TECHNOLOGY FOCUS - MECHANICAL ENGINEERING - Preferred Component: The exhaust after-treatment system includes a leading conduit through which the exhaust passes prior to entering the branches; a diesel particulate filter configured within the trailing exhaust conduit; a fuel reformer configured upstream of the NOx adsorber-catalyst and within the branch containing the NOx adsorber-catalyst; and a sulfur trap within each branch and positioned upstream of the NOx adsorber-catalysts. The diesel particulate filter is configured upstream of the ammonia-SCR catalyst. The exhaust after-treatment system is configured without valves or dampers adapted to selectively alter the division of the exhaust flow between the branches. It is configured to operate the NOx adsorber-catalyst in lean adsorption and rich regeneration phases. It is configured so that the fraction of the exhaust that will enter the branch containing the NOx adsorber-catalyst while that branch is in it rich regeneration phase is greater than or equal to50 (preferably greater than or equal to80)% of the fraction of the exhaust that will enter that branch while that branch is in it lean adsorption phase. A second of the branches contains a fuel reformer and a NOx adsorber-catalyst, in which the fuel reformer is configure upstream of the NOx adsorber-catalyst. The branches containing fuel reformers are configured with structures to facilitate heat transfer between the reformers. The system provides higher inter-branch heat transfer coefficients on a per unit passage length basis at a point downstream of where the fuel reformers are located as compared to a point at which the fuel reformers are located. The sulfur traps are positioned downstream of the reformers. The particulate filters are located between the reformers and the NOx adsorber-catalysts. A turbo-charger is provided for the engine intake air powered by a turbine to be driven by the exhaust in the leading conduit. An EGR system for the engine is configured to recirculate exhaust from the leading conduit. A lean-NOx catalyst is hydrocarbon-SCR catalysts, carbon monoxide SCR catalysts, or hydrogen-SCR catalysts within the trailing conduit or the leading conduit. A fuel injector (121) is configured within the branch containing the NOx adsorber-catalyst, upstream of the fuel reformer.