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This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian action. This aim is attained for homogeneous systems, described by a finite number of state variables depending on time only. In particular, it is shown that away from equilibrium free energy and entropy are independent constitutive functions.

Background Tumor progression is based on a close interaction between cancer cells and Tumor MicroEnvironment (TME). Here, we focus on the role that Cancer Associated Fibroblasts (CAFs), Mesenchymal Stem Cells (MSCs) and microRNAs (miRs) play in breast cancer and melanoma malignancy. Methods We used public databases to investigate miR-214 expression in the stroma compartment of primary human samples and evaluated tumor formation and dissemination following tumor cell injections in miR-214 overexpressing (miR-214over) and knock out (miR-214ko) mice. In addition, we dissected the impact of Conditioned Medium (CM) or Extracellular Vesicles (EVs) derived from miR-214-rich or depleted stroma cells on cell metastatic traits. Results We evidence that the expression of miR-214 in human cancer or metastasis samples mostly correlates with stroma components and, in particular, with CAFs and MSCs. We present data revealing that the injection of tumor cells in miR-214over mice leads to increased extravasation and metastasis formation. In line, treatment of cancer cells with CM or EVs derived from miR-214-enriched stroma cells potentiate cancer cell migration/invasion in vitro. Conversely, dissemination from tumors grown in miR-214ko mice is impaired and metastatic traits significantly decreased when CM or EVs from miR-214-depleted stroma cells are used to treat cells in culture. Instead, extravasation and metastasis formation are fully re-established when miR-214ko mice are pretreated with miR-214-rich EVs of stroma origin. Mechanistically, we also show that tumor cells are able to induce miR-214 production in stroma cells, following the activation of IL-6/STAT3 signaling, which is then released via EVs subsequently up-taken by cancer cells. Here, a miR-214-dependent pro-metastatic program becomes activated. Conclusions Our findings highlight the relevance of stroma-derived miR-214 and its release in EVs for tumor dissemination, which paves the way for miR-214-based therapeutic interventions targeting not only tumor cells but also the TME.

We study the equilibria of a photoresponsive nematic elastomer ribbon within a continuum theory that builds upon the statistical mechanics model put forward by Corbett and Warner (Phys. Rev. E 78:061701, 2008). We prove that the spontaneous deformation induced by illumination is not monotonically dependent on the intensity $I$ I . The ribbon’s deflection first increases with increasing $I$ I , as expected, but then decreases and abruptly ceases altogether at a critical value $I_{\mathrm{e}}$ I e of $I$ I . $I_{\mathrm{e}}$ I e , which is enclosed within a hysteresis loop, marks a first-order shape transition. Finally, we find that there is a critical value of the ribbon’s length, depending only on the degree of cross-linking in the material, below which no deflection can be induced in the ribbon, no matter how intense is the light shone on it.

Sometimes, even a cursory remark at the end of a lecture, if growing out of deep intelligence and directed to a sensitive mind, can have momentous consequences. This was the case in the episode recounted here, which linked Ericksen and de Gennes, albeit indirectly.

The ground state of chromonic liquid crystals, as revealed by a number of recent experiments, is quite different from that of ordinary nematic liquid crystals: it istwistedinstead of uniform. The common explanation provided for this state within the classical elastic theory of Frank demands that one Ericksen’s inequality is violated. Since in general such a violation makes Frank’s elastic free-energy functional unbounded below, the question arises as to whether the twisted ground state can be locally stable. We answer this question in theaffirmative. In reaching this conclusion, a central role is played by the specific boundary conditions imposed in the experiments on the boundary of rigid containers and by a general formula that we derive here for the second variation in Frank’s elastic free energy.

We present a theory of deformation of ribbons made of nematic polymer networks (NPNs). These materials exhibit properties of rubber and nematic liquid crystals, and can be activated by external stimuli of heat and light. A two-dimensional energy for a sheet of such a material has already been derived from the celebrated neo-classical energy of nematic elastomers in three space dimensions. Here, we use a dimension reduction method to obtain the appropriate energy for a ribbon from the aforementioned sheet energy. We also present an illustrative example of a rectangular NPN ribbon that undergoes in-plane serpentine deformations upon activation under an appropriate set of boundary conditions., Published version

Walter Noll (1925–2017) was an American mathematician of German birth who made lasting contributions to the foundations of continuum physics and the classical non-linear field theory. This essay is an attempt to put in a broader perspective Noll’s methods and achievements in the hope that young generations of researchers may find their inspiration in the talent and depth of the old. By no means should this be considered as a historical account on the development of continuum mechanics through the second half of the twentieth century. We are content to illuminate Noll’s precious legacy.

