We generalize the parity-time reversal or PT symmetric nonlinear Dirac equation in 1+1 dimensions consisting of scalar-scalar (S-S) minus vector-vector (V-V) interaction terms discussed by Alexeeva et al. (2019, which we will refer to as the ABS model) to arbitrary nonlinearity power kappa (> 0). We also introduce a parameter p which changes the relative weight of the two interactions, breaking the PT Symmetry. The nonlinear Dirac equation we consider has interaction Lagrangian given by L-I = g(2)/(kappa+1) ((psi) over bar psi)(kappa+1) - 1/p[(psi) over bar gamma(mu) psi (psi) over bar gamma(mu) psi]((kappa+1)/2), where g(2) > 0 and p > 1. We find exact solitary wave solutions of the form psi(x, t) = psi(x)e(-i omega t). We show that the solitary wave solutions exist in the entire allowed (kappa, p) plane for omega/m > 1/p(1/(kappa+1)), for frequency omega and mass m. These solutions have the property that their energy E divided by their charge Q is of the coupling constant g(2). As omega/m increases, there is a transition from the double hump to the single hump solitary wave and we determine this transition as a function of omega/m, k and p. When k > 2, E/Q has a maximum at a critical value of omega/m which depends on p and decreases with increasing p. We obtain the nonrelativistic reduction of the two-parameter family of generalized ABS models to a modified nonlinear Schrodinger equation (NLSE) and discuss the stability of the single hump solitary waves in the domain of validity of the modified NLSE.

We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $ \Psi(x,t) =\Phi(x) \rme^{-\rmi \omega t}$ where the nonlinear interactions are a combination of vector-vector and scalar-scalar interactions with the interaction Lagrangian given by $L_I = \frac{g^2}{(\kappa+1)}[\bar{\psi} \gamma_{\mu}\psi \bar{\psi} \gamma^{\mu} \psi]^{(\kappa+1)/2} - \frac{g^2}{q(\kappa+1)}(\bar{\psi} \psi)^{\kappa+1}$, where $\kappa>0$ and $q>1$. This is the complement of the generalization of the ABS model \cite{abs} that we recently studied \cite{ak} and denoted as the gABS model. We show that like the gABS model, in the complementary gABS models the solitary wave solutions also exist in the entire $(\kappa, q)$ plane and further in both models energy of the solitary wave divided by its charge is {\it independent} of the coupling constant $g$. However, unlike the gABS model here all the solitary waves are single humped, any value of $0 < \omega < m$ is allowed and further unlike the gABS model, for this complementary gABS model the solitary wave bound states exist only in case $\kappa \le \kappa_c$, where $\kappa_c$ depends on the value of $q$. Here $\omega$ and $m$ denote frequency and mass, respectively. We discuss the regions of stability of these solutions as a function of $\omega,q,\kappa$ using the Vakhitov-Kolokolov criterion. Finally we discuss the non-relativistic reduction of the two-parameter family of this complementary generalized ABS model to a modified nonlinear Schr\"odinger equation (NLSE) and discuss the stability of the solitary waves in the domain of validity of the modified NLSE.

Previous studies aimed at defining the mechanistic basis of hypertrophic cardiomyopathy caused by A331P cardiac actin have reported conflicting results. The mutation is located along an actin surface strand, proximal to residues that interact with tropomyosin. These F-actin-tropomyosin associations are vital for proper contractile inhibition. To help resolve disease pathogenesis, we implemented a multidisciplinary approach. Transgenic Drosophila, expressing A331P actin, displayed skeletal muscle hypercontraction and elevated basal myocardial activity. A331P thin filaments, reconstituted using recombinant human cardiac actin, exhibited higher in vitro myosin-based sliding speeds, exclusively at low Ca2+ concentrations. Cryo-EM-based reconstructions revealed no detectable A331P-related structural perturbations in F-actin. In silico, however, the P331-containing actin surface strand was less mobile and established diminished van der Waal’s attractive forces with tropomyosin, which correlated with greater variability in inhibitory tropomyosin positioning. Such mutation-induced effects potentially elevate resting contractile activity among our models, and may stimulate pathology in patients.

