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While awaiting direct velocity measurement of gas motions in the hot intracluster medium, we rely on indirect probes, including gas perturbations in galaxy clusters. Using a sample of $\sim 80$ clusters in different dynamic states from Omega500 cosmological simulations, we examine scaling relations between the fluctuation amplitudes of gas density, $\delta\rho/\rho$, pressure, $\delta P/P$, X-ray surface brightness, Sunyaev-Zeldovich (SZ) y-parameter, and the characteristic Mach number of gas motions, $M_{\rm 1d}$. In relaxed clusters, accounting for halo ellipticities reduces $\delta\rho/\rho$ or $\delta P/P$ by a factor of up to 2 within $r_{500c}$. We confirm a strong linear correlation between $\delta\rho/\rho$ (or $\delta P/P$) and $M_{\rm 1d}$ in relaxed clusters, with the proportionality coefficient $\eta \approx 1$. For unrelaxed clusters, the correlation is less strong and has a larger $\eta\approx 1.3\pm 0.5$ ($1.5\pm0.5$) for $\delta\rho/\rho$ ($\delta P/P$). Examination of the power-law scaling of $M_{\rm 1d}$ with $\delta\rho/\rho$ shows that it is almost linear for relaxed clusters, while for the unrelaxed ones, it is closer to $\delta\rho/\rho\propto M_{\rm 1d}^2$, supporting an increasing role of non-linear terms and compressive modes. In agreement with previous studies, we observe a strong correlation of $M_{\rm 1d}$ with radius. Correcting for these correlations leaves a residual scatter in $M_{\rm 1d}$ of $\sim 4 (7)$ per cent for relaxed (perturbed) clusters. Hydrostatic mass bias correlates with $M_{\rm 1d}$ as strongly as with $\delta\rho/\rho$ in relaxed clusters. The residual scatters after correcting for derived trends is $\sim 6-7$ per cent. These predictions can be verified with existing X-ray and SZ observations of galaxy clusters combined with forthcoming velocity measurements with X-ray microcalorimeters., Comment: 15 pages, 11 figures, submitted

Buoyant bubbles of relativistic plasma are essential for active galactic nucleus feedback in galaxy clusters, stirring and heating the intracluster medium (ICM). Observations suggest that these rising bubbles maintain their integrity and sharp edges much longer than predicted by hydrodynamic simulations. In this study, we assume that bubbles can be modelled as rigid bodies and demonstrate that intact bubbles and their long-term interactions with the ambient ICM play an important role in shaping gas kinematics, forming thin gaseous structures (e.g. H α filaments), and generating internal waves in cluster cores. We find that well-developed eddies are formed in the wake of a buoyantly rising bubble, and it is these eddies, rather than the Darwin drift, that are responsible for most of the gas mass uplift. The eddies gradually elongate along the bubble’s direction of motion due to the strong density stratification of the atmosphere and eventually detach from the bubble, quickly evolving into a high-speed jet-like stream propagating towards the cluster center in our model. This picture naturally explains the presence of long straight and horseshoe-shaped H α filaments in the Perseus cluster, inward and outward motions of the gas, and the X-ray-weighted gas velocity distributions near the northwestern bubble observed by Hitomi. Our model reproduces the observed H α velocity structure function of filaments, providing a simple interpretation for its steep scaling and normalization: laminar gas flows and large eddies within filaments driven by the intact bubbles, rather than spatially homogeneous small-scale turbulence, are sufficient to produce a structure function consistent with observations. © 2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society., Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number TM1-22008X issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. Part of the simulations presented in this paper were carried out using the Midway computing cluster provided by the University of Chicago Research Computing Center. IZ is partially supported by a Clare Boothe Luce Professorship from the Henry Luce Foundation. The work of AAS was supported in part by UK EPSRC grant EP/R034737/1. WF acknowledges support from the Smithsonian Institution, the Chandra High Resolution Camera Project through NASA contract NAS8-03060, and NASA Grants 80NSSC19K0116, GO1-22132X, and GO9-20109X., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

Acoustic nonlinear parameter β, was of great interest in tissue characterization in recent years. Nonlinear imaging methods have been reported to provide improved spatial and contrast resolution. We introduce a nonlinear imaging method derived from nonlinear wave equation based on Gaussian-form solution assumption, which can be applied in pulse-echo mode on diagnostic ultrasound. Through making the use of two pulse transmission, only nonlinear effects are reserved and other effects like scattering, diffraction and linear attenuation can be eliminated. For validation of this method a set of simulation results are generated with a nonlinear simulator. Simulated images also indicate that our method clearly describes the spatial distribution of B/A in the medium.

