Pore space network characterization with sub-voxel definition

Morphological measurements in 3D for pore space characterization (connectivity pore-body/throat classification, shape factors, virtual fluid intrusion) are based on computed intensive digital-thinning operations for skeletonization and medial axis extraction from 3D digital images. We present an alternative method that is measurably faster and allows sub-voxel definition of the pore space network. The method allows extracting—based on morphological considerations only—the centered and shortest stream-lines—i.e., the paths—to follow in order to go through the pore space from one given point to another and to exit. In addition the method penalizes long and narrow pore-throats in favor of short stubby/ones—i.e., it has a built-in exemplification capacity. It exploits well-established mathematical methods successfully applied in medical endoscopy.     

From 3-D Nonlinear Elasticity Theory to 1-D Bars with Nonconvex Energy

This paper represents a first attempt to derive one-dimensional models with non-convex strain energy starting from “genuine” three-dimensional, nonlinear, compressible, elasticity theory. Following the usual method of obtaining beam theories, we show here for a constrained kinematics appropriate for long cylinders governed by a polyconvex, objective, stored energy function, that the bar model originally proposed by Ericksen [3] is obtainable but enriched by an additional term in the strain gradient. This term, characteristic of nonsimple grade-2 materials, penalizes interfacial energies and makes single-interface two-phase solutions preferred. The resulting model has been proposed by a number of authors to describe the phenomenon of necking and cold drawing in polymeric fibers and, here, we discuss its suitability to interpret also the elastic-plastic behavior of metallic tensile bars under monotone loading.     

Neural network prediction of load from the morphology of trabecular bone

Bone adaptation models are often solved in the forward direction, meaning that the response of bone to a given set of loads is determined by running a bone tissue adaptation model. The model is generally solved using a numerical technique such as the finite element model. Conversely, one may be interested in the loads that have resulted in a given state of bone. This is the inverse of the former problem. Even though the inverse problem has several applications, it has not received as much attention as the forward problem, partly because solving the inverse problem is more difficult. A nonlinear system identification technique is needed for solving the inverse problem. In this study, we use artificial neural networks for prediction of tissue adaptation loads from a given density distribution of trabecular bone. It is shown that the proposed method can successfully identify the loading parameters from the density distribution of the tissue. Two important challenges for all load prediction algorithms are the non-uniqueness of the solution of the inverse problem and the inaccuracies in the measurement of the morphology of the tissue. Both challenges are studied, and it is shown that the load prediction technique proposed in this paper can overcome both.     

Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation.     

Ultra-stable microwave generation with a diode-pumped solid-state laser in the 1.5-μm range

We demonstrate the first ultra-stable microwave generation based on a 1.5-μm diode-pumped solid-state laser (DPSSL) frequency comb. Our system relies on optical-to-microwave frequency division from a planar-waveguide external cavity laser referenced to an ultra-stable Fabry–Perot cavity. The evaluation of the microwave signal at ~10 GHz uses the transportable ultra-low-instability signal source ULISS^®, which employs a cryo-cooled sapphire oscillator. With the DPSSL comb, we measured ?125 dBc/Hz phase noise at 1 kHz offset frequency, likely limited by the photo-detection shot-noise or by the noise floor of the reference cryo-cooled sapphire oscillator. For comparison, we also generated low-noise microwave using a commercial Er:fiber comb stabilized in similar conditions and observed >20 dB lower phase noise in the microwave generated from the DPSSL comb. Our results confirm the high potential of the DPSSL technology for low-noise comb applications.     

Variational Characterization of a Quasi-rigid Body

The rigidity of a body usually is characterized by the kinematical assumption that the mutual distance between any two of its particles remains unaltered in any possible deformation. However, from this alone nothing can be said about the internal contact forces exerted between adjacent sub-bodies. Therefore, the determination and form of an internal state of stress for a rigid body is problematical. Here, we will show that by considering such a kinematical characterization as an internal constraint for an elastic body, the constrained body inherits the mechanical structure of the elastic parent theory, i.e., the internal constraint generates an associated set of Lagrange multiplier fields which can be interpreted as an internal constraint reaction pseudo-stress field with the same structure as the state of stress in the parent elastic body. Thus, although the final deformation is the same for both the rigid body and the rigidly constrained elastic body, the latter corresponds to a richer model and, to emphasize this distinction, we refer to it as a quasi-rigid body. While in equilibrium the pseudo-stress field of a quasi-rigid body will satisfy equations identical to the equilibrium equations for the stress field in the elastic parent theory, such equations are not, in general, sufficient to assure uniqueness. In order to overcome this indeterminacy, we consider the quasi-rigid body as the limit of a sequence of deformable bodies, where each member of the sequence is identified by a material parameter such that, as this parameter tends to infinity, the body to which it refers is rigidified. Our approach is variational, i.e., we consider a sequence of minimization problems for hyperelastic bodies whose elastic strain energy is multiplied by a penalty term, say 1/ε . As ε→?0, body distortions are more and more penalized so that the sequence of the displacement fields tends to a rigid displacement field, whereas the sequence of the associated stress fields tends to a definite non-zero limit. It will be shown that among all pseudo-stress fields that satisfy the equilibrium equations for the quasi-rigid body, the unique limit of the sequence as ε→0 minimizes a functional analogous to the complementary energy functional in classical linearized elasticity. This result permits its unique determination without having to consider the whole sequence of penalty problems.