We present the Geocentric Datum of Australia 2020, the latest update to the Australian national datum. This update results in a more accurate and precise datum that is better suited to modern positioning needs. Improvements include the removal of the distortions present in the previous national datum, a reduction in the offset to the current International Terrestrial Reference Frame, and the provision of rigorous uncertainties. We also describe the input data and the methods used to perform a rigorous, all-station, continental-scale least-squares adjustment of the national geodetic network, consisting of more than 2.4 million measurements to more than 330,000 survey control marks.

In this work, we discuss an application of the "inverse problem" method to find the external trapping potential, which has particular N trapped soliton-like solutions of the Gross-Pitaevskii equation (GPE) also known as the cubic nonlinear Schrödinger equation (NLSE). This inverse method assumes particular forms for the trapped soliton wave function, which then determines the (unique) external (confining) potential. The latter renders these assumed waveforms exact solutions of the GPE (NLSE) for both attractive (g<0) and repulsive (g>0) self-interactions. For both signs of g, we discuss the stability with respect to self-similar deformations and translations. For g<0, a critical mass Mc or equivalently the number of particles for instabilities to arise can often be found analytically. On the other hand, for the case with g>0 corresponding to repulsive self-interactions which is often discussed in the atomic physics realm of Bose-Einstein condensates, the bound solutions are found to be always stable. For g<0, we also determine the critical mass numerically by using linear stability or Bogoliubov-de Gennes analysis, and compare these results with our analytic estimates. Various analytic forms for the trapped N-soliton solutions in one, two, and three spatial dimensions are discussed, including sums of Gaussians or higher-order eigenfunctions of the harmonic oscillator Hamiltonian.

Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the coupled massive Thirring and the coupled Soler model to arbitrary nonlinear parameter κ and obtain exact solitary wave solutions in both cases. Remarkably, it turns out that in both the models, because of the conservation laws of charge and energy, the exact solutions we find seem to not depend on how we parameterize them, and the charge density of these solutions is related to the charge density of the single field solutions found earlier by a subset of the present authors. In both the models, a nonrelativistic reduction of the equations leads to the same conclusion that the solutions are proportional to those found in the one component field case.

In this work, we consider a ``reverse-engineering'' approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr\"odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to $\pm g \psi^{\ast}\psi$ gets added to the confining potential and $\pm g M$, where $M$ is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of $M$ (related to the number of particles in the BEC). Comparing the stability criteria from Derrick's theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass $M$ for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry $x\rightarrow-x$ assumed by Derrick's theorem.

In this work, we show the application of the ``inverse problem'' method to construct exact $N$ trapped soliton-like solutions of the nonlinear Schr\"odinger or Gross-Pitaevskii equation (NLSE and GPE, respectively) in one, two, and three spatial dimensions. This method is capable of finding the external (confining) potentials which render specific assumed waveforms exact solutions of the NLSE for both attractive ($g<0$) and repulsive ($g>0$) self-interactions. For both signs of $g$, we discuss the stability with respect to self-similar deformations and translations. For $g<0$, a critical mass $M_c$, or equivalently the number of particles, for instabilities to arise can often be found analytically. On the other hand, for the case with $g>0$ corresponding to repulsive self interactions which is often discussed in the atomic physics realm of Bose-Einstein condensates (BEC), the bound solutions are found to be always stable. For $g<0$, we also determine the critical mass numerically by using linear stability or Bogoliubov-de Gennes analysis, and compare these results with our analytic estimates. Various analytic forms for the trapped $N$-soliton solutions are discussed, including sums of Gaussians or higher-order eigenfunctions of the harmonic oscillator Hamiltonian.

