Gravitational wave echoes from strange quark stars in the equation of state with density-dependent quark masses

According to the recent studies,the gravitational wave(GW)echoes are expected to be generated by quark stars composed of ultrastiff quark matter.The ultrastiff equations of state(EOS)for quark matter were usually obtained either by a simple bag model with artificially assigned sound velocity or by employing interacting strange quark matter(SQM)depicted by simple reparameterization and rescaling.In this study,we investigate GW echoes with EOSs for SQM in the framework of the equivparticle model with density-dependent quark masses and pairing effects.We conclude that strange quark stars(SQSs)can be sufficiently compact to possess a photon sphere capable of generating GW echoes with frequencies in the range of approximately 20 kHz.However,SQSs cannot account for the observed 72 Hz signal in GW170817 event.Furthermore,we determined that quark-pairing effects play a crucial role in enabling SQSs to satisfy the necessary conditions for producing these types of echoes.

About the Strange Tree Paradox and Possible Inconsistency of Set Theory

The existence of “strange trees” is proven and their paradoxical nature is discussed, due to which set theory is suspected of being contradictory. All proofs rely on informal set-theoretic reasoning, but without using elements that were prohibited in axiomatic set theories in order to overcome the difficulties encountered by Cantor’s naive set theory. Therefore, in fact, the article deals with the possible inconsistency of existing axiomatic set theories, in particular, the ZFC theory. Strange trees appear when uncountable cardinals appear.

Bulk viscosity of interacting magnetized strange quark matter

The bulk viscosity of interacting strange quark matter in a strong external magnetic field B m with a real equation of state is investigated.It is found that interquark interactions can significantly increase the bulk viscosity,and the magnetic field B_(m) can cause irregular oscillations in both components of the bulk viscosity,ξ||(parallel to B_(m))and ξ⊥(perpendicular to B_(m)).A comparison with non-interacting strange quark matter reveals that when B_(m) is sufficiently large,ξ⊥is more affected by interactions than ξ||.Additionally,the quasi-oscillation of the bulk viscosity with changes in density may facilitate the for-mation of magnetic domains.Moreover,the resulting r-mode instability windows are in good agreement with observational data for compact stars in low-mass X-ray binaries.Specifically,the r-mode instability window for interacting strange quark matter in high magnetic fields has a minimum rotation frequency exceeding 1050 Hz,which may explain the observed very high spin frequency of a pulsar with V=1122 Hz.

Symmetry energy of strange quark matter and tidal deformability of strange quark stars

Research performed during the past decade revealed an important role of symmetry energy in the equation of state(EOS)of strange quark matter(SQM).By introducing an isospin-dependent term into the quark mass scaling,the SQM stability window in the equivparticle model was studied.The results show that a sufficiently strong isospin dependence C_(I)can significantly widen the SQM region of absolute stability,yielding results that simultaneously satisfy the constraints of the astrophysical observations of PSR J1614-2230 with 1.928±0.017 Mand tidal deformability 70≤Λ_(1:4)≤580 measured in the event GW170817.With increasing C_(I),the difference between the u,d,and s quark fractions for the SQM inβ-equilibrium becomes inconspicuous for C>0,leading to small isospin asymmetryδ,and further resulting in similar EOS and structures of strange quark stars(SQSs).Moreover,unlike the behavior of the maximum mass of ud QSs,which varies with C_(I)depending on the sign of the parameter C,the maximum mass of the SQSs decreases monotonously with increasing CI.

一本有新意的微积分教材——评美国MIT教授Strang新编《CALCULUS》

微积分教材数以千计,每年都有不少新作问世,但有新意者却如凤毛麟角。91年夏我到美国参加第二届国际工业与应用数学大会(ICIAM’91),在大会展厅看到美国麻省理工学院(MIT)数学系教授、美国工业与应用数学学会(SIAM)教育委员会主席Strang教授刚刚出版的《CALCULUS》,很有特色,会后应邀访问MIT。

Strangeness to increase the density of finite nuclear systems in constraining the high-density nuclear equation of state

As the high-density nuclear equation of state(EOS) is not very well constrained, we suggest that the structural properties from the finite systems can be used to extract a more accurate constraint. By including the strangeness degrees of freedom, the hyperon or anti-kaon, the finite systems can then have a rather high-density core which is relevant to the nuclear EOS at high densities directly. It is found that the density dependence of the symmetry energy is sensitive to the properties of multi-K hypernuclei, while the high-density EOS of symmetric matter correlates sensitively to the properties of kaonic nuclei.

Effects of non-Newtonian gravity on the properties of strange stars

The properties of strange star matter are studied in the equivparticle model with inclusion of non-Newtonian gravity. It is found that the inclusion of non-Newtonian gravity makes the equation of state stiffer if Witten＇s conjecture is true. Correspondingly, the maximum mass of strange stars becomes as large as two times the solar mass, and the maximum radius also becomes bigger. The coupling to boson mass ratio has been constrained within the stability range of strange quark matter.

