Reconstruction of f(R,T) gravity in anisotropic cosmological models of accelerating universe

In this paper, we search the existence of Bianchi type I cosmological model in f(R,T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, and reconstruct the corresponding f(R,T) functions. Attention is attached to the special case, f(R,T)=f ₁(R)+f ₂(T) and two examples are assumed for this model. In the first example, we consider the unification of matter dominated and accelerated phases with f(R) gravity in anisotropic universe, and in the second instance, model of f(R,T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, f(R,T) is proportional to a power of R with exponents depending on the input parameters.     

Es-q layer at huancayo during the March 1970 geomagnetic storm

The paper describes a comparison of vertical electron drift in the F-region (V_z) measured by VHP incoherent scatter radar at Jicamarca with the corresponding variations of geomagnetic horizontal field (H) and the maximum frequency reflected from The E_s layer (E_s) at Huancayo during the geomagnetic storm period 7–9 March, 1970. The V_z is generally upward during the daytime at the equator, but during 7–9, March, 1970, V_z was negative for brief periods associated with negative bays in H. These periods of abnormally low or of downward V_z correspond closely with the period of complete disappearance of the q type of E_s layer. The magnetic bays associated with the intensification of ring current do not affect the equatorial E_s- q and it is only the negative bays in H at the equator due to the ionospheric current flowing westward, that cause sudden disappearance of E_s? q. It is suggested that the q type of E_s is due to cross-field instability created in the electrojet region due to interaction of northward magnetic field and vertical upward Hall polarization electric field when the plasma density gradient is upward. The sudden disappearances of E_s? q are due to the reversal of the horizontal electric field in the equatorial ionosphere and thereby due to the reversal of the equatorial electrojet currents. These reversals of electric field may be due to the imposition on the normal S_q field of another westward electric field.     

The broad band spectral index of blazars in a low state

Using the broad band spectral index of 164 blazars in a low state, we studied the possible correlation between different broad band spectral index (α _r.ir , α _r.o , α _r.x , α _r.γ , α _ir.o , α _ir.x , α _ir.γ , α _o.x , α _o.γ , α _x.γ ). We also studied the possible correlation between different broad band spectral index of high-frequency peaked Bl Lac object (HBL), low-frequency peaked BL Lac object (LBL) and flat spectral radio quasars (FSRQs), respectively. The strong anti-correlations were found between α _r.o and α _o.γ , between α _r.o and α _x.γ in a low state for our blazar sample. For LBL and FSRQs, the strong anti-correlations were found between α _r.ir and α _ir.x , between α _r.o and α _o.x , and between α _r.o and α _o.γ in a low state. Based on these results, we suggested that the seed photons of the γ-ray drive from both the jet and the external accretion disk or the broad-line region, and that the subclasses of blazars seem to the different emission mechanism.     

A Statistical Analysis on the Color and Orbit Parameters of Centaurs

In order to study the statistical characters and physical significance of the color indexes and orbital parameters of Centaurs, we have analyzed the color and orbit parameter correlations by using statistical methods according to the known color indexes of 39 Centaurs and their respective orbital parameters. We find that all the correlations of B − V vs. V − R, V − R vs. R − I, B − V vs. R − I and B − R vs. R − I are strong. The Centaurs exhibit obvious redblue double-color property, and the point of demarcation is close to B − R = 1.4. The distributions of the various color indexes of Centaurs exhibit the normal distribution. For the correlations between colors and orbital parameters, except for the weak correlations between B − V and the orbital inclination i as well as between V − R and the orbital semi-major axis a, no evident correlation has been found between color indexes and orbital parameters.     

Mach’s principle and Yukawa-like corrections to the Newtonian potential as a bound for the mean energy density of the universe

The (Newton + Yukawa)-type gravitational potential V(r)=?(γ M/r)[1+Aexp?(?r/B)](γ= the gravitational constant as measured at infinity, M= the mass of the source, A, B are constants) is considered in the framework of the Sciama linear approach to Mach’s principle. The coupling constant A of the Yukawa component is found to be related to the mass density and size of the observable (causally connected) universe.     