Actin forms many cytostructural elements, including the backbone of striated muscle thin filaments. Our mechanistic understanding of most actin-dependent processes remains limited, partly due to difficulty with recombinant actin expression. While fully-functional actin cannot be produced in bacteria, it can be generated using baculovirus expression systems. Here, we created an additional tool for recombinant actin production, for hypothesis testing and for resolving the molecular properties and cellular effects of unique variants. Specifically, we engineered Drosophila that can express untagged actins exclusively in indirect flight muscles (IFMs). Act88F encodes sarcomeric IFM actin. Attempts to rescue IFM function (i.e. flight) in Act88F-nulls, by inserting transgenic Act88F (Act88FTG-WT) ectopically throughout the genome have failed, potentially due to ineffective cis/trans regulation of Act88FTG-WT expression. To circumvent these problems, we used CRISPR-editing and introduced an attP landing site directly into Act88F, to disrupt the endogenous gene and serve as a target for site-specific transgene insertion. attP-mediated disruption of Act88F yielded flightlessness and actin-free IFMs. Transformants expressing GFP or Act88FTG-WT, from the endogenous Act88F integration locus, demonstrated robust IFM-specific protein production and restored flight, respectively. Having established the expression system, we designed Drosophila mutants to test the roles of specific actin residues in tropomyosin/myosin-binding and nemaline myopathy pathogenesis. Both Act88FTG-R147Q and Act88F TG-F352Striggered IFM hypercontraction and impaired flight. Finally, we determined whether mammalian actin could be generated and observed high-level expression of human α-cardiac actin (ACTC1), which behaved indistinguishably from bovine ACTC1 in unregulated and regulated motility (IVM) assays. We are currently comparing IVM properties of IFM-purified vs. baculovirus/Sf12-purified ACTC1. Overall, our novel fly line permits transgenic actin expression in mature muscle fibers that are themselves amenable to structural and functional analyses, and serves as a cost-effective, perpetual source of ample protein for biophysical experimentation.

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the ‘mass’ (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. We observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M *( κ ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick’s theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M *( κ ) versus κ lies below the two curves found by Derrick’s theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the ‘frustrated’ blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d .

In this work, we study the existence and stability of constant density (flat-top) solutions to the Gross-Pitaevskii equation (GPE) in confining potentials. These are constructed by using the "inverse problem" approach which corresponds to the identification of confining potentials that make flat-top waveforms exact solutions to the GPE. In the one-dimensional case, the exact solution is the sum of stationary kink and antikink solutions, and in the overlapping region, the density is constant. In higher spatial dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed-out finite square well with minima also at the edges. When self-interactions are added, terms proportional to ±gψ^{*}ψ and ±gM with M representing the mass or number of particles in Bose-Einstein condensates get added to the confining potential and total energy, respectively. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M. Comparing the stability criteria from Derrick's theorem with Bogoliubov-de Gennes (BdG) analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. This is due to the emergence of symmetry-breaking instabilities that were detected by the BdG analysis and violate the symmetry x→-x assumed by Derrick's theorem.

The ACTC A331P HCM mutation is located on a subdomain 3, surface strand of actin that is vital for troponin-tropomyosin-based regulation of contraction. Previous studies found A331P ACTC mouse models were indistinguishable from control, and data generated with reconstituted bovine trabeculae suggested the variant reduced calcium sensitivity and tension, results at odds with those found for other HCM mutations. Here we employed a multidisciplinary approach to further examine the effects of the mutation across numerous levels of organization to better understand disease pathogenesis.

This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [ | ψ ( x , t ) | 2 + | ψ ( − x , t ) | 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick’s theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ , i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ ( x , t = 0) = ψ ⋆ ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.

We discuss the response of both moving and trapped solitary wave solutions of a two-component nonlinear Schrödinger system in 1 + 1 dimensions to an odd- PT external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of parameter values and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic PT -symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case are a good indicator for the onset of dynamic instabilities in the present setup.