Controlling Strange Attractor in Dynamics

A nonlinear system which exhibits a strange attractor is considered, with the goal of illustrating how to control the chaotic dynamical system and how to obtain a desired attracting periodic orbit by the OGY control algorithm.

推荐G. Strang的两本数学教材

一、理工科大学数学教学内容改革已提上议事日程 1989年8月18日,钱学森在中国数学会数学教育与科研座谈会上作了题为《发展我国的数学科学》的讲话。讲话全文登载在《数学进展》杂志1990年(第19卷)第二期上。钱学森说:

GENERATION OF STRANGE ATTRACTOR IMAGES WITH GENETIC ALGORITHM

This paper presents a method for the generation of satisfied strange attractor images, which is based on the idea of Genetic Algorithm and is realized by adding a controller to a chaotic system.The principle of the method is introduced. Some problems which exist in genetic algorithm’s parameter optimization are discussed in detail. Finally, the effectiveness of the method for finding pretty strange attractors is verified. It is helpful to pattern design and works of arts and crafts.

MODEL SHIFT AND STRANGE ATTRACTOR ON MBIUS STRIP

A new model shift mapping was given in bilateral symbol space. It is topologically conjugate with the traditional shift mapping. Similar to Smale Horseshoe, a model was constructed correspondent to the model shift mapping, i.e., a class of mapping on Mbius strip was given. Its attractors' structure and dynamical behaviour were described.

A Gaussian Model for Anisotropic Strange Quark Stars

For studying the anisotropie strange quark stars, we assume that the radial pressure inside an anisotropic star can be obtained simply by isotropie pressure plus an additional Gaussian term with three free parameters （A, μ and X）. According to recent observations, a pulsar in a mass range of 1.97±0.04M has been measured. Hence, we take this opportunity to set the free parameters of our model. We fix X by applying boundary and stability conditions and then search the A - μ parameter space For a maximum mass range of 1.9M 〈 Mmax 〈 2.1M. Our results indicate that anisotropy increases the maximum mass M and also its corresponding radius R for a typical strange quark star. Furthermore, our model shows magnetic field and electric charge increase the anisotropy factor △. In fact, △ has a maximum on the surface and this maximum goes up in the presence of magnetic field and electric charge. Finally, we show that anisotropy can be more effective than either magnetic field or electric charge in raising maximum mass of strange quark stars.

Strange Attractor of KdV-Burgers Equation

The existence of isolated travelling wave solution for the KdV-Burgers equation is proved. It isshown that the strange attractor of the KdV-Burgers equation to isolated travelling wave is prevailing. Thechaotic phenomena in numerical computation might provide a reasonable interpretation of turbulence.

A Fat Strange Repeller

This article reports an observation on a fat strange repeller, which appears after a characteristic crisis observed in a kicked rotor subjected to a piecewise continuous force field. The discontinuity border in the definition range of the two-dimensional mapping, which describes the system, oscillates as the discrete time develops. At a threshold of a control parameter a fat chaotic attractor suddenly transfers to a fat transient set. The strange repeller, which appears after the crisis, is also a fat fractal. This is the reason why super-transience happens

Strange Attractors in the Resonance Interaction of Two-State Atoms with Single-Mode Laser Field

The resonance interaction of two-state atoms with single mode field is described theoretically by using the semi-classical theory and Jaynes-Cummings model. The nonlinear characteristics of this system are calculated by using FFT and Runge-Kutta methods. The chaotic strange attractors in this system are obtained from the numerical results.

SINAI BOWEN RUELLE MEASURE AND THE STRUCTURE OF STRANGE ATTRACTORS IN THE LAUWERIER MAP

In this paper,the Lauwerier map F a,b (x,y)=(bx(1-2y)+y,ay(1-y)) is considered for a=4 . This map possesses a nontrivial topologically transitive attractor Λ which is the closure of the unstable set of some hyperbolic fixed point. Periodic points are dense in Λ and all of them are hyperbolic with eigenvalues uniformly bounded away from 1 in norm. Moreover,any two periodic points are heteroclinically related (transversal intersection of their stable and unstable sets). The Sinai Bowen Ruelle measure supported on the attractor is constructed and its properties are studied.