Gut motility malfunction and pathological changes in the enteric nervous system (ENS) are observed in the early stages of Parkinson's disease (PD). In many cases disturbances in the autonomous functions such as gut motility precedes the observed loss of central motor functions in PD. However, the mechanism by which ENS degeneration occurs in PD is unknown. We show that parkinsonian mimetics rotenone and MPP+ induce neurite degeneration that precedes cell death in primary enteric neurons cultured in vitro. If the neuronal death signals originate from degenerating neurites, neuronal death should be prevented by inhibiting neurite degeneration. Our data demonstrate that overexpression of cytNmnat1, an axon protector, maintains healthy neurites in enteric neurons treated with either of the parkinsonian mimetics, but cannot protect the soma. We also demonstrate that neurite protection via cytNmnat1 is independent of mitochondrial dynamics or ATP levels. Overexpression of Bcl-xl, an anti-apoptotic factor, protects both the neuronal cell body and the neurites in both rotenone and MPP+ treated enteric neurons. Our data reveals that Bcl-xl and cytNmnat1 act through separate mechanisms to protect enteric neurites. Our findings suggest that neurite protection alone is not sufficient to inhibit enteric neuronal degeneration in rotenone or MPP+ toxicity, and enteric neurodegeneration in PD may be occurring through independent somatic and neuritic mechanisms. Thus, therapies targeting both axonal and somal protection can be important in finding interventions for enteric symptoms in PD.

A large body of research suggests that children with ADHD tend to overestimate their functioning across multiple domains. This overestimation, termed a positive illusory bias (PIB), is most often examined in controlled research settings in which child ratings are compared to ratings from an adult. We sought to advance our understanding of how a PIB presents in daily life for children with ADHD by using mixed methodology to assess mothers’ (N = 12) perceptions of their child’s self-awareness. Information was gathered from mothers of children with ADHD using surveys and an interview protocol. A grounded theory approach was used to identify themes that emerged through interview data and discrepancy methodology to confirm the presence of the PIB. Qualitative and quantitative data suggested that children with ADHD displayed limited self-awareness, with mothers reporting overestimation of competence across domains. However, some children were reported to be aware of their areas of difficulty, with variability in self-awareness based on domain, feedback, and setting. Mothers reported that children responded to evidence of their impairment both with apathy and frustration. Results help to clarify past evidence of heterogeneity in PIB levels and provide examples of how limited self-awareness and denial of difficulties are manifested in the family context for children with ADHD, according to mother’s observations. These results demonstrate the value of using mixed methodology to better understand the self-perceptions of children with ADHD in their daily lives.

Ultrasound acquisitions are typically affected by deformations due to the pressure applied onto the contact surface. While a certain amount of pressure is necessary to ensure good acoustic coupling and visibility of the anatomy under examination, the caused deformations hinder accurate localization and geometric analysis of anatomical structures. These complications have even greater impact in case of 3D ultrasound scans as they limit the correct reconstruction of acquired volumes. In this work, we propose a method to estimate and correct the induced deformation based solely on the tracked ultrasound images and information about the applied force. This is achieved by modeling estimated displacement fields of individual image sequences using the measured force information. By representing the computed displacement fields using a graph-based approach, we are able to recover a deformation-less 3D volume. Validation is performed on 30 in vivo human datasets acquired using a robotic ultrasound framework. Compared to ground truth, the presented deformation correction shows errors of $$3.39 \, \pm \, 1.86\,\hbox {mm}$$ for an applied force of 5 N at a penetration depth of 55 mm. The proposed technique allows for the correction of deformations induced by the transducer pressure in entire 3D ultrasound volumes. Our technique does not require biomechanical models, patient-specific assumptions or information about the tissue properties; it can be employed based on the information from readily available robotic ultrasound platforms.

Nematic shells are thin films of nematic liquid crystal deposited on the boundary of colloidal particles, where liquid crystal molecules may freely glide, while remaining tangent to the surface substrate. The surface nematic order is described here by an appropriate tensor field Q, which vanishes wherever a defect occurs in the molecular order. We show how the classical concept of parallel transport on a manifold introduced by Levi-Civita can be adapted to this setting to define the topological charge m of a defect. We arrive at a simple formula to compute m from a generic representation of Q. In a number of separate appendices, we revisit in a unified language several, apparently disparate applications of Levi-Civita’s parallel transport.

