Munirah Aali Alotaibi , Azza M. Algatheem , Shreen El–Sapa
{"title":"Magneto-slip interaction in the migration of two rigid spheres in infinite couple stress fluid","authors":"Munirah Aali Alotaibi , Azza M. Algatheem , Shreen El–Sapa","doi":"10.1016/j.cjph.2025.01.044","DOIUrl":"10.1016/j.cjph.2025.01.044","url":null,"abstract":"<div><div>This study investigates the motion of two rigid spheres, arranged linearly, immersed in an incompressible couple stress fluid subjected to a magnetic field. The spheres, possessing unique forms, traverse the axis linking their centers at varying velocities. The analysis begins with an incompressible analytical examination of a couple stress fluid around an axially symmetric particle. A general solution for the flow of couple stress fluid around the two moving spheres is then developed using the superposition principle. The boundary collocation method is implemented to the surfaces of the two spheres to satisfy the boundary conditions. Numerical estimations of the dimensionless drag forces exerted on the spheres are provided in tables and graphs. The results demonstrate that a reduction in the Hartmann number or an elevation in couple stress viscosity results in an augmentation of the dimensionless drag force on each sphere. Also, the slippage parameter is more significant on the hydrodynamic drag force. Additionally, the results are compared with earlier studies on specific scenarios, including the movement of a single rigid sphere across an infinite magnetic media, the flow of viscous fluids, and the behavior of Couple stress fluid without magnetohydrodynamics (MHD) within two concentric spheres (Madasu et al., 2019) and with magnetic field as Kashyap et al. (2019). Also, the results agree with the most recent work, the migration of two hard spheres that translate within an infinite couple stress fluid influenced by the magnetic field (El-Sapa and Alotaibi, 2024).</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"95 ","pages":"Pages 173-189"},"PeriodicalIF":4.6,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shanshan Yang , Qiong Sheng , Mingqing Zou , Qian Zheng
{"title":"Fractal study on spontaneous imbibition characteristics of the non-Newtonian fracturing fluids in porous media with rough surfaces","authors":"Shanshan Yang , Qiong Sheng , Mingqing Zou , Qian Zheng","doi":"10.1016/j.cjph.2025.02.011","DOIUrl":"10.1016/j.cjph.2025.02.011","url":null,"abstract":"<div><div>To explore the spontaneous imbibition characteristics of non-Newtonian fluid in tight reservoirs, the fractal model of spontaneous imbibition of non-Newtonian fluid in porous media with rough surface is established in the article. The function expressions of imbibition height and imbibition mass in the process of imbibition in rough porous media are derived. Through sensitivity analysis, it is found that the increase in roughness and tortuosity makes the imbibition height decrease. In addition, the increase of tortuosity fractal dimension and porosity makes the imbibition mass increase, while the increase of power law index and roughness makes the imbibition resistance increase, so the imbibition quality decreases. In addition, this paper verifies the rationality and correctness of the model by comparing it with the experimental data and other existing models.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"95 ","pages":"Pages 1155-1166"},"PeriodicalIF":4.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143887394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Debabrata Das , Kuppalapalle Vajravelu , Rishi Raj Kairi
{"title":"Irreversibility estimation in electroosmotic MHD shear thinning nanofluid flow through a microchannel with slip-dependent zeta potentials","authors":"Debabrata Das , Kuppalapalle Vajravelu , Rishi Raj Kairi","doi":"10.1016/j.cjph.2025.01.043","DOIUrl":"10.1016/j.cjph.2025.01.043","url":null,"abstract":"<div><div>Shear-thinning nanofluid is extremely useful in medical diagnostics and engineering devices for controlling transport processes. This involves using microchannel flow under pressure-driven and electromagnetic forces. Moreover, a combined model of non-Newtonian fluid provides a versatile framework to accurately simulate or predict fluid behavior in various industrial, scientific, and biomedical applications. In this study, we investigate the heat and mass transfer of a shear-thinning nanofluid as it flows through a vertical microchannel with permeable walls, with electrokinetic effects, slip-dependent zeta potential, and convective boundary conditions. To characterize the shear-thinning behavior, a combined Casson-Williamson non-Newtonian fluid model is utilized. The fluid motion comprises a fusion of pressure-induced and electroosmotic forces, influenced by thermal radiation and slip-dependent zeta potential. Using the MATLAB bvp4c solver, we highlight the effect of electroosmotic flow (EOF) for the nanofluid by solving the non-dimensional differential equations resulting from the governing equations. Graphical representations of important engineering quantities are used to identify the critical influential factors. Our results show that thinner electric double layers (EDLs) amplify the influence of the