Impact fragmentation experiments of basalts and pyrophyllites

Results of impact fragmentation experiments for basalts and pyrophyllites are reported. Aluminum cylindrical projectiles were impacted on cubic basalt and pyrophyllite targets at velocities of 70 to 990 m/sec. The targets and projectiles were 20 g to 3.3 kg and 2 to 20 g in weight respectively. Weights of the fragments produced by impacts were measured and the size distributions of fragments were examined. Data of the largest fragment mass (m_L) normalized to the original target mass (M_t), m_L/M_t, correlate better with the nondimensional impact stress, P_I, a new scaling parameter introduced by H. Mizutani, Y. Takagi, and S. Kawakami (1984, in preparation) than the conventional projectile's kinetic energy per unit target mass, E/M_t, used in the previous studies. All the m_L/M_t data for basalts obtained in the present study are summarized by m_L/M_t = 2.95 × 10^?2P_I^?1 where P_I = P₀L³/YR³, P₀ = peak shock pressure, L = projectile size, R = target size and Y = material strength of target. For aluminum targets, however, the m_L/M_t is 2.5 orders of magnitude larger than that for brittle targets at impacts with the same P_I. Size distributions of fragments expressed in a log N - log (m/M_t) diagram divided into three regimes bounded by two inflection points. In each regime the curve is expressed by $\text{N (>}\text{m}\text{M}{}_{\mathrm{t}}\text{) = A (}\text{m}\text{M}{}_{\mathrm{t}}\text{)}{}^{\mathrm{?a}}$. The slopes, a, of the log $\text{N -}\text{log}\text{(}\text{m}\text{M}{}_{\mathrm{t}}\text{)}$ curves in the regimes of a large and a medium size range are positively correlated with the nondimensional impact stress, P_I, and expressed as a = C₃ + a₃log P_I. The slopes, a, in the smallest size range are, on the other hand, nearly constant and have values of $\text{0.5}\text{to}\text{0.7 (}\text{1}\text{2}\text{?}\text{2}\text{3}\text{)}$. Present results indicate that the impact fragmentation is scaled well by the new scaling parameter, P_I, of Mizutani, Takagi, and Kawakami and that the present experimental data may shed new light on planetary impact processes.     

Variable cosmological “constant” and motion of a test particle in a cloud of dust

We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ(x ⁱ ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ?Λ/? x ⁱ and, in the weak field approximation, causes an anomalous acceleration A～(Vc ²/γ ρ)?Λ/? t+(c ⁴/γ ρ)?Λ/? r where V=dr/dt, c=the speed of light, γ=8π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ(t) give A<10^?8 cm/s² when ρ>10^?29 g/cm³ i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.     

On the ring current energy injection rate

Assuming that the formation of the ring current belt is a direct consequence of an enhanced crosstail electric field and hence of an enhanced convection, we calculate the total ring current kinetic energy (K_R) and the ring current energy injection rate (U_R) as a function of the cross-tail electric field (E_CT); the cross-tail electric field is assumed to have a step function-like increase. The loss of ring current particles due to recombination and charge-exchange is assumed to be distributed over the whole ring current region. It is found that: (1) the steady-state ring current energy K_R is approximately linearly proportional to E_CT; (2) the characteristic time t_c for K_R to reach the saturation level is 3–4 h; (3) the injection rate U_R is proportional to E_CT^β where β ? 1.33?1.52; and (4) the characteristic time t_p for U_R to reach the peak value is 1–2 h and the peak U_R value is 50% higher than the steady-state value. Since β is now determined specifically for an enhanced convection, an observational determination of the relationship between E_CT(or φ_CT) and U_R is essential to a better understanding of ring current formation processes. If the observed β is greater than 1.5, additional processes (e.g. an injection of heavy ions from the ionosphere to the plasma sheet and subsequently to the ring current region) may be required.     

