as above.
    

     

Synthesis Strategies for Ultrastable Zeolite GIS Polymorphs as Sorbents for Selective Separations

Designing zeolites with tunable physicochemical properties can substantially impact their performance in commercial applications, such as adsorption, separations, catalysis, and drug delivery. Zeolite synthesis typically requires an organic structure‐directing agent to produce crystals with specific pore topology. Attempts to remove organics from syntheses to achieve commercially viable methods of preparing zeolites often lead to the formation of impurities. Herein, we present organic‐free syntheses of two polymorphs of the small‐pore zeolite P (GIS), P1 and P2. Using a combination of adsorption measurements and density functional theory calculations, we show that GIS polymorphs are selective adsorbents for H₂O relative to other light gases (e.g., H₂, N₂, CO₂). Our findings refute prior theoretical studies postulating that GIS‐type zeolites are excellent materials for CO₂ separation/sequestration. We also show that P2 is significantly more thermally stable than P1, which broadens the operating conditions for GIS‐type zeolites in commercial applications and opens new avenues for exploring their potential use in processes such as catalysis.     

On the design of deterministic dielectrophoresis for continuous separation of circulating tumor cells from peripheral blood cells

Detection and analysis of circulating tumor cells (CTCs) have emerged as a promising way to diagnose cancer, study its cellular mechanism, and test or develop potential treatments. However, the rarity of CTCs among peripheral blood cells is a big challenge toward CTC detection. In addition, in cases where there is similar size range between certain types of CTCs (e.g. breast cancer cells) and white blood cells (WBCs), high‐resolution techniques are needed. In the present work, we propose a deterministic dielectrophoresis (DEP) method that combines the concept of deterministic lateral displacement (DLD) and insulator‐based dielectrophoresis (iDEP) techniques that rely on physical markers such as size and dielectric properties to differentiate different type of cells. The proposed deterministic DEP technology takes advantage of frequency‐controlled AC electric field for continuous separation of CTCs from peripheral blood cells. Utilizing numerical modeling, different aspects of coupled DLD‐DEP design such as the required applied voltages, velocities, and geometrical parameters of DLD arrays of microposts are investigated. Regarding the inevitable difference and uncertainty ranges for the reported crossover frequencies of cells, a comprehensive analysis is conducted on applied electric field frequency as design's determinant factor. Deterministic DEP design provides continuous sorting of CTCs from WBCs even with similar size and has the future potential for high throughput and efficiency.     

The effect of shocks on second order sensitivities for the quasi-one-dimensional Euler equations

The effect of discontinuity in the state variables on optimization problems is investigated on the quasi-one-dimensional Euler equations in the discrete level. A pressure minimization problem and a pressure matching problem are considered. We find that the objective functional can be smooth in the continuous level and yet be non-smooth in the discrete level as a result of the shock crossing grid points. Higher resolution can exacerbate that effect making grid refinement counter productive for the purpose of computing the discrete sensitivities. First and second order sensitivities, as well as the adjoint solution, are computed exactly at the shock and its vicinity and are compared to the continuous solution. It is shown that in the discrete level the first order sensitivities contain a spike at the shock location that converges to a delta function with grid refinement, consistent with the continuous analysis. The numerical Hessian is computed and its consistency with the analytical Hessian is discussed for different flow conditions. It is demonstrated that consistency is not guaranteed for shocked flows. We also study the different terms composing the Hessian and propose some stable approximation to the continuous Hessian.     

$C^1$ error estimation on the boundary for an exterior Neumann problem in $\mathbb R^3$

Summary.   In this paper we establish a error estimation on the boundary for the solution of an exterior Neumann problem in . To solve this problem we consider an integral representation which depends from the solution of a boundary integral equation. We use a full piecewise linear discretisation which on one hand leads to a simple numerical algorithm but on the other hand the error analysis becomes more difficult due to the singularity of the integral kernel. We construct a particular approximation for the solution of the boundary integral equation, for the solution of the Neumann problem and its gradient on the boundary and estimate their error. Received May 11, 1998 / Revised version received July 7, 1999 / Published online August 24, 2000