Casson-Williamson parameters on the temperature profile. Additionally, the impact of the Williamson parameter at <span><math><mrow><mi>η</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></math></span> on concentration distribution is enhanced for higher electroosmotic parameters. We observe that heat transfer plays a minimal role in entropy generation in the core region of the channel but increases exponentially near the walls. Conversely, entropy production due to mass transfer is negligible away from the walls. However, the Casson parameter <span><math><mi>β</mi></math></span> favors entropy production throughout the channel cross-section, while the Williamson parameter <span><math><mi>Γ</mi></math></span> shows the reverse effect in both halves of the channel. This study has significant implications for the advancement of electro-magneto-mechanical devices and the improvement of efficiency and functionality, particularly in micro-scale thermal management applications.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"95 ","pages":"Pages 118-139"},"PeriodicalIF":4.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jingxu Zhang , Guodong Li , Hepeng Pan , Xiangkun Chen
{"title":"Multi-scroll expansion of 3D and 4D Jerk systems and its DSP implement","authors":"Jingxu Zhang , Guodong Li , Hepeng Pan , Xiangkun Chen","doi":"10.1016/j.cjph.2025.02.002","DOIUrl":"10.1016/j.cjph.2025.02.002","url":null,"abstract":"<div><div>The multi-scroll chaotic systems have significant potential in practical applications. By introducing control functions and modifying variable dimensionality, we achieve both single-scroll and dual-scroll expansions in the three-dimensional Jerk system, with Lyapunov exponent analysis confirming that the system retains its chaotic nature. The distribution of equilibrium points and the bifurcation diagrams further illustrate the scroll generation mechanism. By extending the system to four dimensions, we validate the feasibility of multi-scroll expansion in this higher-dimensional framework through numerical simulations. Furthermore, the DSP implementation demonstrates that the constructed multi-scroll system offers flexibility in both the number and arrangement of scrolls, thus laying a foundation for further research and practical engineering applications.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"94 ","pages":"Pages 627-649"},"PeriodicalIF":4.6,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Galal M. Moatimid, Mona A.A. Mohamed, Khaled Elagamy
{"title":"Insights in the nonlinear instability of an annular jet inclosing an electrified Eyring–Powell viscoelastic fluid","authors":"Galal M. Moatimid, Mona A.A. Mohamed, Khaled Elagamy","doi":"10.1016/j.cjph.2025.02.001","DOIUrl":"10.1016/j.cjph.2025.02.001","url":null,"abstract":"<div><div>The exploration of nonlinear instability in an annular jet containing an electrified Eyring–Powell viscoelastic fluid (EPF) is essential in industrial and biological applications, enhancing fluid control and optimizing intricate processes. The current model is pervaded by the impact of a uniform axial electric field (EF). Additionally, the flow is assumed to flow in a permeable media. The study explores the impact of EF effects on jet breakup and stability, providing new criteria of instability thresholds and deformation patterns. It is well known that the implementation of an axial EF may produce multiple instability modes, potentially leading to breakdown or formation of complex structures within the annular jet. The viscous potential theory (VPT) is exploited to abbreviate the mathematical intricacy. The nonlinear methodology foundations in solving the linear governing partial differential equations (PDEs) of motion are resolved through the applicable nonlinear boundary conditions (BCs) to yield coupled nonlinear ordinary differential equations (ODEs) that judge the interface displacements. The study scrutinizes the surface tensions (STs) in a broad context, together with the symmetric and anti-symmetric perturbation modes. He's frequency formulation (HFF) strengthens the innovative non-perturbative approach (NPA). It is employed to transform conventional nonlinear ODEs into linear ones. A set of non-dimensional physical parameters is accomplished. The validation between the nonlinear and linear ODEs is constructed by consuming the Mathematica Software (MS). A series of graphs are provided to illustrate the impact of various non-dimensional physical parameters in the stability configuration. The efficacy and accuracy of the NPA are validated by some figures and tables. It is found that the structure becomes gradually stable as the permeability of the medium; the inner and outer radii grow. Simultaneously, it converts fewer stable with the rise of the electric Bond number and the non-Newtonian parameter. Consistent decay behavior is seen in the temporal histories of the periodic solutions, suggesting that the outcomes are stable. Additionally, the associated phase plane curves are shown in a variety of plots that resemble symmetric closed curves and feature spiral curves pointing inward at a single point.