A self-similar spherical collapse model predicts a dark matter (DM) splashback and accretion shock in the outskirts of galaxy clusters while misses a key ingredient of structure formation - processes associated with mergers. To fill this gap, we perform simulations of merging self-similar clusters and investigate their DM and gas evolution in an idealized cosmological context. Our simulations show that the cluster rapidly contracts during the major merger and the splashback radius $r_{\rm sp}$ decreases, approaching the virial radius $r_{\rm vir}$. While $r_{\rm sp}$ correlates with a smooth mass accretion rate (MAR) parameter $\Gamma_{\rm s}$ in the self-similar model, our simulations show a similar trend with the total MAR $\Gamma_{\rm vir}$ (includes both mergers and $\Gamma_{\rm s}$). The scatter of the $\Gamma_{\rm vir}-r_{\rm sp}/r_{\rm vir}$ relation indicates a generally low $\Gamma_{\rm s}\sim1$ in clusters in cosmological simulations. In contrast to the DM, the hot gaseous atmospheres significantly expand by the merger-accelerated (MA-) shocks formed when the runaway merger shocks overtake the outer accretion shock. After a major merger, the MA-shock radius is larger than $r_{\rm sp}$ by a factor of up to $\sim1.7$ for $\Gamma_{\rm s}\lesssim1$ and is $\sim r_{\rm sp}$ for $\Gamma_{\rm s}\gtrsim3$. This implies that (1) mergers could easily generate the MA-shock-splashback offset measured in cosmological simulations, and (2) the smooth MAR is small in regions away from filaments where MA-shocks reside. We further discuss various shocks and contact discontinuities formed at different epochs of the merger, the ram pressure stripping in cluster outskirts, and the dependence of member galaxies' splashback feature on their orbital parameters., Comment: 25 pages, 24 figures, submitted to MNRAS. Comments are welcome

When a subcluster merges with a larger galaxy cluster, a bow shock is driven ahead of the subcluster. At a later merger stage, this bow shock separates from the subcluster, becoming a "runaway" shock that propagates down the steep density gradient through the cluster outskirts and approximately maintains its strength and the Mach number. Such shocks are plausible candidates for producing radio relics in the periphery of clusters. We argue that, during the same merger stage, a secondary shock is formed much closer to the main cluster center. A close analog of this structure is known in the usual hydrodynamics as N-waves, where the trailing part of the "N" is the result of the non-linear evolution of a shock. In merging clusters, spherical geometry and stratification could further promote its development. Both the primary and the secondary shocks are the natural outcome of a single merger event and often both components of the pair should be present. However, in the radio band, the leading shock could be more prominent, while the trailing shock might conversely be more easily seen in X-rays. The latter argument implies that for some of the (trailing) shocks found in X-ray data, it might be difficult to identify their "partner" leading shocks or the merging subclusters, which are farther away from the cluster center. We argue that the Coma cluster and A2744 could be two examples in a post-merger state with such well-separated shock pairs., 9 pages, 8 figures, submitted to MNRAS. Comments are welcome

Two Mpc-size contact discontinuities have recently been identified in the XMM-Newton and Suzaku X-ray observations of the outskirts of the Perseus cluster (Walker et al. 2020). These structures have been tentatively interpreted as "sloshing cold fronts", which are customarily associated with differential motions of the cluster gas, perturbed by a merger. In this study we consider an alternative scenario, namely, that the most prominent discontinuity near the cluster virial radius is the result of the collision between the accretion shock and the "runaway" merger shock. We also discuss the possible origin of the second discontinuity at ~1.2 Mpc., Comment: 5 pages, 3 figures; accepted for publication in MNRAS Letters

Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of "runaway merger shocks", which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster center. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius) affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper. We show examples of such MA-shocks in 1D and 3D simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a "flower-like" morphology. In 3D, MA-shocks occupy space between the dense accreting filaments. (2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius., Comment: 10 pages, 9 figures; published in MNRAS

We analyse archival XMM-Newton observations of the massive galaxy group NGC 4839 falling into the Coma cluster core, which reveal a complex morphology for the merger. By comparing high quality X-ray maps of the merging subcluster with SPH simulations, we propose an infall scenario which qualitatively reproduces the observed structure of the NGC 4839 tail.

Moderately strong shocks arise naturally when two subclusters merge. For instance, when a smaller subcluster falls into the gravitational potential of a more massive cluster, a bow shock is formed and moves together with the subcluster. After pericenter passage, however, the subcluster is decelerated by the gravity of the main cluster, while the shock continues moving away from the cluster center. These shocks are considered as promising candidates for powering radio relics found in many clusters. The aim of this paper is to explore the fate of such shocks when they travel to the cluster outskirts, far from the place where the shocks were initiated. In a uniform medium, such a "runaway" shock should weaken with distance. However, as shocks move to large radii in galaxy clusters, the shock is moving down a steep density gradient that helps the shock to maintain its strength over a large distance. Observations and numerical simulations show that, beyond $R_{500}$, gas density profiles are as steep as, or steeper than, $\sim r^{-3}$, suggesting that there exists a "Habitable zone" for moderately strong shocks in cluster outskirts where the shock strength can be maintained or even amplified. A characteristic feature of runaway shocks is that the strong compression, relative to the initial state, is confined to a narrow region just behind the shock. Therefore, if such a shock runs over a region with a pre-existing population of relativistic particles, then the boost in radio emissivity, due to pure adiabatic compression, will also be confined to a narrow radial shell., 9 pages, 8 figures; published in MNRAS

Buoyant bubbles of relativistic plasma in cluster cores plausibly play a key role in conveying the energy from a supermassive black hole to the intracluster medium (ICM) - the process known as radio-mode AGN feedback. Energy conservation guarantees that a bubble loses most of its energy to the ICM after crossing several pressure scale heights. However, actual processes responsible for transferring the energy to the ICM are still being debated. One attractive possibility is the excitation of internal waves, which are trapped in the cluster's core and eventually dissipate. Here we show that a sufficient condition for efficient excitation of these waves in stratified cluster atmospheres is flattening of the bubbles in the radial direction. In our numerical simulations, we model the bubbles phenomenologically as rigid bodies buoyantly rising in the stratified cluster atmosphere. We find that the terminal velocities of the flattened bubbles are small enough so that the Froude number ${\rm Fr}\lesssim 1$. The effects of stratification make the dominant contribution to the total drag force balancing the buoyancy force. In particular, clear signs of internal waves are seen in the simulations. These waves propagate horizontally and downwards from the rising bubble, spreading their energy over large volumes of the ICM. If our findings are scaled to the conditions of the Perseus cluster, the expected terminal velocity is $\sim100-200{\,\rm km\,s^{-1}}$ near the cluster cores, which is in broad agreement with direct measurements by the Hitomi satellite., 15 pages, 13 figures, submitted to MNRAS

X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre- (post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre- and post-merger stages., Comment: 11 pages, 12 figures. Including major revision and matched to accepted version in MNRAS

Nonlinear imaging is more sensitive to changes in components, structure and pathological state of a tissue in comparison with the traditional ultrasound imaging. However, in view of the particularity of nonlinear imaging, the contrast of an image is generally very low and thus a doctor cannot clearly distinguish distribution of nonlinear parameters clearly. Therefore, the paper aims to design a self-adaptive sigmoid function to enhance the original nonlinear image. First of all, we needed to find an interesting area which included the different nonlinear acoustic parameters according to harmonic energy. Next, then the histogram of ROI was analyzed to obtain two parameters of sigmoid function values, and the contrast of the image was increased prominently by this method. At last, the contrast to noise ratio (CNR) was calculated to prove that the contrast of the image which was enhanced by this method improved by 5 times in comparison with the raw nonlinear image.

