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In this paper, a force-based general model, named the CosForce model, has been developed. To the best of our knowledge, this may represent the most simplified version of the social force model. Considering the anisotropic influence of the environment on pedestrian interaction, the model solely focuses on interactions between pedestrians and their nearest neighbors, rather than all surrounding pedestrians. Specifically, cosine functions are employed to describe the interactions between nearest neighbors, allowing the model to simulate the anticipation and reaction mechanisms. Notably, due to the simplification of binary interactions between pedestrians, the simulation efficiency of this model is significantly improved compared to the classical social force model. By applying this model to simulations across various scenarios, a wide range of pedestrian dynamics can be simulated, including pedestrian fundamental diagrams and self-organized phenomena such as lane formation, stripe formation, and cross-channel formation, among others. The open-source codes of the model can be found at: https://drive.google.com/drive/folders/1NYVnRp0z8VPuskfezMr51gB-sraOf6Iq?usp=drive_link, and a short video summary is available at: https://www.bilibili.com/video/BV17B1oYVEQm/., Comment: 7 pages, 5 figures

We performed a pump-probe experiment on the chiral magnet Cu$_2$OSeO$_3$ to study the relaxation dynamics of its non-collinear magnetic orders, employing a millisecond magnetic field pulse as the pump and resonant elastic x-ray scattering as the probe. Our findings reveal that the system requires $\sim$0.2 s to stabilize after the perturbation applied to both the conical and skyrmion lattice phase; significantly slower than the typical nanosecond timescale observed in micromagnetics. This prolonged relaxation is attributed to the formation and slow dissipation of local topological defects, such as emergent monopoles. By unveiling the experimental lifetime of these emergent singularities in a non-collinear magnetic system, our study highlights a universal relaxation mechanism in solitonic textures within the slow dynamics regime, offering new insights into topological physics and advanced information storage solutions., Comment: 6 pages, 4 figures

The demand for low-power devices is on the rise as semiconductor engineering approaches the quantum limit and quantum computing continues to advance. Two-dimensional (2D) superconductors, thanks to their rich physical properties, hold significant promise for both fundamental physics and potential applications in superconducting integrated circuits and quantum computation. Here, we report a gate-controlled superconducting switch in GaSe/NbSe$_2$ van der Waals (vdW) heterostructure. By injecting high-energy electrons into NbSe$_2$ under an electric field, a non-equilibrium state is induced, resulting in significant modulation of the superconducting properties. Owing to the intrinsic polarization of ferroelectric GaSe, a much steeper subthreshold slope and asymmetric modulation are achieved, which is beneficial to the device performance. Based on these results, a superconducting switch is realized that can reversibly and controllably switch between the superconducting and normal state under an electric field. Our findings highlight a significant high-energy injection effect from band engineering in 2D vdW heterostructures combining superconductors and ferroelectric semiconductors, and demonstrate the potential applications for superconducting integrated circuits., Comment: 19 pages, 5 figures

Nonreciprocal superconductivity, also called as superconducting diode effect that spontaneously breaks time-reversal symmetry, is characterized by asymmetric critical currents under opposite applied current directions. This distinct state unveils a rich ore of intriguing physical properties, particularly in the realm of nanoscience application of superconductors. Towards the experimental realization of superconducting diode effect, the construction of two-dimensional heterostructures of magnets and $s$-wave superconductors is considered to be a promising pathway. In this study, we present our findings of superconducting diode effect manifested in the magnetic Mott insulator $\alpha$-RuCl$_3$. This phenomenon is induced by the proximity effect within a van der Waals heterostructure, consisting of thin $\alpha$-RuCl$_3$/NbSe$_2$ flakes. Through transport property measurements, we have confirmed a weak superconducting gap of 0.2 meV, which is significantly lower than the intrinsic gap of NbSe$_2$(1.2 meV). Upon the application of a weak magnetic field below 70 mT, we observed an asymmetry in the critical currents under positive and negative applied currents. This observation demonstrates a typical superconducting diode effect in the superconducting $\alpha$-RuCl$_3$. The superconducting diode effect and nonreciprocal resistance are observed exclusively when the magnetic field is aligned out-of-plane. This suggests that an Ising-type spin-orbit coupling in the superconducting $\alpha$-RuCl$_3$ may be responsible for the mechanism. Our findings furnish a platform for the exploration of superconducting diode effect via the artificial construction of heterostructures.