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"94 ","pages":"Pages 751-788"},"PeriodicalIF":4.6,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stagnation slip flow of ternary hybrid nanofluid over an exponentially shrinking/Stretching sheet with joule heating, MHD, and thermal radiation effects","authors":"Farah Nadzirah Jamrus , Iskandar Waini , Umair Khan , Anuar Ishak","doi":"10.1016/j.cjph.2025.01.042","DOIUrl":"10.1016/j.cjph.2025.01.042","url":null,"abstract":"<div><div>The stagnation point flow of a ternary hybrid nanofluid (THNF) over a sheet that stretches or shrinks exponentially is investigated in this study. The primary goal is to assess the implication of Joule heating, magnetohydrodynamics (MHD), thermal radiation, and boundary slips on the physical quantities and flow profiles. Besides, attention is also given to the occurrences of multiple solutions in this fluid flow situation. The continuity, momentum and energy equations that described the fluid flow problem are converted into a simpler form of ordinary differential equations (ODEs). This is achieved by applying a similarity transformation, which make the equations easier to solve. Solving the resulting equations using the bvp4c solver in MATLAB software yields results that are analyzed and illustrated through a combination of tables and graphical representations. The analysis reveals that, for a shrinking sheet, an increase in Joule heating reduces the heat transfer. Similarly, a higher thermal slip factor leads to a decreased heat transfer rate in this case. In contrast, parameters such as magnetic field strength, radiation, velocity slip and suction contribute to enhancing the heat transfer rate of THNF. Furthermore, the results indicate that the THNF used in this study exhibits a better heat transfer rate compared to nanofluid (NF) and hybrid nanofluid (HNF). Notably, a shrinking sheet is observed to exhibit multiple solutions when the shrinking parameter falls within a defined range, specifically when <span><math><mrow><mi>λ</mi><mo>></mo><msub><mi>λ</mi><mi>c</mi></msub></mrow></math></span>. By scrutinizing the analysis of stability, the first solution (upper solution) was determined to be consistently stable and applicable in real-world settings. These findings offer insightful information into the optimization of heat transfer processes in nanofluid-based systems under complex flow conditions. However, these findings apply only to a THNF mixture of alumina, copper, and titania. THNFs may have different flow dynamics and thermal properties depending on the mixtures of nanoparticles.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"94 ","pages":"Pages 518-539"},"PeriodicalIF":4.6,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jia-Heng Ni , Wang-Chu Lv , Dong-Xuan Zhang , Liang Bin , Yu Zhang , Yang Yu , Qi-Ping Su , Chui-Ping Yang
{"title":"Deterministic preparation of GHZ entangled states with multiple superconducting qutrits in circuit QED","authors":"Jia-Heng Ni , Wang-Chu Lv , Dong-Xuan Zhang , Liang Bin , Yu Zhang , Yang Yu , Qi-Ping Su , Chui-Ping Yang","doi":"10.1016/j.cjph.2025.01.040","DOIUrl":"10.1016/j.cjph.2025.01.040","url":null,"abstract":"<div><div>Over the past decade, several works have been devoted to the generation of entangled states with superconducting (SC) qubits. Recently, attention has shifted to the generation of entangled states with SC qutrits (three-level quantum systems). However, the existing works are limited to the preparation of a maximally entangled EPR pair with two SC qutrits and a Greenberger-Horne-Zeilinger (GHZ) entangled state of three SC qutrits. We here propose a simple method to create a GHZ entangled state of multiple SC qutrits in circuit QED. The GHZ state is generated by employing multiple SC qutrits coupled to a microwave cavity or resonator. This proposal essentially operates by the cavity-qutrit dispersive interaction. By using this proposal, a GHZ state with an arbitrary number of SC qutrits can, in principle, be created. Since only a coupler cavity is utilized, the circuit hardware resources are minimized. No auxiliary energy levels of the qutrits are needed for the entangled state preparation. The GHZ state can be created deterministically. As an example, we analyze the experimental feasibility of preparing a GHZ state of five SC transmon qutrits within current circuit QED technology. This proposal is universal and can be extended to create a GHZ entangled state of multiple matter qutrits (e.g., atomic qutrits, quantum-dot qutrits, NV-center qutrits, Magnon qutrits, and various SC qutrits) by employing multiple natural or artificial three-level atoms coupled to a microwave or optical cavity.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"94 ","pages":"Pages 504-517"},"PeriodicalIF":4.6,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Zeeshan Gul , M. Sharif , Adeeba Arooj , Baiju Dayanandan