This study was aimed at looking into the microbiological/inflammatory parameters predicting the periodontal success/failure of fixed prostheses. Microbiological and inflammatory patterns were studied at 102 sites having metaloceramic crowns in place from 3 to 6 years and divided in healthy sites (HS), gingivitis affected (MG), and periodontitis affected (PB). Total bacterial flora and selected indicator species in subgingival plaque were quantified by quantitative real-time PCR. The concentrations of IL-1β, IL-6, and TNF-α were determined in gingival crevicular fluid (GCF) by enzyme-linked immunosorbent assays. The experimental sites showed no significant difference with respect to the age and gender of the patients and to the position of the crown margins. Poor marginal adaptation was significantly higher in MG and PB. The total amounts of bacteria per probing depth showed no significant differences among the three groups and their controls, while both MG and PB sites showed altered patterns in the distribution of specific bacteria. Both MG and PB sites showed significantly higher levels of inflammatory cytokines in GCF. The control teeth of PB subjects showed significantly higher levels of IL-1β as compared to other control sites. Data confirm that the application of metaloceramic crowns is a factor of risk for the development of gingival/periodontal inflammation. This risk is possibly associated with microbiological and host factors that predispose to the onset of periodontal alterations at sites reconstructed with metaloceramic crowns. These factors, once their role is confirmed by longitudinal studies, could be used to set up rapid tests to early predict the onset of periodontal disease at reconstructed sites.

The extension of Bogoliubov Jr.’s minimax principle to biaxial nematic liquid crystals has recently made it possible to derive the universal mean-field phase diagram for all quadrupolar interactions between nematogenic biaxial molecules, including those rendering the mean-field free energy $${\fancyscript{F}_0}$$ indefinite. To justify this extension, so far largely based on heuristic arguments, we prove here a minimum principle that also applies when $${\fancyscript{F}_0}$$ is indefinite. Bogoliubov Jr.’s minimax principle then emerges as a characterization of this minimum principle. The theory presented here is more general than its application to biaxial nematic liquid crystals could reveal. It essentially builds upon a concavity property of $${\fancyscript{F}_0}$$ in the order tensor associated with the repulsive component of the molecular interaction.

We present a phenomenological theory for the homogeneous phases of nematic liquid crystals constituted by biaxial molecules. We propose a general polynomial potential in two macroscopic order parameter tensors that reproduces the mean-field phase diagram confirmed by Monte Carlo simulations [De Matteis et al. in Phys Rev E 72:041706 (2005)] and recently recognized to be universal [Bisi et al. in Phys Rev E 73:051709 (2006)] for dispersion force molecular pair-potentials enjoying the D 2h symmetry. The requirement that the phenomenological theory comply uniquely with this phase diagram reduces considerably the admissible phenomenological coefficients, both in their number and in the ranges where they can vary.

We propose a model to explore the competition between two mechanisms possibly at work in a nematic liquid crystal confined within a flat cell with strong uniaxial planar conditions on the bounding plates and subject to an external field. To obtain an electric field perpendicular to the plates, a voltage is imposed across the cell; no further assumption is made on the electric potential within the cell, which is therefore calculated together with the nematic texture. The Landau-de Gennes theory of liquid crystals is used to derive the equilibrium nematic order tensor Q. When the voltage applied is low enough, the equilibrium texture is nearly homogeneous. Above a critical voltage, there exist two different possibilities for adjusting the order tensor to the applied field within the cell: plain director reorientation, i.e., the classical Freedericksz transition, and order reconstruction. The former mechanism entails the rotation of the eigenvectors of Q and can be described essentially by the orientation of the ordinary uniaxial nematic director, whilst the latter mechanism implies a significant variation of the eigenvalues of Q within the cell, virtually without any rotation of its eigenvectors, but with the intervention of a wealth of biaxial states. Either mechanism can actually occur, which yields different nematic textures, depending on material parameters, temperature, cell thickness and the applied potential. The equilibrium phase diagram illustrating the prevailing mechanism is constructed for a significant set of parameters.

We study the invariance properties of the molecular Hamiltonian interaction put forward by Straley to describe biaxial nematic phases. We show that the reduction to two out of four scalar order parameters, which was accidently remarked upon in the literature, is indeed a rigorous consequence of the Hamiltonian invariance for specific values of the interaction parameters. The stability analysis of the mean-field free energy in the reduction classes for the order parameters reveals a sequence of Landau triple points.