Simulation of conditioned diffusions

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of another diffusion which is easy for simulation, and the formula for the density is given explicitly

The Lagrangian multiplier method of finding upper and lower limits to critical stresses of clamped plates

The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the true stress, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Rayleigh-Ritz method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz, but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems the Lagrangian multiplier method of finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies

The Lagrangian Multiplier Method of Finding Upper and Lower Limits to Critical Stresses of Clamped Plates

The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the truss, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Raleigh-Rite method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems problems the Lagrangian multiplier method finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies

Fabrication of hierarchical macroporous biocompatible scaffolds by combining Pickering high internal phase emulsion templates with three-dimensional printing

Biocompatible and biodegradable porous scaffolds with adjustable pore structure have aroused increasing interest in bone tissue engineering. Here, we report a facile method to fabricate hierarchical macroporous biocompatible (HmPB) scaffolds by combining Pickering high internal phase emulsion (HIPE) templates with three-dimensional (3D) printing. HmPB scaffolds composed of a polymer matrix of poly(L-lactic acid), PLLA, and poly(ε-caprolactone), PCL, are readily fabricated by solvent evaporation of 3D printed Pickering HIPEs which are stabilized by hydrophobically modified silica nanoparticles (h-SiO2). The pore structure of HmPB scaffolds is easily tailored to be similar to natural extracellular matrix (ECM) by varying the fabrication conditions of the Pickering emulsion or adjusting the printing parameters. In addition, in vivo drug release studies which employ enrofloxacin (ENR) as a model drug indicate the potential of HmPB scaffolds as a drug carrier. Furthermore, in vivo cell culture assays prove that HmPB scaffolds possesses good biocompatibility as mouse bone mesenchymal stem cells (mBMSCs) can adhere and proliferate well on them. All the results suggest that HmPB scaffolds hold great potential in bone tissue engineering applications