{"title":"Impact of non-metricity and matter source on the geometry of anisotropic spheres","authors":"M. Zeeshan Gul , M. Sharif , Adeeba Arooj , Baiju Dayanandan","doi":"10.1016/j.cjph.2024.11.021","DOIUrl":"10.1016/j.cjph.2024.11.021","url":null,"abstract":"<div><div>This paper delves into the impact of extended symmetric teleparallel theory on anisotropic compact stellar structures. The explicit field equations were formulated by considering a minimum model of this extended gravity. Basically, the Darmois junction conditions are used to determine the unknown constants of metric coefficients. We explore some significant properties of the compact stars under consideration to check their viable existence in this modified framework. The Tolman–Oppenheimer–Volkoff equation assess the equilibrium state of the compact stars. Moreover, the stability analysis is defined by using methods based on sound speed (related to how disturbances propagate in the star) and adiabatic index (related to the thermodynamic behavior of the star). We find that the proposed compact stars in the <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> gravity are physically viable and stable.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"93 ","pages":"Pages 256-270"},"PeriodicalIF":4.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143168056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shu Chen , Qingji Zeng , Haisheng Wu , Pin Zhong , Jing Wang , Junmin Liu , Huapeng Ye , Dianyuan Fan , Shuqing Chen
{"title":"Off-axis dispersion-managed metasurface for routing orbital angular momentum mode and wavelength multiplexing channels","authors":"Shu Chen , Qingji Zeng , Haisheng Wu , Pin Zhong , Jing Wang , Junmin Liu , Huapeng Ye , Dianyuan Fan , Shuqing Chen","doi":"10.1016/j.cjph.2024.11.011","DOIUrl":"10.1016/j.cjph.2024.11.011","url":null,"abstract":"<div><div>Offering the strengths of mode orthogonality and physical independence from wavelength dimension, optical orbital angular momentum (OAM) modes hold immense potential for enhancing communication capacity through multi-dimensional channel multiplexing. Although methods using angle-separated gratings have seen advances in multi-dimensional (de)multiplexing, routing these multiplexed channels is impeded by the resultant mode-wavelength dispersion resulting from Bragg diffraction of grating. This induces not only multi-level mode conversion but also confined wavelength separation scope, posing obstacles in spatial reallocation of both OAM modes and wavelengths for routing channels. To tackle these issues, we propose a wavelength-dependent multi-foci transformation solution for OAM mode-wavelength routing that utilizes an off-axis dispersion-managed metasurface. Incorporated with composite lens phases and helical modulations, the metasurface enables the precise manipulation of OAM mode-wavelength dispersion upon multi-foci Fourier transform without multi-level diffraction, facilitating both efficient mode conversion and versatile wavelength separation. Harnessing the multi-dimensional independence, this approach establishes a high-dimensional linear mapping relationship among OAM modes, wavelengths, and spatial positions, thereby achieving the routing of mode-wavelength hybrid channels. In a proof-of-concept simulation, we demonstrated the successful routing of 20 channels with five OAM modes and four wavelengths across four depth planes, with the average channel crosstalk below -15.2 dB. Additionally, 16-ary quadrature amplitude modulation signals carried by these 20 multiplexed channels were successfully routed, and the bit-error-rates approach 1 × 10<sup>-5</sup>. Our method shows flexibility in spatial reallocation of both OAM modes and wavelengths, as further explored by altering the number of routing channels and their spatial positions, which may provide new insights for advanced OAM-based optical communications.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"93 ","pages":"Pages 46-55"},"PeriodicalIF":4.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Transition temperature to the Bose-Einstein condensation of spin polarized tritium, hydrogen, and 4He gases using the second virial coefficient","authors":"B.R. Joudeh","doi":"10.1016/j.cjph.2024.12.011","DOIUrl":"10.1016/j.cjph.2024.12.011","url":null,"abstract":"<div><div>In this study, the transition temperature to the Bose-Einstein condensation of spin-polarized tritium (T↓), hydrogen (H↓), and <sup>4</sup>He gases is obtained based on the second virial coefficient. The computations are performed using the Silvera triplet-state potential and HFDHE2 potential for spin-polarized atomic hydrogen isotopes and <sup>4</sup>He gas, respectively. The thermophysical properties of these Bose systems are computed, including the Helmholtz free energy, entropy, the acoustic virial coefficient, and the second virial coefficient. Large negative values of the second virial coefficient and the acoustic virial coefficient are obtained, reflecting the strong overall attraction of inter-bosonic potential, which gives an indication of the onset of condensation at very low temperatures. At the transition temperature, the stable minimum of the Helmholtz free energy is an indicator of the sort of Bose-Einstein condensation (BEC). As a consequence, the system made a transition to a higher-order state, which is recognized with BEC and explored. The transition temperature is shifted towards a lower value than for the ideal Bose gas.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"93 ","pages":"Pages 318-327"},"PeriodicalIF":4.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}