This paper is devoted to the structural stability of a transonic shock passing through a flat nozzle for two-dimensional steady compressible flows with an external force. We first establish the existence and uniqueness of one-dimensional transonic shock solutions to the steady Euler system with an external force by prescribing suitable pressure at the exit of the nozzle when the upstream flow is a uniform supersonic flow. It is shown that the external force helps to stabilize the transonic shock in flat nozzles and the shock position is uniquely determined. Then we are concerned with the structural stability of these transonic shock solutions when the exit pressure is suitably perturbed. One of the new ingredients in our analysis is to use the deformation-curl decomposition to the steady Euler system developed by Weng and Xin [Sci. Sinica Math., 49 (2019), pp. 307–320] to deal with the transonic shock problem.

We address a recently posed question: ‘Why Do So Many Astronomy (and Astrobiology) Discoveries Fail to Live Up to the Hype?’ We expand it to cover hype within science in general. Our answer relies on working definitions of hype and skin in the game, as applied to research science, and a game theory model for the stability of cooperative science. Low skin in the game allows internal feedbacks, within the research science community, to initiate increased hype and a drift toward structural instability. The instability leads to the deterioration of cooperative equilibria, which further enhances hype. Along the drift, the number of results hyped as breakthroughs will increase and more claims will fail to live up to the hype. This can lead to the public perception that science is moving backwards and a shift in the perception of what scientists, and science, values. Although a hype instability can be initiated by external nudges, a bigger role is played by the internal dynamics of the system, i.e. the collective of working scientists. Corrections for a drift toward instability should, likewise, focus on internal structure. Proposed external shifts on how research is disseminated will add restrictions to a system that can do more harm than good.

A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by Hartman in 1960 for operators on finite-dimensional spaces. The general case was independently obtained by Palis and Pugh around 1968. We will exhibit a class of examples of structurally stable operators that are not hyperbolic, thereby showing that the converse of the above-mentioned result is false in general. We will also prove that an invertible operator on a Banach space is hyperbolic if and only if it is expansive and has the shadowing property. Moreover, we will show that if a structurally stable operator is expansive, then it must be uniformly expansive. Finally, we will characterize the weighted shifts on the spaces $c_{0}(\mathbb{Z})$ and $\ell _{p}(\mathbb{Z})$ ($1\leq p<\infty$) that satisfy the shadowing property.

Antiperovskite materials are of high research interest because of their unusual physical properties and technological applications. Here, we report the structural stability and transport properties of Sr3AsN from first-principles study. The calculated equilibrium lattice parameters are in good agreement with the available data. We find that Sr3AsN is mechanically, energetically and dynamically stable at ambient conditions. Our calculated electronic structure indicates that it is a direct band gap semiconductor, with a band gap value ∼1.2 eV. Sr-4d and N-2p orbitals predominantly contribute to the formation of the direct band gap. The calculated Seebeck coefficient of Sr3AsN is high (298 μV/K at 300 K), while the lattice thermal conductivity is comparatively low (1.73 W/m K). The considerable mass difference between Sr, As, and N gives rise to an intense phonon scattering that results in such low lattice thermal conductivity. Our calculated maximum thermoelectric figure of merit (ZT) is 0.75 at 700 K, indicating that it is a potential material for thermoelectric device applications.

The crystal structure of synthetic Ni-rich tourmaline with a nickel content of 18.96 wt.% NiO (a = 15.890(2), c = 7.1815(8) Å) has been refined to R = 3.1% using single-crystal X-ray diffraction data. It has been shown that Ni is distributed not only over the Y, but also over the Z sites according to the ideal formula Na(Ni22+Al)(Al5Ni2+)(Si6O18)(BO3)3(OH)4. Based on bond valences and charge balance analysis it has been shown that this composition corresponds to the stable disordered member of the solid solution series NaAl3Al6(Si6O18)(BO3)3(O)3(OH) NaNi32+Al6(Si6O18)(BO3)3(OH)4.

Taking into consideration available structural data on Me2+ (Ni, Cu, Co, Fe, Mn)-rich tourmalines, cation-size mismatch and bond-valence calculations we assume that there are no structural constraints precluding occurrence of these cations in both octahedral sites. Divalent transitional metal-rich tourmalines have not been found in Nature probably due to the insufficient concentration of these elements in B-rich geological systems.

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

We study the structural stability of a problem in a porous medium when the density of saturating liquid is a nonlinear function of temperature and an internal heat source is present. We prove a convergence result for the Forchheimer coefficient. That is to say, when λ → 0, the solution of the non-isothermal flow in a porous medium of the Forchheimer type, see (1.1), can converge to the solution of the equivalent Darcy type.