Scaling relation between Sunyaev–Zel’dovich effect and X-ray luminosity and scale-free evolution of cosmic baryon field

It has been revealed recently that, in the scale free range, i.e. from the scale of the onset of nonlinear evolution to the scale of dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the self-similar log-Poisson hierarchy. As a consequence of this evolution, the relations among various physical quantities of cosmic baryon fluid should be scale invariant, if the physical quantities are measured in cells on scales larger than the dissipation scale, regardless the baryon fluid is in virialized dark halo, or in pre-virialized state. We examine this property with the relation between the Compton parameter of the thermal Sunyaev–Zel’dovich effect, y(r), and X-ray luminosity, L_x(r), where r being the scale of regions in which y and L_x are measured. According to the self-similar hierarchical scenario of nonlinear evolution, one should expect that (1) in the y(r) ? L_x(r) relation, y(r) = 10^A(r)[L_x(r)]^α(r), the coefficients A(r) and α(r) are scale-invariant; (2) The relation y(r) = 10^A(r)[L_x(r)]^α(r) given by cells containing collapsed objects is also available for cells without collapsed objects, only if r is larger than the dissipation scale. These two predictions are well established with a scale decomposition analysis of observed data, and a comparison of observed y(r) ? L_x(r) relation with hydrodynamic simulation samples. The implication of this result on the characteristic scales of non-gravitational heating is also addressed.     

The STAROX stellar evolution code

This paper describes the STAROX stellar evolution code for the calculation of the evolution of a model of a spherical star. The code calculates a model at time t _k , that is the run of pressure, density, temperature, radius, energy flux and related variables on a mesh in mass M _i , given the distribution of chemical elements X _j (i) at t _k and the model at the previous time step t _k?1. It then advances the chemical composition to the next time step t _k+1 and calculates a new model at time t _k+1. This process is iterated to convergence. The model equations are solved by Newton–Raphson relaxation; the chemical equations are solved by an iterative procedure, each element being advanced in turn, and the process repeated to convergence. Convection is modelled by a mixing length model and convective mixing is treated as a diffusive process; chemical overshooting can be incorporated in parametric form. The equation of state is taken from OPAL tables and the opacity from a blend of OPAL and Alexander tables. Nuclear reaction rates are from NACRE but only cover the p–p chain and CNO cycle. The atmospheric layers are incorporated in the model by applying the surface boundary condition at small optical depth (τ≈0.001). The mesh in mass M _i is usually taken as fixed except that there is a moveable mesh point at the boundary of a convective core. Results are given for models of mass 0.9 and 5.0M _⊙ with initial composition X=0.7,Z=0.02 evolved to a state where the central hydrogen abundance is X _c =0.35, and for a model of mass 2.0M _⊙ with initial X=0.72,Z=0.02, evolved to X _c =0.01 and with core overshooting. In this latter case we compute two models one with and one without a moveable mesh point at the boundary of the convective core to illustrate the importance of having such a moveable mesh point for the determination of the Brunt–Väisälä frequency in the layers outside the core.     

Anisotropic cosmological models in f(R,T) gravity according to holographic and new agegraphic dark energy

The paper deals with a spatially homogeneous and anisotropic universe filled with perfect fluid and dark energy components. We consider the f(R,T) theory according to holographic and new agegraphic dark energy in the Bianchi type I universe. In this study, we concentrate on two particular models of f(R,T) gravity namely, R+2f(T) and f(R)+λT. We conclude that the derived f(R,T) models can represent phantom or quintessence regimes of the universe.     

Time dependent cylindrical and spherical DIA solitary waves with two populations of thermal electrons in dusty plasma

The propagation of Gardner solitons (GSs) in a nonplanar (cylindrical and spherical) geometry associated with a dusty plasma whose constituents are non-inertial negative static dust, inertial ions, and two population of Boltzmann electrons with two distinctive temperatures, are investigated by deriving the modified Gardner (mG) equation using the reductive perturbation method. The basic features of nonplanar dust-ion-acoustic GSs are analyzed by numerical solutions of mG equation. It has been found that the basic characteristics of GSs, which are shown to exist for the values of μ _c =n _e10/n _i0 around 0.319 for n _e20/n _i0=0.04 and T _e1/T _e2=0.2 [where n _e10 (n _e20) is the cold (hot) electron number density at equilibrium, T _e1 (T _e2) is the temperature of the cold (hot) electron species] are different from those of K-dV (Korteweg-de Vries) solitons, which do not exist around μ _c ?0.319. The implications of our results in understanding the nonlinear electrostatic perturbations observed in many laboratory and astrophysical situations (viz. double-plasma machines, rf discharge plasma, noctilucent cloud region in Earth’s atmosphere, source regions of Auroral Kilometric Radiation, Saturn’s E-ring, etc.) where electrons with different temperatures can significantly modify the wave dynamics, are also briefly discussed.     

