Radial Excitation Research Articles

Doubly heavy tetraquark bound and resonant states

We calculate the energy spectrum of the S-wave doubly heavy tetraquark systems, including the QQ(′)q¯q¯, QQ(′)s¯q¯, and QQ(′)s¯s¯ (Q(′)=b, c and q=u, d) systems within the constituent quark model. We use the complex scaling method to obtain bound states and resonant states simultaneously, and the Gaussian expansion method to solve the complex-scaled four-body Schrödinger equation. With a novel definition of the root-mean-square radii, we are able to distinguish between meson molecules and compact tetraquark states. The compact tetraquarks are further classified into three different types with distinct spatial configurations: compact even tetraquarks, compact diquark-antidiquark tetraquarks, and compact diquark-centered tetraquarks. In the I(JP)=0(1+) QQq¯q¯ system, there exists the D*D molecular bound state with a binding energy of −14 MeV, which is the candidate for Tcc(3875)+. The shallow B¯*B¯ molecular bound state is the bottom analog of Tcc(3875)+. Moreover, we identify two resonant states near the D*D* and B¯*B¯* thresholds. In the JP=1+ bbq¯q¯(I=0) and bbs¯q¯ systems, we obtain deeply bound states with a compact diquark-centered tetraquark configuration and a dominant χ3¯c⊗3c component, along with resonant states with similar configurations as their radial excitations. These states are the QCD analog of the helium atom. We also obtain some other bound states and resonant states with “QCD hydrogen molecule” configurations. Moreover, we investigate the heavy quark mass dependence of the I(JP)=0(1+) QQq¯q¯ bound states. We strongly urge the experimental search for the predicted states. Published by the American Physical Society 2024

The ground states of hidden-charm tetraquarks and their radial excitations

Inspired by the great progress in the observations of charmonium-like states in recent years, we perform a systematic analysis about the ground states and the first radially excited states of qcq¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$qc\\bar{q}\\bar{c}$$\\end{document} (q = u/d and s) tetraquark systems. Their mass spectra, root mean square (r.m.s.) radii and radial density distributions are predicted within the framework of relativized quark model. By comparing with experimental data, some potential candidates for hidden-charm tetraquark states are suggested. For qcq¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$qc\\bar{q}\\bar{c}$$\\end{document} (q = u/d) system, if Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(3900)$$\\end{document} is supposed to be a compact tetraquark state with JPC=1+-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=1^{+-}$$\\end{document}, Z(4430) can be interpreted as the first radially excited states of Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(3900)$$\\end{document}. Another broad structure Zc(4200)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(4200)$$\\end{document} can also be explained as a partner of Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{c}(3900)$$\\end{document}, and it arise from a higher state with JPC=1+-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=1^{+-}$$\\end{document}. In addition, theoretical predictions indicate that the possible assignments for X(3930), X(4050) and X(4250) are low lying 0++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0^{++}$$\\end{document} tetraquark states. As for the scs¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$sc\\bar{s}\\bar{c}$$\\end{document} system, X(4140) and X(4274) structures can be interpreted as this type of tetraquark states with JPC=1++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=1^{++}$$\\end{document}, and X(4350) can be described as a scs¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$sc\\bar{s}\\bar{c}$$\\end{document} tetraquark with JPC=0++\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{PC}=0^{++}$$\\end{document}. With regard to qcs¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$qc\\bar{s}\\bar{c}$$\\end{document} (q = u/d) system, we find two potential candidates for this type of tetraquark, which are Zcs(4000)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{cs}(4000)$$\\end{document} and Zcs(4220)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_{cs}(4220)$$\\end{document} structures. The measured masses of these two structures are in agreement with theoretical predictions for the 1+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1^{+}$$\\end{document} state.

