Composite operator approach to dynamical mass generation in the (2 + 1)-dimensional Gross–Neveu model

Using a nonperturbative approach based on the Cornwall–Jackiw–Tomboulis (CJT) effective action [Formula: see text] for composite operators, the phase structure of the simplest massless [Formula: see text]-dimensional Gross–Neveu model is investigated. We have calculated [Formula: see text] in the first-order of the bare coupling constant [Formula: see text] and have shown that there exist three different specific dependences of [Formula: see text] on the cutoff parameter [Formula: see text], and in each case, the effective action and its stationarity equations have been obtained. The solutions of these equations correspond to the fact that three different masses of fermions can arise dynamically and, respectively, three different nontrivial phases can be observed in the model.

Dispersion and damping rate of Langmuir wave in space plasma with regularized Kappa distributed electrons

The dispersion of Langmuir wave (LW) in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory. The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a solar type III radio burst. It is found that the linear behavior of LW is greatly modified by the suprathermal index κ and the exponential cutoff parameter α. In the region κ<1.5, the damping rate of LW will be much larger than the one with Maxwellian distributed electrons. Hence, the nonlinear process of LW in low κ region may exhibit different properties in comparison with the one in large $\kappa$ region.

A Conceptual Model for the Origin of the Cutoff Parameter in Exotic Compact Objects

A Black Hole (BH) is a spacetime region with a horizon and where geodesics converge to a singularity. At such a point, the gravitational field equations fail. As an alternative to the problem of the singularity arises the existence of Exotic Compact Objects (ECOs) that prevent the problem of the singularity through a transition phase of matter once it has crossed the horizon. ECOs are characterized by a closeness parameter or cutoff, ϵ, which measures the degree of compactness of the object. This parameter is established as the difference between the radius of the ECO’s surface and the gravitational radius. Thus, different values of ϵ correspond to different types of ECOs. If ϵ is very big, the ECO behaves more like a star than a black hole. On the contrary, if ϵ tends to a very small value, the ECO behaves like a black hole. It is considered a conceptual model of the origin of the cutoff for ECOs, when a dust shell contracts gravitationally from an initial position to near the Schwarzschild radius. This allowed us to find that the cutoff makes two types of contributions: a classical one governed by General Relativity and one of a quantum nature, if the ECO is very close to the horizon, when estimating that the maximum entropy is contained within the material that composes the shell. Such entropy coincides with the Bekenstein–Hawking entropy. The established cutoff corresponds to a dynamic quantity dependent on coordinate time that is measured by a Fiducial Observer (FIDO). Without knowing the details about quantum gravity, parameter ϵ is calculated, which, in general, allows distinguishing the ECOs from BHs. Specifically, a black shell (ECO) is undistinguishable from a BH.

Nanoindentation Properties of 18CrNiMo7-6 Steel after Carburizing and Quenching Determined by Continuous Stiffness Measurement Method

In this work, the nanomechanical properties involving the indentation size effect (ISE) and yield strength of a surface-modified layer of 18CrNiMo7-6 steel after case hardening were investigated via nanoindentation experiments. The experimental results showed that the hardness increased with an increase in strain rate; the contact stiffness versus indentation depth curves take the form of upper convexity due to residual compressive stress relaxation. On the basis of the Ruiz-Moreno model, a modified model considering the cutoff parameter as a function of indentation depth was proposed. This model was able to better describe the ISE of the surface-modified layer. With the Hough transform error angle of 0.1° as the critical value (h0.1° is the corresponding depth), when h > h0.1°, the yield strength calculated by the Ma model started to disperse at the depth of h0.1°. These results provide useful insight into the local mechanical properties of 18CrNiMo7-6 steel after carburizing and quenching treatment.

Rotational behavior of thermally excited 56Fe, 58Fe and 60Fe isotopes

Thermal and rotational behaviors of neutron rich fp-shell isotopes such as [Formula: see text], [Formula: see text] and [Formula: see text] were analyzed microscopically within the framework of statistical theory of hot rotating nuclei (STHRN) for the angular momentum range (0–15)[Formula: see text] at excitation energy above 4[Formula: see text]MeV. Pair-breaking phenomenon and band-crossing phenomenon of Fe isotopes were discussed with and without the inclusion of BCS pairing. The STHRN method with BCS effect was extended to the Fe isotopes to determine the critical temperature [Formula: see text], where the pair-breaking phenomenon takes place and it is found to occur below [Formula: see text][Formula: see text]MeV. The observation of band-crossing phenomenon above the [Formula: see text] was explained without considering the effect of BCS pairing. The single particle energy levels were engendered from triaxially deformed Nilsson Hamiltonian. The outcomes of the present investigation on moment of inertia (MOI), back-bending phenomenon, spin cutoff parameter show a strong evidence of band-crossing phenomenon and it eventually led to a shape transition from spherical to noncollective oblate. Moreover, attention on separation energy of protons and neutrons reveals that the neutron pairs are responsible for band-crossing. STHRN method was able to reproduce results in good agreement with experiments and comparable with other theories such as projected shellmodel (PSM) and shellmodel Monte Carlo (SMMC) method.

The isospin strange asymmetry from the chiral effective theory

The proposal of the present work is to study the difference between the strange quark–antiquark amount in the proton and neutron. For this purpose, the possible nucleon–hyperon–kaon fluctuations are analyzed with the effective chiral theory. The small difference of particle masses is shown to be in the origin of this isospin asymmetry. The dependence of the results on the mass cutoff parameter and with the coupling constants is analyzed.

CUTTING SELF-SIMILAR SPACE-FILLING SPHERE PACKINGS

Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we prove that cutting along a random hyperplane leads in general to a packing with a fractal dimension of the one of the uncut packing minus one. Second, we find special cuts which can be constructed themselves by inversive geometry. Such special cuts have specific fractal dimensions, which we demonstrate by cutting a three- and a four-dimensional packing. The increase in the number of found special cuts with respect to a cutoff parameter suggests the existence of infinitely many topologies with distinct fractal dimensions.

Mass Renormalization in the Nelson Model

The asymptotic behavior of the effective mass meff(Λ) of the so-called Nelson model in quantum field theory is considered, where Λ is an ultraviolet cutoff parameter of the model. Let m be the bare mass of the model. It is shown that for sufficiently small coupling constant α of the model, meff(Λ)/m can be expanded as meff(Λ)/m=1+∑n=1∞an(Λ)α2n. A physical folklore is that an(Λ)=O(logΛ(n-1)) as Λ→∞. It is rigorously shown that 0<limΛ→∞a1(Λ)<C, C1≤limΛ→∞a2(Λ)/log⁡Λ≤C2 with some constants C, C1, and C2.