Narrow Results

Quantum mechanical states are normally described by the Schrödinger equation, which generates real eigenvalues and quantizable solutions which form a basis for the estimation of quantum mechanical observables, such as momentum and kinetic energy. Studying transition in the realm of quantum physics and continuum physics is however more difficult and requires different models. We present here a new equation which bears similarities to the Korteweg–DeVries (KdV) equation and we generate a description of transitions in physics. We describe here the two- and three-dimensional form of the KdV like model dependent on the Plank constant $\hslash$ and generate soliton solutions. The results suggest that transitions are represented by soliton solutions which arrange in a spiral-fashion. By helicity, we propose a conserved pattern of transition at all levels of physics, from quantum physics to macroscopic continuum physics.

The classical limit of wave quantum mechanics is analyzed. It is shown that the basic requirements of continuity and finiteness to the solution of the form ψ(x) = Ae^{i ϕ (x)} + Be^{-i ϕ (x)}, where and W(x) is the reduced classical action of the physical system, give the asymptote of the wave equation and general quantization condition for the action W(x), which yields the exact eigenvalues of the system.

In this paper, we give a contribution to the taxonomy of physical theories. We provide here a thorough description of the axiomatic foundations of the most relevant physical theories, Mechanics, Special Relativity, General Relativity and Quantum Mechanics. The corresponding interactions will be dealt with as well, i.e. Gravity in the Minkowskian limit, Electricity without quantized energy, Gravity without quantized energy and Electricity with quantized energy. We pose the problem of whether the extension of the principle of solidarity to all interactions can impose to consider all variables as dynamic.

The mechanical properties of single-walled nanotubes (SWNTs) filled with small fullerenes (C20, C36 and C60) were investigated using molecular dynamics (MD) simulation. The interaction between carbon atoms was described by a combination of the many-body Brenner potential with a two-body pair potential. We found that below the critical value of the strain, the stress of SWNT increases linearly with the strain and the Young's modulus of certain SWNT with different filling densities is almost the same for small strain. It was also observed that the buckling force, which corresponds to the critical strain, becomes higher as the filling density of SWNT is increased in general. However, in the case of SWNT of larger radius filled with smaller fullerenes, the dependence of the buckling force on the filling density is expected to be different, which was attributive to the long-distance attractive interaction between atoms of fullerene and those of SWNT.

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.

The effect of aging on long bone mechanical properties and bone formative capacity was characterized in the male Fisher 344 rat. The femurs of rats from three age groups (4 mo., 12 mo. and 28 mo.) were tested in three-point bending to determine their structural properties. The apparent material properties were then calculated by adjusting for bone geometry. Bone formation was assessed by dynamic histomorphometry of both cortical and cancellous bone as well as by Northern blot analysis for the expression of the osteoblast phenotypic proteins osteopontin (OP), osteocalcin (OC), type I collagen (COL) and alkaline phosphatase (AP). Aging resulted in a decline in the apparent material properties that was associated with a compensatory alteration of bone geometry that preserved structural strength and stiffness. Histomorphometric analysis revealed significant age-related decreases in cancellous bone volume, trabecular number and increased trabecular separation suggesting the existence of senile osteopenia in the proximal tibia of the male Fisher 344 rat. A significant decline in bone formation rate (BFR), but not mineral apposition rate, suggests that a reduction in osteoblast number, but not osteoblast activity, contributes to age-related bone loss. The decline in BFR with aging was reflected in a decreased mRNA expression for OP, OC and COL but not AP. Further, the pattern of mRNA expression was consistent with reduced osteoblast differentiation with aging. The present study indicates the age-related decline in material properties of long bones is paralleled by a decrease in osteogenesis.

The article is about single cell mechanics and its connection to human diseases. It touches on the biomechanics used to perform quantitative study in the physical properties of cells with the progression of certain diseases such as malaria, sickle cell anemia and cancer.

A brief retrospective of the evolution of mechanics and its reciprocal impacts on medicine and biology is offered, from the limited viewpoint of an early contributor to some aspects of biomechanics. The development of the field after World War II, and particularly in the nineteen sixties and seventies, set the foundation for today's remarkable achievements. Looking ahead, the expanding complexity and challenges of the interaction of mechanics with biology and medicine, together with the loss of centrality of the mechanistic view in the physical sciences, compel a reexamination of the role, potential and limits of mechanics in this context. Future advances call for a broader metamechanics conception encompassing forces, energies, fields, information, network and systems theory, as well as for models spanning the range of scales from atom and molecule to cell, organ and organism.

The premetric formalism is an alternative representation of a classical field theory in which the field equations are formulated without the spacetime metric. Only the constitutive relations between the basic field variables can involve the metric of the underlying manifold. In this paper, we present a brief pedagogical review of the premetric formalism in mechanics, electromagnetism, and gravity.