This work focuses on the study of solitary wave solutions to a nonlocal, nonlinear Schrödinger system in 1+1 dimensions with arbitrary nonlinearity parameter κ. Although the system we study here was first reported by Yang (Phys. Rev. E, 98 (2018), 042202) for the fully integrable case κ=1, we extend its considerations and offer criteria for soliton stability and instability as a function of κ. In particular, we show that for κ <2 the solutions are stable whereas for κ >2 they are subject to collapse or blowup. At the critical point of κ=2, there is a critical mass necessary for blowup or collapse. Furthermore, we show there is a simple one-component nonlocal Lagrangian governing the dynamics of the system which is amenable to a collective coordinate approximation. To that end, we introduce a trial wave function with two collective coordinates to study the small oscillations around the exact solution. We obtain analytical expressions for the small oscillation frequency for the width parameter in the collective coordinate approximation. We also discuss a four collective coordinate approximation which in turn breaks the symmetry of the exact solution by allowing for translational motion. The ensuing oscillations found in the latter case capture the response of the soliton to a small translation. Finally, our results are compared with numerical simulations of the system.

Global Positioning System (GPS) position verification and legal traceability in Australia supports industry, trade, science and innovation and is trusted and recognized domestically and internationally. At the end of 2017, the Australia’s national datum was transitioned from the Geocentric Datum of Australia 1994 (GDA94) to the Geocentric Datum of Australia 2020 (GDA2020). As such, the datum for the legal traceability of GPS positions in Australia has also moved to GDA2020. This paper highlights the importance of legal metrology and measurement in terms of GPS positions in accordance with the National Measurement Act 1960 (Commonwealth of Australia). Here we provide an overview of the process of issuing the so-called ‘Regulation 13 Certificates’ for Continuously Operating Reference Stations (CORS) across Australia. The position verification methodology is detailed, including the quality control, metadata assurance, and dynamic management of the certificates as well as positional uncertainty determination of CORS with varying quality. A quality monitoring system of positions is also discussed along with how measurement traceability is ensured including short-term and long-term position monitoring schemes.

1.引言2018年,澳大利亚联邦政府承诺为Positioning Australia计划提供2.249亿澳元（合1.6亿美元）,以向所有澳大利亚人提供10 cm精度的精确定位服务,并进一步加速定位技术的升级与应用。与目前市场消费级别的5～10 m的定位精度相比,该计划将极大提升定位服务精度。从地理位置上讲,澳大利亚可借助全球或者区域星座获取高质量、准确以及高效的天基定位星座,包括美国（Global Positioning System, GPS）、俄罗斯（Global Navigation Satellite System, GLONASS）、欧盟（Galileo）、中国（北斗）、日本（Quasi-Zenith Satellite System,QZSS）和印度（Indian Regional Navigation Satellite System, IRNSS）的星座。

We present trapped solitary wave solutions of a coupled nonlinear Schrodinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex PT-symmetric potential. The Schrodinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.

The Gray-Scott model can be thought of as an effective theory at large spatiotemporal scales coming from a more fundamental theory valid at shorter spatiotemporal scales. The more fundamental theory includes a composite molecule which is trilinear in the molecules of the Gray-Scott model as was shown in the recent derivation of the Gray-Scott model from the master equation. Here we show that at a classical level, ignoring the fluctuations describable in a Langevin description, the late time dynamics of the more fundamental theory leads to the same pattern formation as found in the Gray-Scott model with suitable choices of the parameters describing the diffusion of the composite molecule.

Student evaluations of teaching (SETs) provide both summative and formative feedback. Although it is clear that SETs are used by administrators for summative purposes, such as providing data to support personnel decisions, it is uncertain how instructors use them for formative development such as to inform overall teaching practice. The objective of our study was to determine the frequency and nature of SET use for formative purposes, to explore the perception of SET utility to inform teaching practice, and to determine how perception of SET utility might be improved to enhance its use in a formative context. Participants were all biological sciences instructors at a large, research-intensive University. This research was conducted in two phases, using a combination of focus groups, interviews, and a survey to yield both qualitative and quantitative data. We found that while instructors generally perceive that SET feedback has formative utility, and that most instructors have used SET feedback for formative purposes at some point, there are many elements of SET administration that they are dissatisfied with, and they suggest several ways in which SETs could be improved (such as allowing in class time for SET administration or doing multiple administrations per semester) to yield more useable feedback that could inform their teaching. The results of this study can be used to further inform the ongoing debate about the role that SETs should play in higher education, as they demonstrate both the utility and concerns about using SETs for formative purposes.