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In our world with full of uncertainty, debates and argumentation contribute to the progress of science and society. Despite of the increasing attention to characterize human arguments, most progress made so far focus on the debate outcome, largely ignoring the dynamic patterns in argumentation processes. This paper presents a study that automatically analyzes the key factors in argument persuasiveness, beyond simply predicting who will persuade whom. Specifically, we propose a novel neural model that is able to dynamically track the changes of latent topics and discourse in argumentative conversations, allowing the investigation of their roles in influencing the outcomes of persuasion. Extensive experiments have been conducted on argumentative conversations on both social media and supreme court. The results show that our model outperforms state-of-the-art models in identifying persuasive arguments via explicitly exploring dynamic factors of topic and discourse. We further analyze the effects of topics and discourse on persuasiveness, and find that they are both useful - topics provide concrete evidence while superior discourse styles may bias participants, especially in social media arguments. In addition, we draw some findings from our empirical results, which will help people better engage in future persuasive conversations.