  We have performed the detailed numerical simulations on the propagation of
the UHE protons in the energy range $E=(10^{19.5} - 10^{22.0}$) eV in the
relatively strong extra-galactic magnetic field with strength $B= (10, 100)$ nG
within about 40 Mpc. In this case, the deflection angles of UHECRs become so
large that the no counterparts problem is simply solved. As for the source
distribution, we assumed that it is proportional to the number distribution of
galaxies within the GZK sphere. We have found many clusters, which mean the
small-scale anisotropy, in our simulations. It has been also shown that the
observed energy spectrum is well reproduced in our models without any
fine-tuned parameter. We have used the correlation value in order to
investigate statistically the similarity between the distribution of arrival
directions of UHECRs and that of galaxies. We have found that each correlation
value for each parameter set begins to converge when the number of the detected
events becomes ${\large O}(10^3)$. Since the expected number counts by the
experiment of the next generation such as TA, HiRes, Auger, and EUSO are
thought to be the order of $10^3$, we will be able to determine the source
distribution and values of the parameters in this study in the very near
future. Compared with the AGASA data, the significant anisotropy on the arrival
directions of UHECRs are found in the analysis of first and second harmonics.
This may originate from the incompleteness of the ORS database. This problem
may be also solved if the source distribution is slightly changed. For example,
this problem may be solved if we assume that UHECRs come from some of the
galaxies such as AGNs and radio galaxies.
