Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component ma...Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.展开更多
Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary m...Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary mixed glass former(MGF)system 35Na_(2)O–10V_(2)O_(5)–(55-x)P_(2)O_(5)–xNb_(2)O_(5)(x=0–40,mol%).The dielectric parameters,including the dielectric strength and dielectric loss,are determined from the frequency and temperature-dependent complex permittivity data,revealing a significant dependence on the Nb2O5 content.The transition from a predominantly phosphate glass network(x<10,region I)to a mixed niobate–phosphate glass net-work(10≤x≤20,region II)leads to an increase in the dielectric parameters,which correlates with the observed trend in the direct-cur-rent(DC)conductivity.In the predominantly niobate network(x≥25,region III),the highly polarizable nature of Nb5+ions leads to a fur-ther increase in the dielectric permittivity and dielectric strength.This is particularly evident in Nb-40 glass-ceramic,which contains Na_(13)Nb_(35)O_(94) crystalline phase with a tungsten bronze structure and exhibits the highest dielectric permittivity of 61.81 and the lowest loss factor of 0.032 at 303 K and 10 kHz.The relaxation studies,analyzed through modulus formalism and complex impedance data,show that DC conductivity and relaxation processes are governed by the same mechanism,attributed to ionic conductivity.In contrast to glasses with a single peak in frequency dependence of imaginary part of electrical modulus,M″(ω),Nb-40 glass-ceramic exhibits two distinct contributions with similar relaxation times.The high-frequency peak indicates bulk ionic conductivity,while the additional low-fre-quency peak is associated with the grain boundary effect,confirmed by the electrical equivalent circuit(EEC)modelling.The scaling characteristics of permittivity and conductivity spectra,along with the electrical modulus,validate time-temperature superposition and demonstrate a strong correlation with composition and modification of the glass structure upon Nb_(2)O_(5) incorporation.展开更多
The results of an experimental study of long-term relaxation of the photoelectret state of polycrystalline CdTe:(Ag, Cu, Cd) and Sb<sub>2</sub>Se<sub>3</sub>:Se films with an anomalous photovol...The results of an experimental study of long-term relaxation of the photoelectret state of polycrystalline CdTe:(Ag, Cu, Cd) and Sb<sub>2</sub>Se<sub>3</sub>:Se films with an anomalous photovoltaic property are presented. In such films, the residual photovoltage is caused by the separation of photocarriers by the built-in electrostatic field of the near-surface region of space charges and their asymmetric capture by deep levels of impurities or complexes, including impurity atoms and intrinsic defects, both in the bulk and on the surface of crystal grains. It has been shown that in activated films, a two-step exponential temporary relaxation of the initial photovoltage of the order of V<sub>APV</sub> ≈ (500-600) V is detected, and only 10% of it experiences long-term relaxation (t ≈ 100-120 min).展开更多
The complex permittivity of baijiu varies with frequency,and dielectric spectroscopy has been used to evaluate the quality.To simplify the analysis and reduce the number of the parameters,a dielectric relaxation model...The complex permittivity of baijiu varies with frequency,and dielectric spectroscopy has been used to evaluate the quality.To simplify the analysis and reduce the number of the parameters,a dielectric relaxation model is often used to fit the permittivity data.However,existing fitting methods such as the least squares and particle swarm optimization methods are often computationally complex and require preset initial values.Therefore,a simpler calculation method of the relaxation parameters considering the geometric characteristics of the permittivity spectrum is proposed.It is based on the relationship between the Cole-Cole relaxation parameters and the Cole-Cole diagram,which is fitted by a geometric method.First,the concepts of the Cole-Cole parameters and the diagram are introduced,and then the process of obtaining the parameters from the complex permittivity measurement data is explained.Taking baijiu with 56%alcohol by volume(ABV)as an example,the fitting is better than the least squares method and similar to the particle swarm optimization.This method is then used for the parameter fitting of baijiu with ABV of 42-52%,and the average error is less than 1%,demonstrating its wider applicability.Finally,a prediction model is used for baijiu with 53%ABV,and the error is only 1.51%.Hence,the method can be applied to the measurement of ABV of baijiu.展开更多
Objective:This study aimed to determine the effect of the relaxation breathing exercise(RBE)on fatigue and cortisol levels among Indonesian women with gynecological cancer undergoing chemotherapy.Methods:This pilot st...Objective:This study aimed to determine the effect of the relaxation breathing exercise(RBE)on fatigue and cortisol levels among Indonesian women with gynecological cancer undergoing chemotherapy.Methods:This pilot study consecutively recruited 44 gynecological cancer patients to receive RBE(22)or usual care(22).Cortisol level was measured before and after completion of the intervention(day 8).Fatigue was measured using the Piper Fatigue Scale(PFS).Anxiety and depression were assessed using the Hospital Anxiety and Depression Scale(HADS)at the baseline days of the study for days 1,4,and 8.The obtained data were analyzed using Fisher’s exact test,the independent t-test,and the Mann-Whitney U test.Results:There were significant increases in cortisol levels within the groups,either the intervention or control groups,respectively(P-value=0.0003 and 0.001).Despite there being no statistical significance between the intervention and control groups,there were noticeable differences in the cortisol levels,indicating the extreme increase in cortisol levels in the control group(Median[IQR1-IQR3]:2.30[0.99-9.09];Min-Max:0.43-23.38)compared with the intervention group(Median[IQR1-IQR3]=2.97[1.26-5.18];Min-Max=0.39-6.91).Conclusions:RBE helps prevent a significant increase in cortisol levels that can alleviate fatigue for women with gynecological cancer.Further research was recommended to compare several intervention modalities for fatigue and cancer-related symptom management based on cortisol level changes.展开更多