Experimental Road to a Charming Family of Tetraquarks...and Beyond

Abstract Discovery of the X(3872) meson in 2003 ignited intense interest in exotic (neither $q\bar{q}$ nor $qqq$) hadrons, but a $c\bar{c}$ interpretation of this state was difficult to exclude. An unequivocal exotic was discovered in the $Z_c(3900)^+$ meson—a charged charmonium-like state. A variety of models of exotic structure have been advanced but consensus is elusive. The grand lesson from heavy quarkonia was that heavy quarks bring clarity. Thus, the recently reported triplet of all-charm tetraquark candidates—$X(6600)$, $X(6900)$, and $X(7100)$—decaying to $J/\psi\,J/\psi$ is a great boon, promising important insights. We review some history of exotics, chronicle the road to prospective all-charm tetraquarks, discuss in some detail the divergent modeling of $J/\psi\,J/\psi$ structures, and offer some inferences about them. These states form a Regge trajectory and appear to be a family of radial excitations. A reported, but unexplained, threshold excess could hint at a fourth family member. We close with a brief look at a step beyond: all-bottom tetraquarks.

First radial excitations of baryons in a contact interaction: Mass spectrum

We compute masses of twenty positive parity first radial excitations of spin-1/2 and spin-3/2 baryons composed of u, d, s, c, and b quarks in a quark-diquark picture within a contact interaction model. These excitations comprise of two elements; one characterized by a zero in the Faddeev amplitude, representing a radial excitation of the quark-diquark system and the other marked by a zero in the diquark’s Bethe-Salpeter amplitude, corresponding to an intrinsic excitation of the diquark correlation. Wherever possible, we compare our results with other models and/or experiment. We verify that the masses obtained through our model conform to the spacing rules for all the baryons studied, whether light or heavy and whether of spin-1/2 or spin-3/2. The computed masses do not just offer a guide to the future experimental searches but also compare well with the existing candidates for the possible radial excitations of some heavy baryons. Published by the American Physical Society 2024

Toroidal Alfvén eigenmodes excited by energetic electrons in EAST low-density Ohmic plasmas

Abstract Operation in the quiescent regime with abundant trapped energetic electrons (EEs) has been achieved during the current flattop in EAST low-density Ohmic plasmas. This was facilitated by increasing the electron density to a specified level and subsequently reducing it slowly, resulting in the accumulation of a sufficient number of trapped EEs within the energy range of 150–250 keV. During the phase of decreasing electron density, toroidal Alfvén eigenmodes (TAEs) were observed to be excited by these EEs, with frequencies falling within the range of about 100–300 kHz. The experimental parameters were carefully set to satisfy the resonance conditions for TAE excitation by EEs, aligning well with predictions from ideal MHD theory. Statistical analysis indicated different density dependencies between the frequencies of TAEs and the Alfvén frequencies, due to their different radial excitation positions. The radial positions of the TAEs were found to be influenced by the energy distribution and the evolution of trapped EEs, which in turn were affected by the decay rate of electron density and loop voltage. Measurements of Hard X-rays (HXR) confirmed an energy distribution characterized by a “bump-on-tail” shape, with the TAEs observed near the energy bump. Theoretical considerations also demonstrate the possibility that the e-TAE can be driven unstable under this experiment condition even if the mode does not rotate in the electron-diamagnetic drift direction.

Cascade Ξ0 baryon spectroscopy in the relativistic framework of an independent quark model

The spectroscopy of Ξ0 is performed within the relativistic framework of independent quark model. The equal mixture of scalar and vector components in the potential having Martin-like form is considered for the confinement. With the suitable potential parameters for Ξ0, mass spectra for high radial and orbital excitation is calculated. The experimentally observed values of the ground-state magnetic moment, branching ratios, and asymmetry parameters for radiative weak decays, Ξ0→Λ0+γ0 and Ξ0→Σ0+γ0 are obtained to validate the model. The spin parity of experimentally known resonances like Ξ(1530), Ξ(1820), and Ξ(2030) are confirmed through the Regge trajectories in (J,M2) plane. The spin parity of Ξ(1950), Ξ(2130), and Ξ(2250) are predicted using those Regge trajectories. The radiative decay width and magnetic moment of first resonance is also predicted. Published by the American Physical Society 2024