This paper proposes a Galton board approximation method to analyze the potential walking preferences of pedestrians. We employ the binomial distribution to estimate the walking preferences of pedestrians in dynamic crowds. Estimating the probability of the right-side preference ($p$) based on observed data poses the challenge, as statistical measures such as means and variances often lead to divergent results. This study aims to explore this issue., Comment: 7 pages, 6 figures

This paper aims to investigate the disparities in pedestrian crossing behaviors within static and dynamic crowds through experimental analysis. First, the crossing trajectories of pedestrians in various crowd environments were qualitatively observed. These trajectories have shown significant discrepancies and the phenomenon of cross-channel formation within static crowds was observed, a phenomenon similar to the evolution of human trails. To quantitatively assess these discrepancies, metrics of behavior patterns and swarm factor were introduced. Different behavioral patterns, including anticipation and reaction behaviors in pedestrian motion, were observed. Finally, through orthogonal velocity analysis, the variation trends of crossing motions within static and dynamic contexts were revealed., Comment: 12 pages, 11 figures

In urban streets, the intrusion of pedestrians presents significant safety challenges. Modelling mixed pedestrian-vehicle traffic is complex due to the distinct motion characteristics and spatial dimensions of pedestrians and vehicles, making unified modelling difficult, with few studies addressing these issues. This paper employs a multi-grid cellular automata model to bridge the gap between vehicle and pedestrian models. An Improved Kerner-Klenov-Wolf (IKKW) model and a pedestrian motion model that incorporates Time-To-Collision (TTC) are introduced. Both models update the spatial motions of vehicles and pedestrians uniformly. Empirical analysis indicates that the model achieves high simulation accuracy. This model effectively illustrates the impact of pedestrian intrusion within mixed traffic scenario. The fundamental diagram of heterogeneous traffic reveals substantial differences, highlighting the effects of pedestrian intrusion on traffic flow states and identifying six phase regions in mixed traffic. Additionally, this paper examines conflicts between pedestrians and vehicles under varying speed limits and sidewalk widths, demonstrating that lower speeds and broader sidewalks significantly reduce the frequency of pedestrian-vehicle conflicts. Notably, the frequency of peak conflicts at a vehicle speed limit of 60.48 km/h is more than three times higher than at 30.24 km/h. This model offers a potential approach to studying mixed traffic flows and exhibits substantial scalability., Comment: 34pages, 33figures

Quantum spin liquids (QSLs) represent a novel state where spins are highly entangled but do not order even at zero temperature due to strong quantum fluctuations. Such a state is mostly studied in Heisenberg models defined on geometrically frustrated lattices. Here, we turn to a new triangular-lattice antiferromagnet PrMgAl$_{11}$O$_{19}$, in which the interactions are believed to be of Ising type. Magnetic susceptibility measured with an external field along the $c$ axis is two orders of magnitude larger than that with a field in the $ab$ plane, displaying an ideal easy-axis behavior. Meanwhile, there is no magnetic phase transition or spin freezing observed down to 1.8 K. Ultralow-temperature specific heat measured down to 50 mK does not capture any phase transition either, but a hump at 4.5 K, below which the magnetic specific heat exhibits a quasi-quadratic temperature dependence that is consistent with a Dirac QSL state. Inelastic neutron scattering technique is also employed to elucidate the nature of its ground state. In the magnetic excitation spectra, there is a gapless broad continuum at the base temperature 55~mK, in favor of the realization of a gapless QSL. Our results provide a scarce example for the QSL behaviors observed in an Ising-type magnet, which can serve as a promising platform for future research on QSL physics based on an Ising model., Comment: 11 pages, 5 figures

The significance of the superconducting diode effect lies in its potential application as a fundamental component in the development of next-generation superconducting circuit technology. The stringent operating conditions at low temperatures have posed challenges for the conventional semiconductor diode, primarily due to its exceptionally high resistivity. In response to this limitation, various approaches have emerged to achieve the superconducting diode effect, primarily involving the disruption of inversion symmetry in a two-dimensional superconductor through heterostructure fabrication. In this study, we present a direct observation of the supercurrent diode effect in a NbSe2 nanobridge with a length of approximately 15 nm, created using focused helium ion beam fabrication. Nonreciprocal supercurrents were identified, reaching a peak value of approximately 380 $\mu$A for each bias polarity at $B_{z}^{max} =\pm 0.2$ mT. Notably, the nonreciprocal supercurrent can be toggled by altering the bias polarity. This discovery of the superconducting diode effect introduces a novel avenue and mechanism through nanofabrication on a superconducting flake, offering fresh perspectives for the development of superconducting devices and potential circuits.

