Inertial Sensor-Based Sport Activity Advisory System Using Machine Learning Algorithms.

The aim of this study was to develop a physical activity advisory system supporting the correct implementation of sport exercises using inertial sensors and machine learning algorithms. Specifically, three mobile sensors (tags), six stationary anchors and a system-controlling server (gateway) were employed for 15 scenarios of the series of subsequent activities, namely squats, pull-ups and dips. The proposed solution consists of two modules: an activity recognition module (ARM) and a repetition-counting module (RCM). The former is responsible for extracting the series of subsequent activities (so-called scenario), and the latter determines the number of repetitions of a given activity in a single series. Data used in this study contained 488 three defined sport activity occurrences. Data processing was conducted to enhance performance, including an overlapping and non-overlapping window, raw and normalized data, a convolutional neural network (CNN) with an additional post-processing block (PPB) and repetition counting. The developed system achieved satisfactory accuracy: CNN + PPB: non-overlapping window and raw data, 0.88; non-overlapping window and normalized data, 0.78; overlapping window and raw data, 0.92; overlapping window and normalized data, 0.87. For repetition counting, the achieved accuracies were 0.93 and 0.97 within an error of ±1 and ±2 repetitions, respectively. The archived results indicate that the proposed system could be a helpful tool to support the correct implementation of sport exercises and could be successfully implemented in further work in the form of web application detecting the user's sport activity.

Nematic twist-bend phase in an external field.

The response of the nematic twist-bend ([Formula: see text]) phase to an applied field can provide important insight into the structure of this liquid and may bring us closer to understanding mechanisms generating mirror symmetry breaking in a fluid of achiral molecules. Here we investigate theoretically how an external uniform field can affect structural properties and the stability of [Formula: see text] Assuming that the driving force responsible for the formation of this phase is packing entropy, we show, within Landau-de Gennes theory, that [Formula: see text] can undergo a rich sequence of structural changes with the field. For the systems with positive anisotropy of permittivity, we first observe a decrease of the tilt angle of [Formula: see text] until it transforms through a field-induced phase transition to the ordinary prolate uniaxial nematic phase (N). Then, at very high fields, this nematic phase develops polarization perpendicular to the field ([Formula: see text]). For systems with negative anisotropy of permittivity, the results reveal new modulated structures. Even an infinitesimally small field transforms [Formula: see text] to its elliptical counterpart ([Formula: see text]), where the circular base of the cone of the main director becomes elliptic. With stronger fields, the ellipse degenerates to a line, giving rise to a nonchiral periodic structure, the nematic splay-bend ([Formula: see text]), where the two nematic directors are restricted to a plane. The three structures-[Formula: see text], [Formula: see text], and [Formula: see text]-with a modulated polar order are globally nonpolar. But further increase of the field induces phase transitions into globally polar structures with nonvanishing polarization along the field's direction. We found two such structures, one of which is a polar and chiral modification of [Formula: see text], where splay and bend deformations are accompanied by weak twist deformations ([Formula: see text]). Further increase of the field unwinds this structure into a polar nematic ([Formula: see text]) of polarization parallel to the field.

Twist-bend nematic phases of bent-shaped biaxial molecules.

How can a change in molecular structure affect the relative stability and structural properties of the twist-bend nematic phase (NTB)? Here we extend the mean-field model(1) (C. Greco, G. R. Luckhurst and A. Ferrarini, Soft Matter, 2014, 10, 9318) for bent-shaped achiral molecules, to study the influence of arm molecular biaxiality and the value of the molecule's bend angle on the relative stability of NTB. In particular we show that by controlling the biaxiality of the molecule's arms, up to four ordered phases can become stable. They involve local uniaxial and biaxial variants of NTB, together with uniaxial and biaxial nematic phases. However, a V-shaped molecule shows a stronger ability to form stable NTB than a biaxial nematic phase, where the latter phase appears in the phase diagram only for bend angles greater than 140° and for large biaxiality of the two arms.

Modulated nematic structures induced by chirality and steric polarization.

What kind of one-dimensional modulated nematic structures (ODMNS) can form nonchiral and chiral bent-core and dimeric materials? Here, using the Landau-de Gennes theory of nematics, extended to account for molecular steric polarization, we study a possibility of formation of ODMNS, both in nonchiral and intrinsically chiral liquid crystalline materials. Besides nematic and cholesteric phases, we find four bulk ODMNS for nonchiral materials, two of which, to the best of our knowledge, have not been reported so far. These two structures are longitudinal (N_{LP}) and transverse (N_{TP}) periodic waves where the polarization field being periodic in one dimension stays parallel and perpendicular, respectively, to the wave vector. The other two phases are the twist-bend nematic phase (N_{TB}) and the splay-bend nematic phase (N_{SB}), but their fine structure appears more complex than that considered so far. The presence of molecular chirality converts nonchiral N_{TP} and N_{SB} into new N_{TB} phases. Surprisingly, the nonchiral N_{LP} phase can stay stable even in the presence of intrinsic chirality.

Shapes for maximal coverage for two-dimensional random sequential adsorption.