Open charm tetraquarks in broken SU(3)F symmetry

Prompted by a recent lattice QCD calculation, we review the SU(3) light quark flavor structure of charmed tetraquarks with spin 0 diquarks. Fermi statistics forces the three light quarks to be in the representation 3¯⊗3¯=3⊕6¯. This agrees with the weak repulsion in the 15 of the 3⊗8 in D¯K scattering studied on the lattice. We analyze the 3⊕6¯ multiplet broken by the strange quark mass and determine the five independent masses from the known masses of diquarks. The mass of Ds0*(2317) is predicted within 50 MeV accuracy. The recently observed D¯s−−(2900) and D¯s0(2900), likely part of a I=1 multiplet, with flavor composition c¯q¯q′s, and X0(2900), an isosinglet with flavor composition c¯s¯ud, fit naturally in a 3⊕6¯ structure as the first radial excitations. We discuss also the decay modes of Ds0*(2317), of the radial excitations and of the predicted particles. Published by the American Physical Society 2024

Nonlinear resonant analyses of graphene oxide powder reinforced hyperelastic cylindrical shells containing flowing-fluid

The resonant responses are investigated for the graphene oxide powder reinforced hyperelastic cylindrical (GOPRHC) shells containing flowing-fluid, and the shells are subjected to the radial harmonic excitations. Employing the improved Donnell's nonlinear shell theory, Halpin-Tsai model, hyperelastic constitution relation, velocity potential theory and Lagrange equation, the governing equation of motions are obtained for the GOPRHC shells containing flowing fluid. The amplitude frequency and force amplitude curves are presented by using the harmonic balance method and the pseudo-arc length continuation method. The effects of three distributions of the GOP, weight fraction of the GOP and fluid velocity on the natural frequency for the GOPRHC shells are discussed. The influences of different parameters on the dynamical responses for the GOPRHC shells containing flowing-fluid are conducted, including the external excitation, weight fraction of the GOP, fluid velocity and structural parameters. The results show that the GOPRHC shells with Hypere-X distribution containing flowing-fluid have the largest frequency. The super-harmonic resonance responses appear and present the synchronization effects with the primary resonant responses in the GOPRHC shells containing flowing-fluid. The increases of external excitations, fluid velocity, weight fraction of the GOP and structural parameters enrich the resonant responses for the GOPRHC shells. Compared to the fluid-filled hyperelastic cylindrical shells, the existence of the flowing-fluid makes the GOPRHC shells more prone to the chaotic vibrations. The hysteresis phenomena of chaotic vibrations occur in the GOPRHC shells containing flowing-fluid.

Ground states and first radial excitations of vector tetraquark states with explicit P-waves via QCD sum rules* *Supported by the National Natural Science Foundation of China (12175068)

In this study, we chose the diquark-antidiquark type four-quark currents with an explicit P-wave between the diquark and antidiquark pairs to study the ground states and first radial excitations of the hidden-charm tetraquark states with quantum numbers . We also obtained the lowest vector tetraquark masses and made possible assignments of the existing states. There indeed exists a hidden-charm tetraquark state with at an energy of approximately 4.75 GeV as the first radial excitation that accounts for the BESIII data.

First radial excitations of mesons and diquarks in a contact interaction

We present a calculation for the masses of the first radially excited states of 40 mesons and diquarks made up of u, d, s, c, and b quarks, including states that contain one or both heavy quarks. To this end, we employ a combined analysis of the Bethe-Salpeter and Schwinger-Dyson equations within a self-consistent and symmetry-preserving vector-vector contact interaction. The same set of parameters describes ground and excited states of mesons and their diquark partners. The wave function of the first radial excitation contains a zero whose location is correlated with an additional parameter dF which is a function of dressed quark masses. Our results satisfy the equal spacing rules given by the Gell-Mann Okubo mass relations. Wherever possible, we make comparisons of our findings with known experimental observations as well as theoretical predictions of several other models and approaches including lattice quantum chromodynamics, finding a very good agreement. We report predictions for a multitude of radial excitations not yet observed in experiments. Published by the American Physical Society 2024

Searching for the first radial excitation of the Δ(1232) in lattice QCD

We present a lattice QCD analysis of the Δ-baryon spectrum, with the goal of finding the position of the 2s radial excitation of the Δ(1232) ground state. Using smeared three-quark operators in a correlation matrix analysis, we report masses for the ground, first and second excited states of the J P = 3/2+ spectrum across a broad range of mπ2 . We identify the lowest lying state as being a 1s state, consistent with the well known Δ(1232). The first excitation is identified as a 2s state, but is found to have a mass of approximately 2.15 GeV on our ∼3 fm lattice, which does not appear to be associated with the Δ(1600) resonance in a significant manner. We also report on the spin-1/2 and odd-parity states accessible via our methods. The large excitation energies of the radial excitations provide a potential resolution to the long-standing missing baryon resonances problem.