Shadow mechanism and the opposition effect of brightness of atmosphereless celestial bodies

We consider the Irvine-Yanovistkii modification of the shadow model developed by Hapke for the opposition effect of brightness. The relation between the single scattering albedo ω and the transparency coefficient of particles κ is suggested to be used in the form κ = (1 ? ω) ⁿ , which allows the number of unknowns in the model to be reduced to two parameters (the packing density of particles g and ω) and the single-scattering phase function χ(α). The analysis of spectrophotometric measurements of the moon and Mars showed that the data on the observed opposition effect and the changes in the color index with the phase angle α well agree if the values of n = 0.25 and g = 0.4 (the moon) and 0.6 (Mars) are assumed in calculations. When being applied to asteroids of several types, this method also yielded a satisfactory agreement. For the E-type asteroids, the sets of parameters are [g = 0.6, ω = 0.6, A _g = 0.21, and q = 0.83] or [g = 0.3, ω = 0.4, A _g = 0.15, and q = 0.71] under the Martian single-scattering phase function; for the M-type asteroids, it is [g = 0.4, ω ≤ 0.1, A _g ≤ 0.075, and q ≤ 0.42] under the lunar single-scattering phase function; for the S-type asteroids, it is [g = 0.4, ω = 0.4, A _g = 0.28, and q = 0.49] under the lunar single-scattering phase function; and for the C-type asteroids, it is [g = 0.6, ω ≤ 0.1, A _g ≤ 0.075, and q = 0.43] under the modified lunar single-scattering phase function. The polarization measurements fulfilled by Gehrels et al. (1964) for the bright feature on the lunar surface, Copernicus (L = -20°08′, φ = +10°11′), at a phase angle α = 1.6° revealed the deviations in the position of the polarization plane from that typical for the negative branch. They were 22° and 12° in the G and I filters, respectively. At the same time, the deviation was within the error (±3°) in the U filter and for the dark feature Plato (L = -10°32′, φ = +51°25′), which can be caused by the coherent mechanism of the formation of the polarization peak.     

Orientation and shape of the Earth's bow shock in three dimensions

Nearly 2500 shock crossings from HEOS-1, HEOS-2 and 5 IMP spacecraft, covering most of the northern and part of the southern bow shock surface for X values X > ? 20 R_E, have been used to carry out a detailed study of the three-dimensional shape and location of the bow shock. The influence of the different solar wind conditions has been reduced by normalising the observed crossings to an average solar wind dynamical pressure (N₀ = 9.4 cm^?3, V₀ = 450 kms^?1). It has been shown that the shock surface is symmetric with respect to the ecliptic plane and intersects the coordinate axes at 11.9 R_E (X), + 27.0 and ? 22.9 R_E (Y), + 23.9 and ? 24.5 R_E (Z) for the average dynamical pressure (N₀ = 9.4 cm^?3, V₀ = 450kms^?1, with $\text{M}{}_{\mathrm{A}}\text{= 9.3}$, $\text{M}{}_{\mathrm{MS}}\text{= 6.1)}$. The observed aberration of the shock surface is 8.9° ± 1°, i.e. 5.1° larger than the aberration predicted from the Earth's motion. This asymmetry around the solar wind apparent direction is described by equation (6) for different Mach numbers M_A and confirms the predictions of Walters [J. geophys. Res. 71, 1319 (1964)] and Michel [J. geophys. Res. 70, 1 (1965)].The magnetosheath thickness is 3.3 R_E along the X-axis, 11.4 R_E (+ Y), 8.7 R_E (? Y), 9.9 R_E (+Z) and 10.9 R_E along the negative Z axis.     

A determination of the K-correction for quasars

The K-correction is made up of an emission line component and a continuum component. These two components are iteratively determined in this paper from line widths and intensities, redshifts, U,B,V colours and radio spectral indices for 355 quasars. The colors B-V and U-B, corrected for the emission line portion of the K-correction, are plotted against Z, giving 2 mean relations. Eliminating Z between these gives a mean optical continuum, which is then used to calculate the continuum portion of the K-correction.     

