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Within the framework of the theory of random walks, we present an analytical study of one-dimensional ballistic flux of quasiparticles in the presence of scattering centers (SCs) such as defects or dopants. An explicit analytical expression is derived for the quasiparticle flux and the associated heat flux carried by phonons as a function of the number of SCs and the probabilities of (i) forward and backward scattering at SCs and (ii) absorption of quasiparticles by the SCs and in the conductor between SCs. The practical application of our model to one-dimensional nanostructures and to quasi-one-dimensional heat-conducting systems such as linear polycrystals is discussed. Various limiting cases are also considered. We demonstrate that our model is in excellent agreement with experimental data on the thermal conductance of Si nanowires having geometrically modified S-shaped extremities that act as SCs to the phonon flux. [ABSTRACT FROM AUTHOR]