Objective:To systematically analyze the research status and application of progressive muscle relaxation training(PMRT)in the nursing field in China,and provide a reference basis for scientific research in this field....Objective:To systematically analyze the research status and application of progressive muscle relaxation training(PMRT)in the nursing field in China,and provide a reference basis for scientific research in this field.Methods:The bibliometric method was adopted in“progressive muscle relaxation training”or“PMRT,”and“nursing.”The established database was included in the China National Knowledge Infrastructure(CNKI)and the Wanfang Medical Network.The relevant articles in the Chinese Science and Technology Periodical Database(VIP)were analyzed.Results:A total of 169 literatures were included.The journals,years,and regions of literature publication were uneven,mainly originating from the eastern region(43.19%),and listed the application of progressive muscle relaxation training in the field of nursing in China.Intervention literature information was mainly dominated by experimental studies(97%).Conclusion:The related research and application of progressive muscle relaxation training in nursing in China is increasing,but there is a lack of objective evaluation of outcome indicators and a short intervention period.Further research should be conducted in the future to effectively guide the development of PMRT in the field of nursing in China.展开更多
Objective:To explore the effects of progressive muscle relaxation training on anxiety,depression,and quality of life in patients with cerebral small vessel disease(CSVD).Methods:Sixty-one patients with CSVD in the Dep...Objective:To explore the effects of progressive muscle relaxation training on anxiety,depression,and quality of life in patients with cerebral small vessel disease(CSVD).Methods:Sixty-one patients with CSVD in the Department of Neurology of a tertiary hospital were divided into an observation group(28 patients)and a control group(33 patients)by lottery method.The control group received conventional nursing care,while the observation group received progressive muscle relaxation training interventions in addition to the conventional care.The Hamilton Anxiety Scale(HAMA),the Hamilton Depression Scale(HAMD),and the Stroke-Specific Quality of Life Scale(SS-QOL)were used to compare the effects before the intervention,7 days after the intervention,and 30 days after the intervention.Results:Over time,at different time points after the intervention,the anxiety and depression scores of patients with CSVD in the observation group were significantly lower than those in the control group(P<0.05).The quality of life scores were significantly higher in the observation group compared to the control group(P<0.05),and these differences were statistically significant.Conclusion:Progressive muscle relaxation training can improve anxiety and depression in patients with cerebral small vessel disease and can effectively enhance their quality of life.展开更多
NMR relaxation analysis provides a unique and non-invasive probe of fluid dynamics within porous materials,and may be applied to the interpretation of a wide variety of material and interfacial characteristics.Here,we...NMR relaxation analysis provides a unique and non-invasive probe of fluid dynamics within porous materials,and may be applied to the interpretation of a wide variety of material and interfacial characteristics.Here,we report two-dimensional^(1)H T_(1)-T_(2)relaxation correlation measurements of a range of three-carbon adsorbates(1-propanol,2-propanol and propanoic acid)imbibed within the mesoporous metal oxide gamma-alumina.Our data,acquired across field strengths of 2 MHz,12.7 MHz and 43 MHz,clearly reveal two populations in each measurement,identified as the alkyl and hydroxyl moieties of each adsorbate.These results expand the range of materials in which such functional group resolved relaxation is known to occur,and demonstrate the clear persistence of such phenomena using a range of typical benchtop NMR systems employed to study fluid-saturated porous media.展开更多
How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficien...How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.展开更多
Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical per...Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.展开更多
We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions.The structural study shows that the symmetry changes from one polar point group(mm2)at room t...We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions.The structural study shows that the symmetry changes from one polar point group(mm2)at room temperature to another polar point group(m)at low temperature.Magnetic studies and theory calculations illustrate that the vortex distribution of magnetic dipoles in the triangular dysprosium clusters forms a toroidal magnetic moment.Interestingly,the analysis of AC magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes,corresponding to the Raman,Orbach,and QTM relaxation pathways,respectively.The sum of three modified Debye functions is successfully used to describe the multiple relaxation behavior.展开更多
基金Project supported by the National Key R&D Program of China (Grant No.2021YFB3501300)the National Natural Science Foundation of China (Grant Nos.91963201 and 12174163)the 111 Project (Grant No.B20063)。
文摘Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.