A theory of nonfluidized gas-solids flow, which combines the theory of multiphase flow with the mechanics of particulate media, was proposed on the basis of understanding that the particles contact each other, solids and gas are in movement, and the drag force on the particles caused by interstitial gas flow is similar to gravity force having the property of mass force. Then this theory was verified by experiments on vertical and inclined moving beds, and was applied to calculation and design of equipment and devices with moving beds, such as pneumatic moving bed transport, dipleg, V-value, L-valve, orifice flow, and arching prevention. It can be used to guide the design and operation of moving beds and fixed beds.

Structural hierarchies are universal design paradigms of biological materials, e.g., several materials in nature used for carrying mechanical load or impact protection such as bone, nacre, dentin show structural design at multiple length scales from the nanoscale to the macroscale. Another example is the case of diatoms, microscopic mineralized algae with intricately patterned silica-based exoskeletons, with substructure from the nanometer to micrometer length scale. Previous studies on silica nano-honeycomb structures inspired from these diatom substructures at the nanoscale have shown a great improvement in plasticity, ductility and toughness through these designs over macroscopic silica, though along with a substantial reduction in stiffness. Here, we extend the study of these structural designs to the micron length scale by introducing additional hierarchy levels to implement a multilevel composite design. To facilitate our computational experiments we first develop a mesoscale particle-spring model description of the mechanics of bulk silica/nano-honeycomb silica composites. Our mesoscale description is directly derived from constitutive material behavior found through atomistic simulations at the nanoscale with the first principles-based ReaxFF force field, but is capable of describing deformation and failure of silica materials at tens of micrometer length scales. We create several models of randomly-dispersed fiber-composite materials with a small volume fraction of the nano-honeycomb phase, and analyze the fracture mechanics using J-integral and R-curve studies. Our simulations show a dominance of quasi-brittle fracture behavior in all cases considered. For particular materials with a small volume fraction of the nano-honeycomb phase dispersed as fibers within a bulk silica matrix, we find a large improvement (≈4.4 times) in toughness over bulk silica, while retaining the high stiffness (to 70%) of the material. The increase in toughness is observed to arise primarily from crack path deflection and crack bridging by the nano-honeycomb fibers. The first structural hierarchy at the nanometer scale (nano-honeycomb silica) provides large improvements in ductility and toughness at the cost of a large reduction in stiffness. The second structural hierarchy at the micron length scale (bulk silica/nano-honeycomb composite) recovers the stiffness of bulk silica while substantially improving its toughness. The results reported here provide direct evidence that structural hierarchies present a powerful design paradigm to obtain heightened levels of stiffness and toughness from multiscale engineering a single brittle — and by itself a functionally inferior material — without the need to introduce organic (e.g., protein) phases. Our model sets the stage for the direct simulation of multiple hierarchical levels to describe deformation and failure of complex biological composites.

Organic building blocks inspired by biological systems are promising for fabricating nanostructured materials for a broad range of applications such as antimicrobials, biosensors, electronics, and biomaterials. Self-assembling cyclic peptide organic nanotubes have shown great promise for these applications due to their precise structural features, diverse chemical functionalization capabilities and exceptional stability arising from arrangement of hydrogen bonds into cooperative clusters. Mechanical behavior of organic nanotubes is important for various possible applications ranging from subnanoporous selective membranes to molecular templates for electronics. However, large-scale deformation mechanisms of organic nanotubes have not been studied thus far. Here we investigate the mechanisms involved in the large deformation and failure of self-assembled organic nanotubes, focusing on geometry effects characteristic of protein nanostructures. We carry out molecular dynamics simulations to assess the role of hydrogen bonds as weak interactions in the context of deformation and failure processes involving bending and shear loads. Mechanisms of failure are found to depend on the cross-sectional geometry and the deformation rate, where a transition to localized shear failure is observed at high-strain rates. Our results provide important physical insight into the mechanics of organic nanotubes central to emerging applications of self-assembling peptides in biomedicine and biotechnology.

Background: Dynamic forces acting on the transverse carpal ligament (TCL) may influence the mechanics of the carpal tunnel (CT), thus affecting the occurrence of CT syndrome (CTS). Previous studies demonstrated an association between muscle overlying the CT and the diagnosis of CTS. Understanding the location of insertion/origin of the thenar musculature will allow mechanical analysis of the forces applied to the TCL during performance of individual tasks. Our purpose was to determine the location of muscle overlying the CT on magnetic resonance imaging (MRI) in CTS and controls.