A high mortality of the Yesso scallop Patinopecten yessoensisis (Jay, 1857) larvae occurred during the seedling process: the larvae lost their ability to swim, their cilia fell off and their valves closed, they then sank to the bottom of the nursery pond and died. Total viable vibrio's counts in moribund larvae were 1.1 × 104 colony forming unit/g on tryptone-citrate-bilesucrose agar plates. Two dominant strains, named V1 and V2, accounted for 64.3% and 32.1% of total vibrios counts, respectively. Strain V1 exhibited beta hemolysis, whereas V2 exhibited alpha hemolysis. A challenge test showed that the signs of infected larvae were identical to those of natural moribund larvae, and the cumulative mortality caused by strains V1 and V2 was significantly higher than that of the control (P < 0.05). Strains V1 and V2 shared 99.9% and 99.2% identity with Vibrio splendidus ctt 31/5 and Vibrio tasmaniensis 007, respectively, by 16S rDNA sequencing. The presence of genes coding for virulence factors was e...

The aim of the study was to examine the bacterial community associated with the intestinal mucus of young farmed puffer fish Takifugu rubripes. Polymerase chain reaction and partial 16S rDNA sequencing was performed on DNA from bacteria cultivated on Zobell 2216E medium. All the isolates were classified into two phyla—Proteobacteria and Firmicutes. Proteobacteria were the dominant, culturable intestinal microbiota (68.3%). At the genus level, Vibrio, Enterobacter, Bacillus, Pseudomonas, Exiguobacterium, Staphylococcus, Acinetobacter, Pseudoalteromonas and Shewanella were isolated from the intestine, with representatives of the genera Vibrio, Enterobacter and Bacillus accounting for 70.7% of the total. This is the first report of Enterobacter, Bacillus, Exiguobacterium and Staphylococcus as part of the intestinal bacterial microflora in T. rubripes. The profile of the culturable bacterial community differed between samples collected from the same tank at 2-month intervals, as indicated by Bray-Curtis and Sorensen indices, and the impact on the intestinal physiology and health of puffer fish requires further investigation.

The massive galaxy cluster "El Gordo" (ACT-CL J0102--4915) is a rare merging system with a high collision speed suggested by multi-wavelength observations and the theoretical modeling. Zhang et al. (2015) propose two types of mergers, a nearly head-on merger and an off-axis merger with a large impact parameter, to reproduce most of the observational features of the cluster, by using numerical simulations. The different merger configurations of the two models result in different gas motion in the simulated clusters. In this paper, we predict the kinetic Sunyaev-Zel'dovich (kSZ) effect, the relativistic correction of the thermal Sunyaev-Zel'dovich (tSZ) effect, and the X-ray spectrum of this cluster, based on the two proposed models. We find that (1) the amplitudes of the kSZ effect resulting from the two models are both on the order of $\Delta T/T\sim10^{-5}$; but their morphologies are different, which trace the different line-of-sight velocity distributions of the systems; (2) the relativistic correction of the tSZ effect around $240 {\rm\,GHz}$ can be possibly used to constrain the temperature of the hot electrons heated by the shocks; and (3) the shift between the X-ray spectral lines emitted from different regions of the cluster can be significantly different in the two models. The shift and the line broadening can be up to $\sim 25{\rm\,eV}$ and $50{\rm\,eV}$, respectively. We expect that future observations of the kSZ effect and the X-ray spectral lines (e.g., by ALMA, XARM) will provide a strong constraint on the gas motion and the merger configuration of ACT-CL J0102--4915., Comment: 10 pages, 6 figures, submitted to ApJ