文摘Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary mixed glass former(MGF)system 35Na_(2)O–10V_(2)O_(5)–(55-x)P_(2)O_(5)–xNb_(2)O_(5)(x=0–40,mol%).The dielectric parameters,including the dielectric strength and dielectric loss,are determined from the frequency and temperature-dependent complex permittivity data,revealing a significant dependence on the Nb2O5 content.The transition from a predominantly phosphate glass network(x<10,region I)to a mixed niobate–phosphate glass net-work(10≤x≤20,region II)leads to an increase in the dielectric parameters,which correlates with the observed trend in the direct-cur-rent(DC)conductivity.In the predominantly niobate network(x≥25,region III),the highly polarizable nature of Nb5+ions leads to a fur-ther increase in the dielectric permittivity and dielectric strength.This is particularly evident in Nb-40 glass-ceramic,which contains Na_(13)Nb_(35)O_(94) crystalline phase with a tungsten bronze structure and exhibits the highest dielectric permittivity of 61.81 and the lowest loss factor of 0.032 at 303 K and 10 kHz.The relaxation studies,analyzed through modulus formalism and complex impedance data,show that DC conductivity and relaxation processes are governed by the same mechanism,attributed to ionic conductivity.In contrast to glasses with a single peak in frequency dependence of imaginary part of electrical modulus,M″(ω),Nb-40 glass-ceramic exhibits two distinct contributions with similar relaxation times.The high-frequency peak indicates bulk ionic conductivity,while the additional low-fre-quency peak is associated with the grain boundary effect,confirmed by the electrical equivalent circuit(EEC)modelling.The scaling characteristics of permittivity and conductivity spectra,along with the electrical modulus,validate time-temperature superposition and demonstrate a strong correlation with composition and modification of the glass structure upon Nb_(2)O_(5) incorporation.
文摘The results of an experimental study of long-term relaxation of the photoelectret state of polycrystalline CdTe:(Ag, Cu, Cd) and Sb<sub>2</sub>Se<sub>3</sub>:Se films with an anomalous photovoltaic property are presented. In such films, the residual photovoltage is caused by the separation of photocarriers by the built-in electrostatic field of the near-surface region of space charges and their asymmetric capture by deep levels of impurities or complexes, including impurity atoms and intrinsic defects, both in the bulk and on the surface of crystal grains. It has been shown that in activated films, a two-step exponential temporary relaxation of the initial photovoltage of the order of V<sub>APV</sub> ≈ (500-600) V is detected, and only 10% of it experiences long-term relaxation (t ≈ 100-120 min).
基金financially supported by the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.SJCX23_0099)。
文摘The complex permittivity of baijiu varies with frequency,and dielectric spectroscopy has been used to evaluate the quality.To simplify the analysis and reduce the number of the parameters,a dielectric relaxation model is often used to fit the permittivity data.However,existing fitting methods such as the least squares and particle swarm optimization methods are often computationally complex and require preset initial values.Therefore,a simpler calculation method of the relaxation parameters considering the geometric characteristics of the permittivity spectrum is proposed.It is based on the relationship between the Cole-Cole relaxation parameters and the Cole-Cole diagram,which is fitted by a geometric method.First,the concepts of the Cole-Cole parameters and the diagram are introduced,and then the process of obtaining the parameters from the complex permittivity measurement data is explained.Taking baijiu with 56%alcohol by volume(ABV)as an example,the fitting is better than the least squares method and similar to the particle swarm optimization.This method is then used for the parameter fitting of baijiu with ABV of 42-52%,and the average error is less than 1%,demonstrating its wider applicability.Finally,a prediction model is used for baijiu with 53%ABV,and the error is only 1.51%.Hence,the method can be applied to the measurement of ABV of baijiu.
基金supported by the Research and Community Services Centre of Hasanuddin University,South Sulawesi Province,Indonesia (No.UH18070408).