A parametric study on the effect of ring damper on wheel damping

Ring dampers have been widely applied to control vibration of, and noise from, train wheels due to the simple structure, negligible impact on operational safety and potential in vibration and noise reduction. Yet, parameters affecting the vibro-acoustic performance of a ring-damped wheel are not adequately studied. In this paper, the apparent modal damping ratios of a ring-damped wheel are studied numerically using a finite element model allowing for frictional nonlinearity. Studied parameters include the impact force used to excite the wheel, the preload in the ring, the friction coefficient of the interface between the ring and the wheel, and the number of rings installed. Several findings can be drawn from the study. Installation of one or two rings to the wheel does not change the resonance frequencies (they are also termed the modal frequencies of the ring-damped wheel) but reduces the resonance responses by generating extra damping to the modes. The ring is more effective for radial excitation than for axial excitation. At most modal frequencies, damping with double rings is higher than with a single ring. Although there are few modal frequencies at which the modal damping ratios are reduced by installing the second ring, the average damping ratio with two rings is much higher, by a factor of 2.37 for axial excitation and 1.73 for radial excitation, than that with a single ring. The apparent damping of the ring-damped wheel increases with the level of the impact force, especially for radial excitation. There is an optimal combination of the preload in the ring and the frictional coefficient with which damping induced by the ring is the highest. Besides, the average damping ratios of the modes above 2000 Hz are proposed to be an indicator of the effectiveness of the performance of a ring-damped wheel in noise reduction.

Nonlinear vibrations of porous-hyperelastic cylindrical shell under harmonic force using harmonic balance and pseudo-arc length continuation methods

The resonant responses are investigated for the porous-hyperelastic Mooney–Rivlin cylindrical shell subjected to a radial harmonic excitation. Considering the higher-order shear deformation theory (HSDT), fourth-order strain-displacement relations are derived, which include the radial geometric imperfections varying along the thickness direction. Using the porous-hyperelastic Mooney–Rivlin constitution relation and Lagrange equation, the differential governing equations of motion are obtained for the porous-hyperelastic cylindrical shells. The resonant conditions are presented and the accuracy of the mathematical models is verified. The harmonic balance and pseudo-arc length continuation methods are used to obtain the amplitude-frequency and forced-amplitude curves. The stability of the solutions is analyzed by Floquet theory. The effects of the external excitation amplitudes, structure parameters and porosity infill parameters on the linear frequencies, amplitude-frequency responses and force-amplitude responses are discussed for the imperfect porous-hyperelastic cylindrical shells. The results show that the linear frequencies of the porous-hyperelastic cylindrical shells increase obviously as the uniform and sigmoid function porosity parameters reach the certain values. The increase of the structure parameters enhances the response amplitudes of the first-order mode and minified response amplitudes of the second-order mode. The decreasing porosity ratios weaken the softening nonlinear behaviors of the porous-hyperelastic cylindrical shells. With the changes of the external excitation amplitudes and structure parameters, the motion of the porous-hyperelastic cylindrical shell indicates that the synchronous vibrations occur with the period and chaotic vibrations alternately.