Nonreciprocal charge transport in heterostructural superconductors exhibits appealing quantum physical phenomena and holds the promising potential for superconducting circuits applications. Realizing a nonreciprocity is, however, fundamentally and technologically challenging, as it requires a material structure without a centre of inversion, which is scarce among superconducting materials. Here, we report an evidence of helical superconductivity, in which the Rashba spin-orbit coupling induces momentum-dependent superconducting gap in the inversion symmetry breaking heterointerface superconductor consisting of Mott insulating Ti$_2$O$_3$ and polar semiconducting GaN. Remarkably, the nonlinear responses emerge in the superconducting transition regime, when the magnetic field is precisely aligned in-plane orientations perpendicular to the applied current. In particular, the observed nonreciprocal supercurrent is extremely sensitive to the direction of the magnetic field for 0.5 degree, suggestive of a crossover from a symmetry breaking state to a symmetric one. Our finding not only unveils the underlying rich physical properties in heterointerface superconductors, but also provides an exciting opportunity for the development of novel mesoscopic superconducting devices.

Precise assessment of Space-speed time delay (TD) is critical for distinguishing between anticipation and reaction behaviors within pedestrian motion. Besides, the TD scale is instrumental in the evaluation of potential collision tendency of the crowd, thereby providing essential quantitative metrics for assessing risk. In this consideration, this paper introduced the CosIn algorithm for evaluating TD during pedestrian motion, which includes both the CosIn-1 and CosIn-2 algorithms. CosIn-1 algorithm analytically calculates TD, replacing the numerical method of discrete cross-correlation, whereas the CosIn-2 algorithm estimates the TD from a statistical perspective. Specifically, the CosIn-1 algorithm addresses the precise computation of TD for individual pedestrians, while the CosIn-2 algorithm is employed for assessing TD at the crowd scale, concurrently addressing the imperative of real-time evaluation. Efficacy analyses of the CosIn-1 and CosIn-2 algorithms are conducted with data from single-file pedestrian experiments and crowd-crossing experiments, respectively. During this process, the discrete cross-correlation method was employed as a baseline to evaluate the performance of both algorithms, which demonstrated notable accuracy. This algorithm facilitate the precise evaluation of behavior patterns and collision tendency within crowds, thereby enabling us to understand the crowds dynamics from a new perspective., Comment: 29 pages, 18 figures

We characterized the dosimetric properties of a clinical linear accelerator configured to deliver ultra-high dose rate (UHDR) irradiation to mice and cell-culture FLASH radiobiology experiments. UHDR electron beams were controlled by a microcontroller and relay interfaced with the respiratory gating system. We produced beam collimators with indexed stereotactic mouse positioning devices to provide anatomically specific preclinical treatments. Treatment delivery was monitored directly with an ionization chamber, and charge measurements were correlated with radiochromic film at the entry surface of the mice. The setup for conventional (CONV) dose rate irradiation was similar but the source-to-surface distance was longer. Monte Carlo simulations and film dosimetry were used to characterize beam properties and dose distributions. The mean electron beam energies before the flattening filter were 18.8 MeV (UHDR) and 17.7 MeV (CONV), with corresponding values at the mouse surface of 17.2 MeV and 16.2 MeV. The charges measured with an external ion chamber were linearly correlated with the mouse entrance dose. Use of relay gating for pulse control initially led to a delivery failure rate of 20% ($+/-$ 1 pulse); adjustments to account for the linac latency improved this rate to <1/20. Beam field sizes for two anatomically specific mouse collimators (4x4 $cm^2$ for whole-abdomen and 1.5x1.5 $cm^2$ for unilateral lung irradiation) were accurate within <5% and had low radiation leakage (<4%). Normalizing the dose at the center of the mouse (~0.75 cm depth) produced UHDR and CONV doses to the irradiated volumes with >95% agreement. We successfully configured a clinical linear accelerator for increased output and developed a robust preclinical platform for anatomically specific irradiation, with highly accurate and precise temporal and spatial dose delivery, for both CONV and UHDR applications., Comment: Jinghui Wang and Stavros Melemenidis are co-first authors, and Emil Sch\"uler and Peter G. Maxim are co-senior/co-corresponding authors