文摘Objective:This study aimed to determine the effect of the relaxation breathing exercise(RBE)on fatigue and cortisol levels among Indonesian women with gynecological cancer undergoing chemotherapy.Methods:This pilot study consecutively recruited 44 gynecological cancer patients to receive RBE(22)or usual care(22).Cortisol level was measured before and after completion of the intervention(day 8).Fatigue was measured using the Piper Fatigue Scale(PFS).Anxiety and depression were assessed using the Hospital Anxiety and Depression Scale(HADS)at the baseline days of the study for days 1,4,and 8.The obtained data were analyzed using Fisher’s exact test,the independent t-test,and the Mann-Whitney U test.Results:There were significant increases in cortisol levels within the groups,either the intervention or control groups,respectively(P-value=0.0003 and 0.001).Despite there being no statistical significance between the intervention and control groups,there were noticeable differences in the cortisol levels,indicating the extreme increase in cortisol levels in the control group(Median[IQR1-IQR3]:2.30[0.99-9.09];Min-Max:0.43-23.38)compared with the intervention group(Median[IQR1-IQR3]=2.97[1.26-5.18];Min-Max=0.39-6.91).Conclusions:RBE helps prevent a significant increase in cortisol levels that can alleviate fatigue for women with gynecological cancer.Further research was recommended to compare several intervention modalities for fatigue and cancer-related symptom management based on cortisol level changes.
文摘Objective:To systematically analyze the research status and application of progressive muscle relaxation training(PMRT)in the nursing field in China,and provide a reference basis for scientific research in this field.Methods:The bibliometric method was adopted in“progressive muscle relaxation training”or“PMRT,”and“nursing.”The established database was included in the China National Knowledge Infrastructure(CNKI)and the Wanfang Medical Network.The relevant articles in the Chinese Science and Technology Periodical Database(VIP)were analyzed.Results:A total of 169 literatures were included.The journals,years,and regions of literature publication were uneven,mainly originating from the eastern region(43.19%),and listed the application of progressive muscle relaxation training in the field of nursing in China.Intervention literature information was mainly dominated by experimental studies(97%).Conclusion:The related research and application of progressive muscle relaxation training in nursing in China is increasing,but there is a lack of objective evaluation of outcome indicators and a short intervention period.Further research should be conducted in the future to effectively guide the development of PMRT in the field of nursing in China.
文摘Objective:To explore the effects of progressive muscle relaxation training on anxiety,depression,and quality of life in patients with cerebral small vessel disease(CSVD).Methods:Sixty-one patients with CSVD in the Department of Neurology of a tertiary hospital were divided into an observation group(28 patients)and a control group(33 patients)by lottery method.The control group received conventional nursing care,while the observation group received progressive muscle relaxation training interventions in addition to the conventional care.The Hamilton Anxiety Scale(HAMA),the Hamilton Depression Scale(HAMD),and the Stroke-Specific Quality of Life Scale(SS-QOL)were used to compare the effects before the intervention,7 days after the intervention,and 30 days after the intervention.Results:Over time,at different time points after the intervention,the anxiety and depression scores of patients with CSVD in the observation group were significantly lower than those in the control group(P<0.05).The quality of life scores were significantly higher in the observation group compared to the control group(P<0.05),and these differences were statistically significant.Conclusion:Progressive muscle relaxation training can improve anxiety and depression in patients with cerebral small vessel disease and can effectively enhance their quality of life.
基金the Forrest Research Foundation.Carmine D’Agostino would like to acknowledge the EPSRC for grant no.EP/S019138/1.
文摘NMR relaxation analysis provides a unique and non-invasive probe of fluid dynamics within porous materials,and may be applied to the interpretation of a wide variety of material and interfacial characteristics.Here,we report two-dimensional^(1)H T_(1)-T_(2)relaxation correlation measurements of a range of three-carbon adsorbates(1-propanol,2-propanol and propanoic acid)imbibed within the mesoporous metal oxide gamma-alumina.Our data,acquired across field strengths of 2 MHz,12.7 MHz and 43 MHz,clearly reveal two populations in each measurement,identified as the alkyl and hydroxyl moieties of each adsorbate.These results expand the range of materials in which such functional group resolved relaxation is known to occur,and demonstrate the clear persistence of such phenomena using a range of typical benchtop NMR systems employed to study fluid-saturated porous media.
基金supported in part by the National Natural Science Foundation of China under grants 61873304,62173048,62106023in part by the China Postdoctoral Science Foundation Funded Project under grants 2018M641784 and 2019T120240+1 种基金also in part by the Key Science and Technology Projects of Jilin Province,China,under grant 20210201106GXalso in part by the Changchun Science and Technology Project under grant 21ZY41.
文摘How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.
基金the National Natural Science Foundation of China(Nos.12172017 and 12202021)。
文摘Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.
基金Project supported by the National Key Research and Development Program of China(Grant No.2021YFA1400303)the National Natural Science Foundation of China(Grant No.12227806)。
文摘We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions.The structural study shows that the symmetry changes from one polar point group(mm2)at room temperature to another polar point group(m)at low temperature.Magnetic studies and theory calculations illustrate that the vortex distribution of magnetic dipoles in the triangular dysprosium clusters forms a toroidal magnetic moment.Interestingly,the analysis of AC magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes,corresponding to the Raman,Orbach,and QTM relaxation pathways,respectively.The sum of three modified Debye functions is successfully used to describe the multiple relaxation behavior.