Methods: Case-control study of 21 normal adult wrist MRI scans. MRI measurements were performed on an axial cut at the level of the hook-of-hamate. Median nerve cross-sectional area (CSA), median nerve shape and increased signal intensity within the CT were associated with CTS. The amount and length of muscle crossing the midline and the CT on the same cut was measured and the association with the occurrence of CTS was analysed.

Results: We found an inverse relationship between the amount of muscle crossing the midline and the size of the CT, and a direct relationship with occurrence of CTS p less than 0.01, but no differences regarding length of muscle crossing the midline.

Conclusions: This study supports an association between the thenar musculature location relative to the CT and the predictors of CTS on MRI. Since the location of muscle origin/insertion is variable, their effect may differ accordingly, therefore, further study is needed to describe the exact location of origin/insertion and its differential dynamic or static effect on the pathogenesis of CTS.

Level of Evidence: Level IV (Diagnostic)

In this work, we proposed a homogenization model to treat the coupled mechanical-diffusion moving interface problem. The Eshelbian homogenization method is applied to find the effective mechanical properties and diffusivity. On the one hand, the diffusion of solute elements would induce the formation of inclusion phases, affecting the mechanical equilibrium, properties and diffusivity. On the other hand, the stress condition will also have effects on the chemical potential and diffusion process. The coupling of the mechanical and diffusion processes were simulated using the present model, i.e., normal diffusion process and that with previous diffusion treatment. In the former case, thicknesses of outer and inner diffusion parts both increased with time. In the latter case, decomposition of the outer diffusion part might take place to maintain the growth of the inner part.

In the topics of mechanics, readily available instruments such as the Force Concept Inventory (FCI) and the Mechanics Baseline Test (MBT) have been extensively used to assess students’ conceptual understanding, especially for high school and undergraduate students. In this paper, the relevancy of these two instruments in excerpting conceptual understanding of high-performing students was examined and the results were elaborated. The findings in this paper suggest that the FCI and MBT are indeed effective to show students’ basic conceptual understanding in mechanics but should not be used to assess improvement after learning intervention or to differentiate students’ conceptual understanding in a population of high performers. More advanced assessments, such as those that comprise higher order thinking questions, should be used for such purposes.

Recently, the use of video analysis technique has emerged as an effective and facile learning tool, due to the richness of spatial and temporal data useful to investigate the complex physical phenomena related to kinematics. In this study, we have investigated the motion of solid and annular cylinders rolling down an inclined wooden plane at different angles. The linear accelerations of the cylinders for the case of rolling (with and without slipping) have been derived theoretically and have been compared with their experimental counterparts. Specifically, the experimental values have been determined by performing a series of experiments, wherein the motion of the cylinders has been captured via a digital camera (recording at 240 frames s${}^{-1}$) and later analyzed frame by frame utilizing in-house developed GUI-based “Phystrack” video tracking library. We have measured the transition angles corresponding to the transition of motion (a) from rest to rolling, and (b) from pure rolling to a combination of rolling and slipping mode of motion, for the case of two distinct cylinders. This has eventually allowed us to compute the coefficient of static, kinetic and rolling friction for the aforementioned cylinders. In general, the coefficient of kinetic friction is regarded as an intrinsic material-dependent constant and considered as independent of the geometry of the object. However, in the case of rolling motion, the coefficients of friction are strongly dependent upon the geometrical parameters of the rolling object. The study emphasizes on developing the conceptual understanding ability of physics students pertaining to the friction coefficient of rolling objects.

4D printing is a fast-developing technique which enables the transformation of shape, property, and function after a structure is manufactured. Here the ’fourth dimension’ refers to a time-dependent deformation, and thus 4D printing technique is closely related to the mechanical design strategies of materials and structures. This review concentrates on the recent progress of fundamental mechanical theories, analytical methods, and designing tools, for three categories of designing principles in 4D printing. The first type of 4D printing relies on active materials that respond to external stimuli. The second type includes a wide range of 4D-printed innovative structures, where the automatic actuation mainly comes from a combination of different deformation mechanisms. The third type of 4D printing focuses on mechanical designs related to the manufacturing process. The classification bridges the gaps between materials, microarchitectures, and large-scale structures, while some 4D printing strategies might involve more than one aforementioned design principle. This review provides reference and guidance for future 4D printings with customized deformation modes and multiple functionalities.

Model-based crack identification problems are considered for static and dynamic loadings with an emphasis on unilaterally working cracks. The inverse problem is formulated as an output, for instance least square, error minimization problem. If only restricted knowledge on the position and the properties of the crack is available, the latter nonlinear least square problem is nonconvex and, due to the unilateral contact effects, possibly nondifferentiable as well. The computational mechanics modelling of the problem on hand is outlined in this paper, previous attempts using optimization and neural networks are briefly described and some numerical results obtained with genetic optimization techniques are presented.