This study integrates pedestrian flow characteristics to formulate a mesoscopic cellular automata model tailored for simulating evacuations in large-scale scenarios. Departing from the conventional planar grid cell division, the model employs road cell segmentation, thereby physically enlarging the dimensions of individual cells. This augmentation accommodates an increased occupancy of individuals per cell, representing pedestrian flow parameters within each cell through state variables. The source loading cell facilitates the simulation of pedestrian behavior transitioning from buildings to roads during an actual evacuation event, while the unloading cell situated at the exit removes evacuees from the system. The continuity equation for state transitions comprehensively encapsulates the dynamics of pedestrians throughout the evacuation process. Potential challenges in actual evacuation processes are identified through the simulation, offering valuable insights for improvement. This research aims to contribute to a more effective and informed approach to evacuation planning and management., Comment: 13 pages, 14figures

Crowd studies have gained increasing relevance due to the recurring incidents of crowd crush accidents. In addressing the issue of the crowd's persistent dynamism, this paper explored the macroscopic and microscopic features of pedestrians crossing in static and dynamic contexts, employing a series of systematic experiments. Firstly, empirical evidence has confirmed the existence of crowd's persistent dynamism. Subsequently, the research delves into two aspects, qualitative and quantitative, to address the following questions:(1) Cross pedestrians tend to avoid high-density areas when crossing static crowds and particularly evade pedestrians in front to avoid deceleration, thus inducing the formation of cross-channels, a self-organization phenomenon.(2) In dynamic crowds, when pedestrian suffers spatial constrained, two patterns emerge: decelerate or detour. Research results indicate the differences in pedestrian crossing behaviors between static and dynamic crowds, such as the formation of crossing channels, backward detours, and spiral turning. However, the strategy of pedestrian crossing remains consistent: utilizing detours to overcome spatial constraints. Finally, the empirical results of this study address the final question: pedestrians detouring causes crowds' persistent collective dynamism. These findings contribute to an enhanced understanding of pedestrian dynamics in extreme conditions and provide empirical support for research on individual movement patterns and crowd behavior prediction., Comment: 31pages, 17figures

Nontrivial topological superconductivity has received enormous research attentions due to its potential for diverse applications in topological quantum computing. The intrinsic issue concerning the correlation between a topological insulator and a superconductor is, however, still widely open. Here, we systemically report an emergent superconductivity in a cross-junction composed of a magnetic topological insulator MnBi2Te4 and a conventional superconductor NbSe2. Remarkably, the interface indicates existence of a reduced superconductivity at surface of NbSe2 and a proximity-effectinduced superconductivity at surface of MnBi2Te4. Furthermore, the in-plane angular-dependent magnetoresistance measurements reveal the fingerprints of the paring symmetry behaviors for these superconducting gaps as a unconventional nature. Our findings extend our views and ideas of topological superconductivity in the superconducting heterostructures with time-reversal symmetry breaking, offering an exciting opportunity to elucidate the cooperative effects on the surface state of a topological insulator aligning a superconductor., Comment: 6 pages, 4 figures

Time reversal symmetry breaking in superconductors, resulting from external magnetic fields or spontaneous magnetization, often leads to unconventional superconducting properties. In this way, a conventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by the Cooper pairs with nonzero total momentum, may be realized by the Zeeman effect caused from external magnetic fields. Here, we report the observation of superconductivity in a few-layer antiferromagnetic insulator CrOCl by utilizing superconducting proximity effect with NbSe2 flakes. The superconductivity demonstrates a considerably weak gap of about 0.12 meV and the in-plane upper critical field reveals as behavior of the FFLO state at low temperature. Our first-principles calculations indicate that the proximitized superconductivity may exist in the CrOCl layer with Cr vacancies or line-defects. Moreover, the FFLO state could be induced by the inherent larger spin splitting in the CrOCl layer. Our findings not only demonstrate the fascinating interaction between superconductivity and magnetism, but also provide a possible path to construct FFLO state by intrinsic time reversal symmetry breaking and superconducting proximity effect.

