The fine silt deposits of Jammu (J & K State, India) stretch all along the Siwalik foothills from Jammu to the Potwar Plateau in Pakistan. The post-Siwalik deposits, first discussed by de Terra and Paterson (1939), are attributed to wind action. The deposits termed as ‘Potwar loessic silt’ comprising sandy silt are essentially of late Quaternary age (75–18 ka) and are re-looked herein from the point of view of genesis and climatic significance. The sorting, skewness and kurtosis parameters of fine silts of Jammu suggest fluvial environment of the deposits wherein the water budget fluctuated. The weak pedogenesis of fine silts at certain intervals corroborate to periods of less or no sedimentation. The bivariant plot studies further suggest fluvial environment of deposition for the fine silt at Jammu, with regular fluctuations in the budget of river water that was perhaps in consonance with oscillations in the climate of the region.

Indoor radon is considered as one of the potential dangerous radioactive elements. Common building materials and soil are the major source of this radon gas in the indoor environment. In the present study, the measurement of radon exhalation rate in the soil and building material samples of Una and Hamirpurdistricts of Himachal Pradesh has been done with solid state alpha track detectors, LR-115 type-II plastic track detectors. The radon exhalation rate for the soil samples varies from 39.1 to 91.2 mBq kg⁻¹ h⁻¹with a mean value 59.7 mBq kg⁻¹ h⁻¹. Also the radium concentration of the studied area is found and it varies from 30.6 to 51.9 Bq kg⁻¹ with a mean value 41.6 Bq kg⁻¹ . The exhalation rate for the building material samples varies from 40.72 (sandstone) to 81.40 mBq kg⁻¹ h⁻¹ (granite) with a mean value of59.94 mBq kg⁻¹ h⁻¹.

A review has been made to understand the hydrogeochemical behaviour of groundwater through statistical analysis of long term water quality data (year 2005–2013). Water Quality Index (WQI), descriptive statistics, Hurst exponent, fractal dimension and predictability index were estimated for each water parameter. WQI results showed that majority of samples fall in moderate category during 2005–2013, but monitoring site four falls under severe category (water unfit for domestic use). Brownian time series behaviour (a true random walk nature) exists between calcium (Ca²⁺) and electric conductivity (EC); magnesium (Mg²⁺) with EC; sodium (Na⁺) with EC; sulphate (SO²⁻₄) with EC; total dissolved solids (TDS) with chloride (Cl⁻) during pre- (2005–2013) and post- (2006–2013) monsoon season. These parameters have a closer value of Hurst exponent (H) with Brownian time series behaviour condition (H=0.5). The result of times series analysis of water quality data shows a persistent behaviour (a positive autocorrelation) that has played a role between Cl⁻ and Mg²⁺, Cl⁻ and Ca²⁺, TDS and Na⁺, TDS and SO²⁻₄, TDS and Ca²⁺ in pre- and post-monsoon time series because of the higher value of H (>1). Whereas an anti-persistent behaviour (or negative autocorrelation) was found between Cl⁻ and EC, TDS and EC during pre- and post-monsoon due to low value of H. The work outline shows that the groundwater of few areas needs treatment before direct consumption, and it also needs to be protected from contamination.

In the present study, analytical solutions of the advection dispersion equation (ADE) with spatially dependent concave and convex dispersivity are obtained within the fractal and the Euclidean frameworks by using the extended Fourier series method. The dispersion coefficient is considered to be proportional to the nth power of a non-homogeneous quadratic spatial function, where the index n is considered to vary between 0 and 1.5 so that the spatial dependence of dispersivity remains within the limit to describe the heterogeneity in the fractal framework. Real values like n ¼ 0.5 and 1.5 are considered to delineate heterogeneity of the aquifer in the fractal framework, whereas integral values like n = 1 represent thesame in the Euclidean sense. A concave or convex variation is free from demanding a limiting value as in the case of linear variation, hence it is more appropriate in the ambience of many disciplines in which ADE is used. In this study, concentration at the source site remains uniform until the source is present and becomes zero once it is annihilated forever. The analytical solutions, validated through the respective numerical solutions, are obtained in the form of an extended Fourier series with only first five terms. They are convergent to the desired concentration pattern and are stable with the Peclet number. It has been possible because of the formulation of a new Sturm–Liouville problem with advective information. The analytical solutions obtained in this paper are novel.