JINKENITES——A STRANGE FOSSIL FROM EARLIEST CAMBRIAN IN W. HUBEI

A strange fossil described and illustrated in the present paper was collected by the writer in 1978 from the Huangshandong Member of the Lower Cambrian Tongying Formation in western Hubei. The material was preserved in greyish brown phosphoritic dolomites in association with elements of the Yangtze Micromolluscan Fauna, such as Tchangsichiton notabilus Yu and Sinuconus clypeus, Yu of Class Polyplacophora; Yangtzemerisma rarum Yu and Y.? cancellatum Yu of Class Merismoconchia; Yangtzeconus priscus Yu, Huangshandongoconus pileus Yu, Obtusoconus paucicostatus Yu, O. rostriptutea (Qian) and Spatuloconus rudis Yu of Class Monoplacophora; Bemella simplex Yu, Latouchlla of. memmorabilis Missarzhevsky, L. sanxiaesis Yu and L. lauta Yu of Class uncertain; Archaeospira ornata Yu, A. imbricata Yu and Cambrospira sinensis Yu of Class Gastropoda; Heraultipegma yunnanense He et Yang of Class Rostroconcbia: hyolithids and some other uncertain skeletal fossils. Although the systematic position of this peculiar fossil is unknown at present, it is inferred that this genus may be one of the typical primitive animal groups based on the characters of the shell and the spe cial spines. The shell is bilaterally symmetrical, elliptical in apical view; the dorsal side is roundly convex with three different forms of dorsal spines and several pairs of marginal spines on the anterior margin. Judged from the general morphological characters of the bilaterally symmetrical shell, these lower animals, generally speaking, have adapted themselves readily to different circumstances, and reduced resistance to any directional movement necessary for varied physiological activities. As to the function of the shell’s characteristics, the narrowly rounded side may serve as the anterior. Such a model of the body helps these animals go on with their benthonic creeping or swimming life. On the other hand, the dorsal spines are different from each other in shape, size, mode of arrangement and in number; especially, the end of the hook-shaped spines is generally curved outward, while the geniculate spines are oblique outward, and curved posteriorly all of a sudden. These structures of mechanism also provide us with the evidence that the narrowly rounded side serves as the anterior, while the opposite end as the posterior.It is of particular interest that this genus is somewhat similar to Phylum Mollusca, especially to the tryblidiids of Class Monoplacophora, in some morphological characters, such as: 1) the bilateral symmetry of the shell, 2) the outline elliptical in apical view and cap shaped in lateral view and 3) the dorsal side generally roundly convex. After careful study, it has been found that since this genus is strikingly different from monoplacopharans, may be it belongs to another interesting group of skeletal fossils. The reasons for this are: 1) in the former, there are many pairs of marginal spines on the anterior margin, while in monoplacophorans, no marginal spines can be seen; and 2) in this genus, the sculptures are different from each other in different areas, not only in shape and number, but also in the mode of arrangement, whereas in monoplacophorans, they are identical with each other in the same type and shape. Judged from the different forms of dorsal sculptures, this genus is comparatively similar to such uncertain shelly fossils as Lepidites Zhong, 1977 emend. Yu, 1987 and Xiadongoconus Yu, 1979 from the same horizon in the Yangtze Region of China, but differs from the latter two genera in the presence of marginal spines on the anterior margin. In addition, this new genus also differs from brachiopods and other skeletal fossils in the peculiar type of the shell. According to the above comparison, this genus is entirely different from all the classes of Phylum Mollusca, possibly representing another interesting group of skeletal fossils. It is impossible to determine the exact taxonomic position of this genus until more materials are available.

The Elliptic Flow of Multi-Strange Hadrons in [S_(NN)]^(1/2)= 200 GeV Au + Au Collisions at STAR

Azimuthal anisotropy, especially for the multi-strange hadrons, is expected to be sensitive to the dynamical evolution in the early stage of high energy nuclear collisions. In this paper we present the latest results of multi-strange hadron elliptic flow in Au ＋ Au collisions at √SNN=200GeV from the STAR experiment at RHIC. The number-of-quark scaling is evidenced with φ（ss） and Ω（sss） with highly statistical data, which shows strange quark collectivity at RHIC. The u2 of φ meson is found to be consistent with that of proton within statistical error bars at pw 〈 1 GeV/c.

Small glitches: the role of strange nuggets?

Pulsar glitches, i.e. the sudden spin-ups of pulsars, have been detected for most known pulsars.The mechanism giving rise to this kind of phenomenon is uncertain, although a large data set has been built.In the framework of the starquake model, based on Baym ＆ Pines, the glitch sizes（the relative increases of spin-frequencies during glitches） △Ω/Ω depend on the released energies during glitches, with less released energies corresponding to smaller glitch sizes. On the other hand, as one of the dark matter candidates,our Galaxy might be filled with so called strange nuggets（SNs） which are relics from the early Universe.In this case collisions between pulsars and SNs are inevitable, and these collisions would lead to glitches when enough elastic energy has been accumulated during the spin-down process. The SN-triggered glitches could release less energy, because the accumulated elastic energy would be less than that in the scenario of glitches without SNs. Therefore, if a pulsar is hit frequently by SNs, it would tend to have more small glitches, whose values of ？？/？ are smaller than those in the standard starquake model（with larger amounts of released energy）. Based on the assumption that in our Galaxy the distribution of SNs is similar to that of dark matter, as well as on the glitch data in the ATNF Pulsar Catalogue and Jodrell Bank glitch table, we find that in our Galaxy the incidences of small glitches exhibit tendencies consistent with the collision rates between pulsars and SNs. Further testing of this scenario is expected by detecting more small glitches（e.g.,by the Square Kilometre Array）.