The emergence of quantum metallic state marked by a saturating finite electrical resistance in the zero-temperature limit in a variety of two-dimensional superconductors injects an exciting momentum to the realm of heterostructure superconductivity. Despite much research efforts over last few decades, there is not yet a general consensus on the nature of this unexpected quantum metal. Here, we report the observation of a unique quantum metallic state within the hallmark of Bose-metal in the titanium sesquioxide heterointerface superconductor Ti$_2$O$_3$/GaN. Remarkably, the quantum bosonic metallic state continuously tuned by a magnetic field in the vicinity of the two-dimensional superconductivity-metal transition persists in the normal phase, indicating the existence of composite bosons formed by electron Cooper pairs even in the normal phase. Our findings provide a distinct evidence for electron pairing in the normal phase of heterointerface superconductors, and shed fresh light on the pairing nature underlying heterointerface superconductivity., Comment: 12 pages, 4 figures

Nonreciprocal charge transport phenomena are widely studied in two-dimensional superconductors, which demonstrate unidirectional-anisotropy magnetoresistances as a result of symmetry breaking. Here, we report a strong nonreciprocal transport phenomenon in superconducting CsV$_{3}$Sb$_{5}$ thin flakes. The second harmonic voltages, mainly originating from the rectification effect of vortex motion, are unambiguously developed with in-plane and out-of-plane magnetic fields, and their magnitudes are comparable to those in noncentrosymmetric superconductors. The second harmonic magnetoresistances split into several peaks and some of them reverse their signs by ramping the magnetic field or the current within the superconducting transition. The nonreciprocity suggests a strong asymmetry in CsV$_{3}$Sb$_{5}$. The centrosymmetric structure and symmetric electronic phases in CsV$_{3}$Sb$_{5}$ can hardly induce the distinct nonreciprocal transport phenomenon, which could be correlated to a symmetry breaking from an unconventional superconducting order parameter symmetry.

We have performed inelastic neutron scattering measurements on optimally-doped Fe$_{0.98}$Te$_{0.5}$Se$_{0.5}$ and 10% Cu-doped Fe$_{0.88}$Cu$_{0.1}$Te$_{0.5}$Se$_{0.5}$ to investigate the substitution effects on the spin excitations in the whole energy range up to 300 meV. It is found that substitution of Cu for Fe enhances the low-energy spin excitations ($\le$ 100 meV), especially around the (0.5, 0.5) point, and leaves the high-energy magnetic excitations intact. In contrast to the expectation that Cu with spin 1/2 will dilute the magnetic moments contributed by Fe with a larger spin, we find that the 10% Cu doping enlarges the effective fluctuating moment from 2.85 to 3.13 $\mu_{\rm B}$/Fe, although there is no long- or short-range magnetic order around (0.5, 0.5) and (0.5, 0). The presence of enhanced magnetic excitations in the 10% Cu doped sample which is in the insulating state indicates that the magnetic excitations must have some contributions from the local moments, reflecting the dual nature of the magnetism in iron-based superconductors. We attribute the substitution effects to the localization of the itinerant electrons induced by Cu dopants. These results also indicate that the Cu doping does not act as electron donor as in a rigid-band shift model, but more as scattering centers that localize the system., Comment: Published in PRB, 8 pages, 3 figures

Recently, deep learning-based image denoising methods have achieved promising performance on test data with the same distribution as training set, where various denoising models based on synthetic or collected real-world training data have been learned. However, when handling real-world noisy images, the denoising performance is still limited. In this paper, we propose a simple yet effective Bayesian deep ensemble (BDE) method for real-world image denoising, where several representative deep denoisers pre-trained with various training data settings can be fused to improve robustness. The foundation of BDE is that real-world image noises are highly signal-dependent, and heterogeneous noises in a real-world noisy image can be separately handled by different denoisers. In particular, we take well-trained CBDNet, NBNet, HINet, Uformer and GMSNet into denoiser pool, and a U-Net is adopted to predict pixel-wise weighting maps to fuse these denoisers. Instead of solely learning pixel-wise weighting maps, Bayesian deep learning strategy is introduced to predict weighting uncertainty as well as weighting map, by which prediction variance can be modeled for improving robustness on real-world noisy images. Extensive experiments have shown that real-world noises can be better removed by fusing existing denoisers instead of training a big denoiser with expensive cost. On DND dataset, our BDE achieves +0.28~dB PSNR gain over the state-of-the-art denoising method. Moreover, we note that our BDE denoiser based on different Gaussian noise levels outperforms state-of-the-art CBDNet when applying to real-world noisy images. Furthermore, our BDE can be extended to other image restoration tasks, and achieves +0.30dB, +0.18dB and +0.12dB PSNR gains on benchmark datasets for image deblurring, image deraining and single image super-resolution, respectively.