Optimization of PMSM for EV based on Vibration and Noise Suppression

The key to the suppression of vibration and noise for PMSM is the optimization of electromagnetic excitation force. The method of motor body optimization can effectively reduce the radial excitation force of the motor, so as to suppress the vibration and noise of the motor. Firstly, the stator structure of the motor is optimized with V-shape skew slot based on the analytical modeling of the radial electromagnetic excitation force of the motor. Then, the structural parameters of the motor that affect the electromagnetic excitation force of the motor are determined, and the average torque, torque ripple and radial electromagnetic excitation force generated by tangential electromagnetic excitation force are taken as the optimization objectives. The sensitivity analysis and classification of the structural parameters of the motor are carried out. The multi-objective genetic algorithm and response surface method are combined to optimize the structural parameters of the motor. Finally, the finite element analysis, modal analysis, multi-speed vibration and noise analysis of the optimized motor are done. The performance comparisons before and after optimization have proved that the peak of equivalent sound power level have decreased by 8.65% after the optimization of V-shaped skewed slot structure. After the optimization of structural parameters, the power level of permanent magnet synchronous motor has been reduced by 9.22%. For the vibration noise caused by resonance and the main frequency of vibration noise harmonics, the suppression effects are also better than those of V-shape skewed slots optimization, and the ERPL values are reduced by 9.22% and 10.12%, respectively, in two cases. The results show that the vibration and noise of permanent magnet synchronous motor are effectively suppressed.

The two-body strong decays of the fully-charm tetraquark states

We study the hadronic coupling constants in the two-body strong decays of the fully-charm tetraquark states with the J^{PC}=0^{++}, 1^{+-}, and 2^{++} via the QCD sum rules based on rigorous quark-hadron duality. Then we obtain the hadronic coupling constants and partial decay widths therefore total decay widths, which support assigning the X(6552) as the first radial excitation of the scalar tetraquark state. And other predictions can be used to diagnose exotic states in the future.

Mass spectra, Regge trajectories and decay properties of heavy-flavour mesons

In this article, we study the mass spectra, Regge trajectories and decay properties of heavy-flavour mesons $Q\bar{Q}$ $(Q=c,b)$ within a non-relativistic quark model. The spin hyperfine interaction is used to get the prediction for the heavy-meson masses for radial and orbital excitations. By using the radial and orbital excitations, we construct Regge trajectories for the heavy-mesons in the $(J,M^2)$ and $(n,M^2)$ plane and find their slopes and intercepts. We have computed leptonic, photonic and gluonic decay widths of heavy flavour mesons with and without QCD correction factor. We have compared our results of masses as well as decay widths with other theoretical and lattice QCD predictions for each states. Moreover, the known experimental results are also reasonably close to our predicted results.

RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES

Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective gas permeability of the adjacent finger seals annulus considering the gas slip effect and the temperature change is established, and a finite element calculation method of the two-way thermo-mechanical coupling for the finger seal is proposed. The results show that the solid-phase thermal conductance decreases with the increase of the scale coefficient. When the axial pressure difference is greater than 0.4[Formula: see text]MPa, the rotor speed is greater than 11,000[Formula: see text]r/min, the radial displacement excitation is [0.03[Formula: see text]mm, 0.09[Formula: see text]mm], and the temperature is less than 600[Formula: see text]K, the gas-phase thermal conductance between the finger seal and the rotor shows an increasing trend. The gas-phase thermal conductance of the finger seal and the rotor is always the main position under different working conditions. Under different fractal dimensions, the solid-phase thermal conductance gradually occupies the dominant position. Temperature has a certain effect on the effective gas permeability, and fractal dimension, scale coefficient, and axial pressure difference have less effect on the effective gas permeability. At an axial pressure difference of 0.08[Formula: see text]MPa, the numerical calculation results of the two-way thermo-mechanical coupling calculation method for finger seal are closer to the experimental results, with a maximum error rate of 1.96%. The above results further improve the theoretical research system of the heat transfer characteristics of the finger seal.

Nonlinear Forced Vibration of Functionally Graded Graphene-Reinforced Composite (FG-GRC) Laminated Cylindrical Shells under Different Boundary Conditions with Thermal Repercussions