The impact of the oblateness of Regulus on the motion of its companion

The fast spinning B-star Regulus has recently been found to be orbited by a fainter companion in a close circular path with orbital period P _b=40.11(2) d. Being its equatorial radius R _e 32% larger than the polar one R _p, Regulus possesses a remarkable quadrupole mass moment Q. We investigate the effects of Q on the orbital period P _b of its companion in order to see if they are measurable, given the present-day level of accuracy in measuring P _b. Conversely, we will look for deviations from the third Kepler law, attributed to the quadrupole mass moment Q of Regulus, to constrain the ratio γ=m/M of the system’s masses. The impact of Q on the orbital period is analytically worked out with a straightforward perturbative approach. The resulting correction P ^Q is compared to other competing dynamical effects. P ^Q and the Keplerian period P ^Kep are expressed in terms of the phenomenologically determined system’s parameters; γ is treated as an unknown. P ^Q is compared to the observational accuracy in measuring the orbital period δ P _b=0.02 d and to the systematic uncertainty δ(P ^Kep) due to the errors in the system’s parameters entering it. The discrepancy ΔP=|P _b?P ^Kep| is examined in order to see for which values of γ it becomes statistically significant. The physical meaning of the obtained range of values for γ is discussed in terms of Q. P ^Q is larger than δ P _b but still smaller than the systematic uncertainty in P ^Kep by two orders of magnitude. The major sources of bias are the velocity semiamplitude K of the motion of the primary and its mass M. Assuming edge-on configuration, i.e. i=90 deg, if γ?0.096 Q would be positive, i.e. Regulus would be prolate, contrary to the observations. If γ?0.078 Q would be negative, but its magnitude would be one-two orders of magnitude larger than the approximate estimate Q≈M(R _p ² ?R _e ² )=?2.4±0.5×10⁴⁹ kg?m². Regulus is the first extrasolar binary system in which the orbital effects of the asphericity of the primary are larger than the observational sensitivity; moreover, no other competing aliasing orbital effects are present. Thus, it is desirable that it will become the object of future intensive observational campaigns in order to reduce the systematic uncertainty due to the system’s parameters below the measurability threshold.     

Study of inertial kinetic Alfven waves around cusp region

The effect of electron inertia on kinetic Alfven wave has been studied. The expressions for the dispersion relation, growth/damping rate and growth/damping length of the inertial kinetic Alfven wave (IKAW) are derived using the kinetic approach in cusp region. The Vlasov-kinetic theory has been adopted to evaluate the dispersion relation, growth/damping rate and growth/damping length with respect to the perpendicular wave number k_⊥ρ_i (ρ_i is the ion gyroradius) at different plasma densities. The growth/damping rate and growth/damping length are evaluated for different m_e/βm_i, where β is the ratio of electron pressure to the magnetic field pressure, m_{i, e} are the mass of ion and electron, respectively, as I=m_e/βm_i represent boundary between the kinetic and inertial regimes. It is observed that frequency of inertial kinetic Alfven wave (IKAW) ω is decreasing with k_⊥ρ_i and plasma density. The polar cusp is an ideal laboratory for studies of nonlinear plasma processes important for understanding the basic plasma physics, as well as the magnetospheric and astrophysical applications of these processes.     