Realization of Kondo lattice in superconducting van der Waals materials not only provides a unique opportunity for tuning the Kondo lattice behavior by electrical gating or intercalation, but also is helpful for further understanding the heavy fermion superconductivity. Here we report a low-temperature and vector-magnetic-field scanning tunneling microscopy and spectroscopy study on a superconducting compound (4Hb-TaS2) with alternate stacking of 1T-TaS2 and 1H-TaS2 layers. We observe the quasi-two-dimensional superconductivity in the 1H-TaS2 layer with anisotropic response to the in-plane and out-of-plane magnetic fields. In the 1T-TaS2 layer, we detect the Kondo resonance peak that results from the Kondo screening of the unpaired electrons in the Star-of-David clusters. We also find the intensity of the Kondo resonance peak is sensitive to its relative position with the Fermi level, and it can be significantly enhanced when it's further shifted towards the Fermi level by evaporating Pb atoms onto the 1T-TaS2 surface. Our results are not only important for fully understanding the electronic properties of 4Hb-TaS2, but also pave the way for creating tunable Kondo lattice in the superconducting van der Waals materials., Comment: 10 pages, 4 figures + Supplementary Materials

As one of the most promising Kitaev quantum-spin-liquid (QSL) candidates, $\alpha$-RuCl$_3$ has received a great amount of attention. However, its ground state exhibits a long-range zigzag magnetic order, which defies the QSL phase. Nevertheless, the magnetic order is fragile and can be completely suppressed by applying an external magnetic field. Here, we explore the evolution of magnetic excitations of $\alpha$-RuCl$_3$ under an in-plane magnetic field, by carrying out inelastic neutron scattering measurements on high-quality single crystals. Under zero field, there exist spin-wave excitations near the $M$ point and a continuum near the $\mit\Gamma$ point, which are believed to be associated with the zigzag magnetic order and fractional excitations of the Kitaev QSL state, respectively. By increasing the magnetic field, the spin-wave excitations gradually give way to the continuous excitations. On the verge of the critical field $\mu_0H_{\rm c}=7.5$ T, the former vanish and only the latter is left, indicating the emergence of a pure QSL state. By further increasing the field strength, the excitations near the $\mit\Gamma$ point become more intense. By following the gap evolution of the excitations near the $\mit\Gamma$ point, we are able to establish a phase diagram composed of three interesting phases, including a gapped zigzag order phase at low fields, possibly-gapless QSL phase near $\mu_0H_{\rm c}$, and gapped partially polarized phase at high fields. These results demonstrate that an in-plane magnetic field can drive $\alpha$-RuCl$_3$ into a long-sought QSL state near the critical field., Comment: 9 pages, 4 figures

Disorder is important in the study of quantum spin liquids, but its role on the spin dynamics remains elusive. Here, we explore the disorder effect by investigating the magnetic-field dependence of the low-energy magnetic excitations in a triangular-lattice frustrated magnet YbZnGaO$_4$ with inelastic neutron scattering. With an intermediate field of 2.5 T applied along the $c$-axis, the broad continuum at zero field becomes more smeared both in energy and momentum. With a field up to 10 T, which fully polarizes the magnetic moments, we observe clear spin-wave excitations with a gap of $\sim$1.4 meV comparable to the bandwidth. However, the spectra are significantly broadened. The excitation spectra both at zero and high fields can be reproduced by performing classical Monte Carlo simulations which take into account the disorder effect arising from the random site mixing of nonmagnetic Zn$^{2+}$ and Ga$^{3+}$ ions. These results elucidate the critical role of disorder in broadening the magnetic excitation spectra and mimicking the spin-liquid features in frustrated quantum magnets., Comment: Published in PRB, 10 pages, 3 figures