The key aim of this research is to develop an analytical model for the forced vibration of graphene-reinforced composite (GRC) cylindrical shell with viscous damping and thermal environment effects under several boundary conditions. The prescribed mechanical and thermal characteristics of the GRC layer are evaluated utilizing a micromechanical extended Halpin–Tsai technique. Further, the governing equations are determined to be grounded on the shear deformation theory (SDT) with the von Kármán-form in terms of the geometric nonlinearity. The basic nonlinear partial differential governing equation is transformed into a nonlinear ordinary differential equation with the Galerkin-based method. The resulting ordinary governing differential equations are systematically solved based on the multiple scales scheme in order to obtain the nonlinear forced vibration frequency response of the laminated GRC cylindrical shell in the presence of damping impact and subjected to multiple boundary conditions. The validation of the obtained expressions is achieved by comparing them with the available literature data where the comparison revealed a clear consistency between them. Moreover, a parametric investigation is provided to illustrate the impacts of the distribution of graphene layers, elastic foundation coefficients, damping ratios, temperature effects and dimensionless radial excitation amplitude on the forced nonlinear amplitude-frequency ratio responses for a functionally-graded graphene-reinforced composite (FG-GRC)-layered cylindrical shells. The analytical outcomes indicate that the different distribution types of graphene, elastic foundation coefficients, damping ratios, temperature, and radial excitation parameters have a noteworthy impact on the frequency–amplitude behaviors of an FG-GRC-layered cylindrical shell. In addition, the new insights gained from this research might contribute to a deeper understanding of the nonlinear forced vibration responses in subsequent analysis and design techniques for giving appropriate benchmark findings.

Formula omitted] from QCD Laplace sum rule

We present a review of our recent works on heavy-light exotic states, with new compact integrated expressions of the spectral functions at lowest order (LO) of perturbative (PT) QCD and up to d=6 condensates of the Operator Product Expansion (OPE). Including higher order (HO) PT corrections, which we have estimated by assuming the factorization of the molecule/four-quark spectral functions, we evaluate masses and couplings with the Laplace sum rules (LSR) and finite energy (FESR) QCD spectral sum rules (QSSR) approaches. Our optimal results based on stability criteria are summarized and compared with experimental candidates and some LO QSSR results. We conclude that, our predicted spectra, do not confirm that the X(5568) is a pure molecule or a four-quark state. The masses of the XZ observed states are compatible with (almost) pure JPC=1+±,0++ molecule or/and four-quark states. The SU3 corrections on the meson masses are tiny: ≤10% (respectively ≤3%) for the c (respectively b)-quark channel but can be large for the couplings (≤20%). We expect that the resonance near the D−K+ threshold can be originated from the 0+(D−K+) molecule and/or D−K+ scattering. The X0(2900), XJ(3150) (if J = 0), X1(2900) and the XJ(3350) (if J = 1) can emerge from a minimal mixing model between tetramoles and first radial excitation. The Zc(3900,4025,4040,4430) and Zcs(3983) spectra are well reproduced by the molecules and tetramoles candidates, or radial excitation.

Resonance X(7300): excited 2S tetraquark or hadronic molecule χc1χc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c1}\\chi _{c1}$$\\end{document}?

We explore the first radial excitation X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document} of the fully charmed diquark-antidiquark state X4c=ccc¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}=cc{\\overline{c}}{\\overline{c}} $$\\end{document} built of axial-vector components, and the hadronic molecule M=χc1χc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}} =\\chi _{c1}\\chi _{c1}$$\\end{document}. The masses and current couplings of these scalar states are calculated in the context of the QCD two-point sum rule approach. The full widths of X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document} and M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} are evaluated by taking into account their kinematically allowed decay channels. We find partial widths of these processes using the strong couplings gi∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_i^{*}$$\\end{document} and Gi(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i^{(*)}$$\\end{document} at the X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document}(M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} )-conventional mesons vertices computed by means of the QCD three-point sum rule method. The predictions obtained for the parameters m=(7235±75)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=(7235 \\pm 75)~ \ extrm{MeV}$$\\end{document}, Γ=(144±18)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =(144 \\pm 18)~\ extrm{MeV}$$\\end{document} and m~=(7180±120)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{m}}=(7180 \\pm 120)~\ extrm{MeV}$$\\end{document}, Γ~=(169±21)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{\\Gamma }}=(169 \\pm 21)~\ extrm{MeV}$$\\end{document} of these structures, are compared with the experimental data of the CMS and ATLAS Collaborations. In accordance to these results, within existing errors of measurements and uncertainties of the theoretical calculations, both the excited tetraquark and hadronic molecule may be considered as candidates to the resonance X(7300). Detailed analysis, however, demonstrates that the preferable model for X(7300) is an admixture of the molecule M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} and sizeable part of X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document}.