A marine bacterium, Pseudoalteromonas sp. BC228 was supplemented to feed in a feeding experiment aiming to determine its ability of enhancing the digestive enzyme activity and immune response of juvenile Apostichopus japonicus. Sea cucumber individuals were fed with the diets containing 0 (control), 105, 107 and 109 CFU g−1 diet of BC228 for 45 days. Results showed that intestinal trypsin and lipase activities were significantly enhanced by 107 and 109 CFU g−1 diet of BC228 in comparison with control (P < 0.01). The phagocytic activity in the coelomocytes of sea cucumber fed the diet supplemented with 107 CFU g−1 diet of BC228 was significantly higher than that of those fed control diet (P < 0.05). In addition, 105 and 107 CFU g−1 diet of BC228 significantly enhanced lysozyme and phenoloxidase activities in the coelomic fluid of sea cucumber, respectively, in comparison with other diets (P < 0.01). Sea cucumbers, 10 each diet, were challenged with Vibrio splendidus NB13 after 45 days of feeding. It was found that the cumulative incidence and mortality of sea cucumber fed with BC228 containing diets were lower than those of animals fed control diet. Our findings evidenced that BC228 supplemented in diets improved the digestive enzyme activity of juvenile sea cucumber, stimulated its immune response and enhanced its resistance to the infection of V. splendidus.

The effects of a diet containing Hanseniaspora opuntiae C21 on growth and digestive enzyme activity were estimated in juvenile Apostichopus japonicus. Groups of sea cucumbers were fed diets containing H. opuntiae C21 at 0 (control), 104, 105, and 106 CFU (colony-forming units)/g feed. Results showed that after 45 d the specific growth rate (SGR) of sea cucumbers fed a C21-supplemented diet at 10 4 CFU/g feed was significantly higher than that of the control (P < 0.05). Intestinal trypsin and lipase activities were significantly enhanced by C21 administration at 104 and 105 CFU/g feed compared with the control (P < 0.05). After feeding for 23–42 d, C21 was demonstrated by denaturing gradient gel electrophoresis to be present in the intestine of sea cucumbers. In addition, after feeding the C21-supplemented diets for 15 d, the sea cucumbers were switched to an unsupplemented diet and C21 was confirmed to be capable of colonizing the intestine for at least 31 d after cessation of feeding. In conclusion, C21 was shown to successfully colonize the intestine of juvenile A. japonicus via dietary supplementation, and improve growth and digestive enzyme activity.

To improve the axial resolution of ultrasonic elastography, by taking the advantage of code excitation and frequency compounding, multi-frequency with coded excitation for elastography (FCCE) was proposed. FCCE adopts the Chirp signal excitation scheme and strikes a balance in the selection of sub-signal bandwidth, the bandwidth overlap and the number of sub-strain image based on theoretical derivation, so as to further improve the axial resolution of elastic image. On MATLAB, multi- frequency with coded excitation for elastography was implemented and compared with short pulse. Experiments have proved that, compared with the short pulse, the elastographic signal-to-noise ratio (SNRe) and contrast-to-noise ratio (CNRe) were improved significantly. Moreover, probing depth, axial resolution and target detection were improved too. Therefore, the FCCE technology can effectively improve the elastography quality and can be applied to ultrasonic clinical trials.

Color flow imaging has been well applied in clinical diagnosis. For the high quality color flow images, clutter filter is important to separate the Doppler signals from blood and tissue. Traditional clutter filters, such as finite impulse response, infinite impulse response and regression filters, were applied, which are based on the hypothesis that the clutter signal is sta- tionary or tissue moves slowly. However, in realistic clinic color flow imaging, the signals are non-stationary signals because of accelerated moving tissue. For most related papers, simulated RF signals are widely used without in vivo I/Q signal. Hence, in this paper, adaptive polynomial regression filter, which is down mixing with instantaneous clutter frequency, was proposed based on in vivo carotid I/Q signal in realistic color flow imaging. To get the best performance, the optimal polynomial order of polynomial regression filter and the optimal polynomial order for estimation of instantaneous clutter frequency respective- ly were confirmed. Finally, compared with the mean blood velocity and quality of 2-D color flow image, the experiment results show that adaptive polynomial regression filter, which is down mixing with instantaneous clutter frequency, can sig- nificantly enhance the mean blood velocity and get high quality 2-D color flow image.

