Our main objective is to explore the shape and geometry of the limiting curves of the structures that define the escape properties of a particle from a lobular domain in a multiwell potential. For this purpose, we examine the lower umbilical catastrophe [Formula: see text], for [Formula: see text], by calculating the Lyapunov orbit at the entrance of the lobular region as well as the set of incoming asymptotic trajectories to it and the set of successive intersections of this set with a proper surface of section.

In this paper, a nondestructive cavity-based scheme is proposed to achieve high-resolution bunch length measurement in the Super Tau-Charm Facility (STCF) transport line. By extracting the TM010 and TM020 mode signals excited by the beam within a single pillbox cavity, a beam spectrum can be obtained to deduce the Root-Mean-Square (RMS) bunch length. This scheme is more spatially compact compared to the traditional method using double cavities. In this study, the basic principles of the cavity-based bunch length measurement method are explained, the monitor layout is introduced, and the design methods for the cavity and electronics are described. A prototype cavity was machined. Offline tests demonstrate that the eigenmodes in the cavity meet the design requirements and can be used for the bunch length measurements. Based on the online signal characteristics of the Cavity Beam Position Monitors (CBPMs) and the beam parameters of the STCF, the performance of this measurement method is evaluated. For picosecond-level bunches in the STCF transport line, this scheme can provide a bunch length measurement resolution of 233.5 fs at 1.5 nC.

In this paper, we study the quantum-corrected Schwarzschild AdS black hole surrounded by quintessence matter in two folds: its thermal quantities and shadows. For this purpose, first, we present a detailed analysis of the influences of the quintessence matter field on Hawking temperature, mass, Gibbs free energy, and specific heat functions. Then, we examine the shadows by following Carter’s approach. We find that the shadow radius value takes smaller values for greater quintessence state parameter values. On the other hand, we see that the shadow radius takes greater values for greater values of the normalization parameter. Finally, in a brief section, we discuss the energy emission rate and show that the Gaussian-type plots’ peak values are also affected by the quintessence matter field parameters.

Modeling the worldsheets along the trajectory (a string) of a point particle (a 0-brane) as two timelike surfaces in 3-subspace of Minkowskian spacetime, respectively, the work aims at analyzing the topological structures of these two worldsheets along the trajectory of the point particle from the view point of singularity theory. Different from the regular curves, the traveling trajectory (modeled as framed timelike curve) of the particle is allowed to be singular, two worldsheets are generated by the traveling trajectories of the particle. As applications of singularity theory, we classify the singularities of these two worldsheets along the traveling trajectory of the particle. Using the approach of the unfolding theory in singularity theory, we find two new geometric invariants which are useful for characterizing the local topological structures of singularities of these two worldsheets along the particle. It is revealed that there exist cuspidal edge type and swallowtail type of singularities for these two worldsheets under the appropriate conditions of geometric invariants. Meanwhile, it is also pointed out that the types of singularities of these two worldsheets have a close relationships to the order of contacts between these two worldsheets and two timelike planes, respectively. Finally, some examples are presented to interpret our theoretical results.

The Super Tau-Charm Facility (STCF) is a proposed dual-ring electron–positron collider in China, designed to operate at a center-of-mass energy (CME) range of 2–7[Formula: see text]GeV with symmetric beam energies. The collider aims for a luminosity exceeding [Formula: see text] at the beam energy of 2.0[Formula: see text]GeV. This work presents the preliminary lattice design for the STCF collider ring, specifically optimized for the 2.0[Formula: see text]GeV beam energy. To improve the nonlinear dynamics performance, the optimization of lattice is carried out by adjusting the strengths of sextupole and octupole magnets following the tuning of phase advances.

This paper is related to the dynamics of stellar structure under the influence of modified gravity (in particular [Formula: see text] gravity, where T is associated with a torsion scalar). We contemplate non-static plane geometry equipped with fluid dissipation in the form of diffusion limit. The suitable variables to handle the analysis are explored. To comprehend the dynamics of the system, we acquire the dynamical equations with the aid of Bianchi identities. We calculate the Taub mass for our structure and develop the relations of mass in the form of collapsing velocity, derivative of proper radial, and time. The scalars to comprehend the evolution and structure are explored for non-static plane geometry. These scalars have a novel existence for this structure. We find that the homogeneous expansion and homologous ways of evolution interrelate with each other. We perform the investigation for two cases that is dissipative and non-dissipative. The nature of the fluid in the dissipative case is shear and geodesic. We calculate the variety of solutions in this case. The analysis is concluded by analyzing the stability of the vanishing [Formula: see text] constraint.

The Super Tau-Charm Facility (STCF) is a next-generation positron–electron collider experiment, designed to study various physics topics in the tau-charm energy region. The designed peak luminosity of STCF is [Formula: see text], which is almost two orders of magnitude higher than the current tau-charm factory, BESIII. To implement the offline data processing tasks, as well as tackling the great challenge posed by the huge data volume, the offline software of STCF (OSCAR) is designed to implement the detector simulation, digitization, calibration, reconstruction as well as to provide a common platform for data analysis. This paper presents the status and progress of the OSCAR system, including the design, implementation as well as the preliminary performance of the core software, detector simulation, digitization and background mixing and reconstruction algorithms for all sub-detectors.

In this paper, we propose a nonlocal extension of the mimetic dark matter model based on the FALVA implementation of fractional calculus. Our primary objective to explore how certain properties of dark matter can be modeled within the FALVA framework rather than formulate a phenomenological model. We begin by constructing the action functional of the cosmological extension of the mimetic dark model and deriving the nonlinear equations of motion in the general case. Next, we focus on a fractional-power homogeneous mimetic dark field with an exponential expansion factor. We derive the equation of motion for the lapse field and obtain its general solution. Analytical solutions are then obtained for small time intervals and arbitrary values of the fractionality parameter. These solutions enable us to establish the physical line element of spacetime, incorporating the mimetic dark matter field. From this line element, we derive the Ricci tensor, Ricci scalar, and geodesic equations.

We analyze a recent calculation of the energy levels of some quantum-mechanical models derived from the so-called generalized Cornell potential. We argue that the authors obtained essentially the same spectrum for potentials with considerably different spectra. We show that the authors obtained negative eigenvalues in the case of a positive-definite potential. The reason is due to the approximation used in the solution of the Schrödinger equation. We point out that the omission of the sum over the rotational degrees of freedom in the canonical partition function leads to incomplete expressions for the thermodynamic functions.

The Super Charm-Tau (SCT) Factory project is actively developing in Budker Institute of Nuclear Physics, Novosibirsk. This paper presents the SCT Detector offline software framework Aurora components, status and future prospects.