The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which maximizes the saturated packing fraction. It is found that a concave shape derived from a dimer of disks gives a packing fraction of 0.5833, which is comparable to the maximum packing fraction of ellipsoids and spherocylinders and higher than other studied shapes. Discussion why this shape is beneficial for random sequential adsorption is given.

Motion planning for mobile surgery assistant.

The paper presents a method of motion planning for a mobile manipulator acting as a helper providing the necessary tools or a surgery assistant carrying out pre-planned procedures. Mobility of this system makes it possible to reach the position which will give optimal access to the operating field. The path of the end-effector, determined during operation pre-planning, is defined as a curve parameterised by any scaling parameter, the reference trajectory of a mobile platform is not needed. The motion of the mobile manipulator is planned in order to maximise the manipulability measure, thus to avoid manipulator singularities. The method is based on a penalty function approach and a redundancy resolution at the acceleration level. Constraints connected with the existence of mechanical limits for a given manipulator configuration, collision avoidance conditions and control constraints are considered. A computer example involving a mobile manipulator consisting of a nonholonomic platform (2,0) class and a 3 DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.

Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions.

We present an exhaustive account of phases and phase transitions that can be stabilized in the recently introduced generalized Lebwohl-Lasher model with quadrupolar and octupolar microscopic interactions [L. Longa, G. Pajak, and T. Wydro, Phys. Rev. E 79, 040701(R) (2009)]. A complete mean-field analysis of the model, along with Monte Carlo simulations allows us to identify four distinct classes of the phase diagrams with a number of multicritical points where, in addition to the standard uniaxial and biaxial nematic phases, the other nematic like phases are stabilized. These involve, among the others, tetrahedratic (T), nematic tetrahedratic (N(T)), and chiral nematic tetrahedratic (N(T)(*)) phases of global T(d), D(2d), and D(2) symmetry, respectively. Molecular order parameters and correlation functions in these phases are determined. We conclude with generalizations of the model that give a simple molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed, e.g., in bent-core systems. An estimate of the helical pitch in the N(T)(*) phase is also given.

Molecular theory of the tilting transition in smectic liquid crystals with weak layer contraction and diffused cone orientational distribution.

A molecular field theory of the smectic-A-smectic-C transition has been developed for smectics with a diffused cone orientational distribution of molecules (volcano-like distribution function) in the smectic-A phase and anomalously weak layer contraction in the smectic-C phase. Orientational order parameters and smectic layer spacing have been calculated numerically as functions of temperature and compared with the results obtained using a model with a standard Maier-Saupe-type distribution function that has been considered before. A molecular theory of the electroclinic effect in chiral smectics has also been developed using the recently proposed simple biaxial interaction potential. A comparison has been made between the absolute values and temperature variations of the electroclinic coefficient obtained using the volcano model, the model with Maier-Saupe-type distribution, and the orthodox cone model proposed by de Vries. It has been shown that the model with a conventional "sugar loaf" type orientational distribution function in the smectic-A phase is sufficient to describe the main properties of smectics with anomalously weak layer contraction.

Influence of dipole-dipole correlations on the stability of the biaxial nematic phase in the model bent-core liquid crystal.

A molecular theory of biaxial nematic ordering in the system of bent-core molecules has been developed in the two-particle cluster approximation which enables one to take into account short-range polar correlations determined by both electrostatic dipole-dipole interaction and polar molecular shape. All orientational order parameters and short-range correlation functions are calculated numerically as functions of temperature in the uniaxial and in the biaxial nematic phases, and the results are compared with the ones obtained in the mean-field approximation and in the cluster approximation but without taking into consideration the dipole-dipole interaction. It is shown that short-range polar correlations and, in particular, the dipole-dipole correlations dramatically increase the temperature of the transition into the biaxial nematic phase and enhancing its stability range. The results are also very sensitive to the value of the opening angle of a model bent-core molecule.

Chiral symmetry breaking in bent-core liquid crystals.

By molecular modeling we demonstrate that the nematic long-range order discovered in bent-core liquid-crystal systems should reveal further spatially homogeneous phases. Two of them are identified as a tetrahedratic nematic (N_{T}) phase with D_{2d} symmetry and a chiral tetrahedratic nematic (N_{T};{ *}) phase with D2 symmetry. These phases were found for a lattice model with quadrupolar and octupolar anisotropic interactions using mean-field theory and Monte Carlo simulations. The phase diagrams exhibit tetrahedratic (T) , N_{T} , and N_{T};{ *} phases, in addition to ordinary isotropic (I) , uniaxial nematic (N_{U}) , and biaxial nematic (N_{B}) phases.

Stability of biaxial nematic phase for systems with variable molecular shape anisotropy.

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean-field model of Mulder and Ruijgrok [Physica A 113, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems--a mixture of potassium laurate, 1-decanol, and D2O , where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimericlike or tetrapodlike molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, the stability of the biaxial nematic phase can be either enhanced or depressed, relative to the uniaxial nematic phases. In the former case the splitting of the Landau point into two triple points with a direct phase transition line from isotropic to biaxial phase is observed.