The formation of ring galaxies

The conditions under which a head-on collision between a disk galaxy and a spherical galaxy can lead to ring formation are investigated, using the impulsive approximation. The spherical galaxy is modeled as a polytrope of indexn=4 and radiusR _S and the disk galaxy as an exponential disk whose surface density is given by \(\sigma (r) = \sigma _c e^{ - 4r/R_D } \) , where σ _c is the central density andR _D is the radius of the disk. The formation and properties of the rings are closely related to the fractional change in binding energy of the disk galaxy, given by ΔU/?U?=γ _D β _D , where (GM _S ² R _D )/(V ² M _D R _S ² ),M _S andM _D being the masses of the spherical and disk galaxies, respectively, and β _D ≡β _D (n, σ, ?,i) is a function of the models of the two galaxies, the ratio of the radii of the two galaxies ?=R _S /R _D , and the angle of inclinationi, of the disk to the direction of relative motion of the two galaxies. Calculations are made for the caseR _S =R _D . Since practically the entire mass of the spherical galaxy, for the chosen model, lies within 1/3 of its radius, the radius of the spherical galaxy is effectively \(\tfrac{1}{3}\) that of the disk galaxy. It is found that as a result of the collision, the innermost and the outer parts of the disk galaxy are not much affected, but the intermediate region expands and gets evacuated, leading to the crowding of stars in a preferential region forming a ring structure. The rings are best formed for a normal, on-axis collision. For this case, rings form when ΔU/|U| lies between \(\tfrac{1}{2}\) and 2, while they are very sharp and bright when ΔU/|U| lies between \(\tfrac{1}{2}\) and 1. Within this range, as ΔU/|U| increases, the rings become sharper and their positions shift outwards with respect to the centre of the disk galaxy. The relationship $$\gamma _D = 0.0016 + 0.045s_{{\text{max}}}^2 ,$$ wheres _max is the radial distance of the density maximum of the ring from the centre of the disk galaxy (measured in terms of the radius of the disk galaxy as unit) enables us to finds _max from γ _D and vice versa, and interpret some prominent ring galaxies. The effect of introducing a bulge to the disk is to distribute the tidal disruptive effects more evenly and, hence, reduce the sharpness of the ring.     

Frequency splitting in stria bursts: Possible roles of low-frequency waves

The kinematics of the process L ± F→ L′ are explored where L represents a parallel Langmuir wave, F represents a low frequency fluctuation and L′ represents a secondary Langmuir wave, and the results are used to discuss (a) a possible interpretation of the frequency splitting in stria bursts in terms of the processes L ± F → L′, L′ ± F′ → t, where t represents a transverse wave, and (b) second harmonic emission due to the processes L ± s→ L′, L + L′ → t, where s represents an ion sound wave. The following results are obtained:

1. The processes L ± s → L′ are allowed only for k _s < 2k _L ± k ₀, respectively, with k ₀ = ω _p /65 V _e .
2. The inclusion of a magnetic field does not alter the result (1) and adds further kinematic restrictions related to angles of propagation; the kinematic restriction T _e > 5 × 10⁵ K for second harmonic emission through process (b) above is also unchanged by inclusion of the magnetic field. The effect of a spread in the wavevectors of the Langmuir waves on this restriction is discussed in the Appendix.
3. For parallel Langmuir waves the process L - F → L′ is forbidden for lower hybrid waves and for nearly perpendicular resonant whistlers, and the process L + F → L′ is allowed only for resonant whistlers at ω _F ? 1/2ω _p (Ω _e /ω _p )².
4. The sequential three wave processes L ± s → L′, L′ ± s → t and L + F → L′, L′ ± F′ → t encounter difficulties when applied to the interpretation of the splitting in split pair and triple bursts.
5. The four-wave process L ± F ± F′ → t is kinematically allowed and provides a favourable qualitative interpretation of the splitting when F denotes a resonant whistler near the frequency mentioned in (3) above. The four wave processes should saturate under conditions which are not extreme and produce fundamental plasma emission with brightness temperature T _t equal to the effective temperature T _L of the Langmuir waves.

     

Rigidity Dependence of the Long-Term Variations of Galactic Cosmic-Ray Intensity in Relation to the Interplanetary Magnetic-Field Turbulence: 1968 – 2002

We studied the relationship between the power-law exponent γ on the rigidity R of the spectrum of galactic cosmic-ray (GCR) intensity variation (δD(R)/D(R)∝R ^?γ ) and the exponents ν _y and ν _z of the power spectral density (PSD) of the B _y and B _z components of the interplanetary magnetic field (IMF) turbulence (PSD～f ^?ν , where f is the frequency). We used the data from neutron monitors and IMF for the period of 1968?–?2002. The exponents ν _y and ν _z were calculated in the frequency interval Δf=f ₂?f ₁=3×10^?6 Hz of the resonant frequencies (f ₁=1×10^?6 Hz, f ₂=4×10^?6 Hz) that are responsible for the scattering of GCR particles with the rigidity range detected by neutron monitors. We found clear inverse correlations between γ and ν _y or ν _z when the time variations of the resonant frequencies were derived from in situ measurements of the solar wind velocity U _sw and IMF strength B during 1968?–?2002. We argue that these inverse relations are a fundamental feature in the GCR modulation that is not restricted to the analyzed years of 1968?–?2002.