Accurate estimation of the merger timescale of galaxy clusters is important to understand the cluster merger process and further the formation and evolution of the large-scale structure of the universe. In this paper, we explore a baryonic effect on the merger timescale of galaxy clusters by using hydrodynamical simulations. We find that the baryons play an important role in accelerating the merger process. The merger timescale decreases with increasing the gas fraction of galaxy clusters. For example, the merger timescale is shortened by a factor of up to 3 for merging clusters with gas fractions 0.15, compared with the timescale obtained with zero gas fractions. The baryonic effect is significant for a wide range of merger parameters and especially more significant for nearly head-on mergers and high merging velocities. The baryonic effect on the merger timescale of galaxy clusters is expected to have impacts on the structure formation in the universe, such as the cluster mass function and massive substructures in galaxy clusters, and a bias of "no-gas" may exist in the results obtained from the dark matter-only cosmological simulations., Comment: 9 pages, 6 figures, accepted for publication in the Astrophysical Journal

The observational features of the massive galaxy cluster "El Gordo" (ACT-CL J0102-4915), such as the X-ray emission, the Sunyaev-Zel'dovich (SZ) effect, and the surface mass density distribution, indicate that they are caused by an exceptional ongoing high-speed collision of two galaxy clusters, similar to the well-known Bullet Cluster. We perform a series of hydrodynamical simulations to investigate the merging scenario and identify the initial conditions for the collision in ACT-CL J0102-4915. By surveying the parameter space of the various physical quantities that describe the two colliding clusters, including their total mass (M), mass ratio (\xi), gas fractions (f_b), initial relative velocity (V), and impact parameter (P), we find out an off-axis merger with P~800h_{70}^{-1}kpc, V~2500km/s, M~3x10^{15}Msun, and \xi=3.6 that can lead to most of the main observational features of ACT-CL J0102-4915. Those features include the morphology of the X-ray emission with a remarkable wake-like substructure trailing after the secondary cluster, the X-ray luminosity and the temperature distributions, and also the SZ temperature decrement. The initial relative velocity required for the merger is extremely high and rare compared to that inferred from currently available Lambda cold dark matter (LCDM) cosmological simulations, which raises a potential challenge to the LCDM model, in addition to the case of the Bullet Cluster., Comment: 30 pages, 12 figures

Observations reveal that the peaks of the X-ray map and the Sunyaev-Zel'dovich (SZ) effect map of some galaxy clusters are offset from each other. In this paper, we perform a set of hydrodynamical simulations of mergers of two galaxy clusters to investigate the spatial offset between the maxima of the X-ray and the SZ surface brightness of the merging clusters. We find that significantly large SZ-X-ray offsets (>100kpc) can be produced during the major mergers of galaxy clusters. The significantly large offsets are mainly caused by a `jump effect' occurred between the primary and secondary pericentric passages of the two merging clusters, during which the X-ray peak may jump to the densest gas region located near the center of the small cluster, but the SZ peak remains near the center of the large one. Our simulations show that merging systems with higher masses and larger initial relative velocities may result in larger offset sizes and longer offset time durations; and only nearly head-on mergers are likely to produce significantly large offsets. We further investigate the statistical distribution of the SZ-X-ray offset sizes and find that (1) the number distribution of the offset sizes is bimodal with one peak located at low offsets ~0 and the other at large offsets ~350-450kpc/h, but the objects with intermediate offsets are scarce; and (2) the probabilities of the clusters in the mass range higher than 2x10^{14}Msun/h that have offsets larger than 20, 50, 200, 300, and 500kpc/h are 34.0%, 11.1%, 8.0%, 6.5%, and 2.0% respectively at z=0.7. The probability is sensitive to the underlying pairwise velocity distribution and the merger rate of clusters. Future observations on the offsets for a large number of clusters may put strong constraints on the cosmic velocity fields on the cluster scale and the cluster merger rate. (Abridged), 25 pages, 15 figures